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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2014.03.027 Byline: Julia Kallrath, Steffen Rebennack, Josef Kallrath, Rudiger Kusche Abstract: acents We bridge research in optimization to real world cutting stock problems (CSPs). acents We develop two advanced column generation algorithms for 1D CSPs. acents We develop an Exhaustion Method for 1-CSPs with two criteria. acents We develop a sophisticated solution method for 2D-trim-loss minimization problems. acents We assemble a benchmark data set of 25 real world 1D cutting stock instances. Article History: Received 8 February 2013; Accepted 17 March 2014

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2007.10.019 Byline: Kazuki Matsumoto (a), Hiroyoshi Miwa (b), Toshihide Ibaraki (b) Keywords: Scheduling; Corrugated paper; Complexity; Contiguous set; Integer programming Abstract: Corrugated paper is produced by gluing three types of papers of the same breadth. Given a set of orders, we first assign each order to one of the standard breadths, and then sequence those assigned to each standard breadth so that they are continuously manufactured from the three rolls of the specified standard breadth equipped in the machine called corrugator. Here we are asked to achieve multi-goals of minimizing total length of roll papers, total loss of papers caused by the differences between standard breadths and real breadths of the orders, and the number of machine stops needed during production. We use integer programming to assign orders to standard breadths, and then develop a special purpose algorithm to sequence the orders assigned to each standard breadth. This is a first attempt to handle scheduling problems of the corrugator machine. Author Affiliation: (a) Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan (b) Department of Informatics, School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen Sanda, Hyogo 669-1337, Japan Article History: Received 24 March 2007; Accepted 5 October 2007

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2007.08.033 Byline: Philip C. Jones, Jeffrey W. Ohlmann Keywords: OR in agriculture; Forest economics; Normal forest; Regulated forest; Newsvendor model; Forestry supply chain management Abstract: We consider a vertically integrated papermaking operation composed of an integrated pulp and paper mill with its regional supply network. Considering land procurement and harvest rotation as strategic decision variables, we construct a model to establish a long-range timber supply plan that minimizes the total discounted cost of meeting annual virgin wood fiber demand over an infinite horizon. Under appropriate assumptions on costs and storage, the land procurement and harvest rotation decisions are separable with harvest rotation being determined via a forest economics-type equation and land procurement being determined by a newsvendor-type equation. Author Affiliation: Department of Management Sciences, 108 John Pappajohn Business Building, University of Iowa, Iowa City, IA 52242-1994, United States Article History: Received 18 January 2006; Accepted 24 August 2007

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2014.10.035 Byline: Gabriel Sauvageau, Jean-Marc Frayret Abstract: * We propose an agent-based model of a two-echelon recycled pulp supply chain. * Extensive simulation experiments are based on industrial data from a partner. * We examine how Production Flexibility impacts cost, quality and inventory level. * We examine how contract flexibility impact cost, quality and inventory level. Author Affiliation: Ecole Polytechnique de Montreal, Departement de mathematiques et genie industriel, 2500, chemin de Polytechnique, Montreal, H3T 1J4, Canada Article History: Received 2 October 2013; Accepted 17 October 2014

A container loading software package for solving the different problems involved in the containerization of pulp and paper products is presented. The software boasts of a packing algorithm for creating a two-dimensional pattern for placing reels on the floor of container, a heuristic algorithm for two-dimensional stowing of reels of a common diameter and a second packing algorithm for stowing pallets of various sizes. Its applicability has been validated in several decision situations which include the determination of feasible reel diameters and efficient stowage patterns.

Issues are presented concerning the primitive concepts and oversights in the 'jump search' heuristic presented by S. Tsubakitani and J.R. Evans in their research paper entitled 'An empirical study of a new metaheuristic for the traveling salesman problem'.

Keywords Environmental Efficiency; Shadow price of emissions; Marginal rate of transformation between emissions; Irreversible investment; DEA Highlights * An adjustment-cost directional output distance function is specified using DEA to investigate environmental inefficiency. * This framework is applied to the pulp and paper sector of 39 countries during 1996-2009. * USA, China, and Ireland are the most environmentally inefficient countries in the pulp and paper sector. * For those nations where the shadow price of CO.sub.2 is lower than the carbon tax, there is still an opportunity to abate emissions further. * Adjustment costs associated with net investment and disinvestment are found to be asymmetric Abstract Assessing the production of goods and services while minimizing the damage to the environment is a key component to advance sustainable development at national and global levels. The nonparametric estimation of lower and upper bounds on shadow prices of pollutants is undertaken to support the design of policies promoting environmental efficiency in the presence of asymmetry in adjusting productive and abatement capital capacity. This framework is applied to the pulp and paper sector of 39 countries for 1996-2009, and finds that the USA, China and Ireland are the most environmentally inefficient countries in the pulp and paper sector. The adjustment costs associated with net investment and disinvestment are found to be asymmetric. For those nations where the shadow price of CO.sub.2 is lower than the carbon tax, there is still an opportunity to abate emissions further. Results on complementarity or substitutability between pollutants are in general inconclusive. Author Affiliation: (a) Faculty of Economics & Center for Economics and Finance, University of Porto, Porto, PT, Portugal (b) Department of Economic Theory and Economic History, University of Málaga, Spain, and CEFAGE, Portugal * Corresponding author. Article History: Received 25 June 2019; Accepted 8 August 2022 (footnote) The authors are grateful to Spiro Stefanou for his helpful comments on earlier versions of this manuscript. Byline: Elvira Silva (a), Manuela Magalhães [mane.magalhaes@gmail.com] (b,*)

Usage of pairwise comparison method in sense of analytic hierarchy process to rank factors affecting industrial decision making process is discussed.

A revision was made of the Christofides, Alvarez-Valdez and Tamarit (CAT) procedure for solving the single project scheduling problem. A 9-activity counterexample problem was used to prove that the branching strategy that was originally implemented can generate nonoptimal solutions. The construction of additional precedence relations or delay arcs used in the original CAT procedure for delaying activities was proven to be highly restrictive.

Keywords Data envelopment analysis; Undesirable output; Weak disposability; Efficiency Highlights * This paper proposes a model to measure the effects of undesirable outputs on efficiency. * The model is able to calculate the minimum amount of undesirable outputs allowed to be generated. * The efficiency is decomposed into those related to producing the desirable and undesirable outputs. * Efficiency of producing desirable outputs is independent of generating undesirable outputs. Abstract The data envelopment analysis technique produces higher efficiency scores for the assessed decision making units (DMUs) when more input/output factors are considered. This feature generates an intuitively unreasonable result in which the efficiency of a DMU measured considering the accompanying undesirable outputs is greater than or equal to that measured without considering them. In order to obtain a reasonable measure of efficiency, this paper proposes a concept for determining the minimum amount of undesirable outputs that a DMU is allowed to generate based on the assertion of weak disposability, and the results are used to construct the production frontier. The efficiency of the DMUs measured from this frontier can be decomposed into two parts, one of which shows the efficiency of consuming the observed inputs to produce the observed desirable outputs and the other of which, a reduction factor, shows the effect of producing excessive amounts of undesirable outputs on efficiency. A case of thirty paper mills taken from the literature is used to illustrate this idea. The results are helpful for DMU decision-makers to identify sources of inefficiency and for the government to formulate standards for generating allowable amounts of undesirable outputs. Author Affiliation: (a) Department of Industrial and Information Management, National Cheng Kung University, Tainan, Taiwan (b) Department of Business Administration, Ming Chuan University, Taipei, Taiwan * Corresponding author. Article History: Received 19 July 2020; Accepted 15 November 2020 Byline: Chiang Kao [ckao@mail.ncku.edu.tw] (a,*), Shiuh-Nan Hwang [snhwang@mail.mcu.edu.tw] (b)

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2006.09.007 Byline: Eric Taillard Author Affiliation: HEIG-VD, University of Applied Sciences of Western Switzerland, 1, Route de Cheseaux, Case postale CH-1401 Yverdon-Les-Bains, Switzerland

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2005.08.011 Byline: J.B.G. Frenk Abstract: In this technical note, we give a short proof based on some standard results in convex analysis of some important characterization results listed in Theorems 3 and 4 of Benson [Benson, H.P., 2006. Fractional programming with convex quadratic forms and functions. European Journal of Operational Research]. Actually our result is slightly more general since we do not specify the nonempty convex set X. For clarity we use the same notation for the different equivalent optimization problems as done in Benson (2006). Author Affiliation: Econometric Institute, Erasmus University, P.O. Box 1738, 3000DR Rotterdam, The Netherlands Article History: Received 11 February 2005; Accepted 3 August 2005

Convex analysis of quadratic equations, using fractional programming, is discussed.

Research describing project scheduling problems is examined. In particular a critical analysis of classification schemes compatible with machine scheduling proposed by Brucker et al. is presented.

The trim loss problem of a paper-converting company is considered using mixed integer non-linear programming and mixed integer linear programming (MILP). The resulting algorithm incorporating MILP has been found to be globally optimal in generating cutting patterns as it takes into account widths and lengths of paper rolls as well as cutting patterns and constraints in conversion.

Supply chain problem of a large international pulp producer with five pulp mills located in Scandinavia is studied. The company currently uses manual planning for harvesting and transportation of pulp, production scheduling, and distribution of products to customers.

Keywords Transportation; Aircraft routing; Prescriptive analytics; Primary delay prediction Highlights * We gather extensive proprietary and third-party data on flight operations. * We develop predictive analytics models to infer flight-level primary delays. * We leverage delay predictions to optimize day-ahead aircraft routing. * The prescriptive analytics pipeline can result in significant delay reductions. * This paper provides a data-driven approach toward robust airline operations. Abstract Flight delays are major sources of disruptions in airline operations. To mitigate them, day-ahead aircraft routing aims to create flight sequences that can absorb delays and minimize their propagation. However, flight delays are unknown ahead of operations; moreover, predicting delays is complicated by the fact that historical data encompass both primary delays (arising from exogenous sources) and propagated delays (arising from cascading effects in an airline's network). This paper thus develops predictive and prescriptive analytics models to forecast primary delays and to optimize day-ahead aircraft routing toward delay mitigation. We develop a quantile regression model to reconstruct primary delays from historical data, and an ensemble machine learning model to predict them based on flight-level features, environmental features, and traffic features--estimated via a queuing model of airport operations. Then, we formulate deterministic and stochastic optimization models to support day-ahead aircraft routing. Using real-world data from Vueling Airlines, we evaluate the models out of sample against real-world counterfactuals. Results show that our predictive model achieves a mean absolute error of 7--8 minutes and that our prescriptive models can reduce delay costs by 3--5%. This paper shows the benefits of predictive and prescriptive analytics to enhance the robustness of airline operations by (i) creating shorter aircraft rotations, and (ii) strategically allocating schedule slack to avoid the propagation of long delays in later phases of the day. This research led to the deployment of the models in collaboration with the Vueling data science unit. Author Affiliation: (a) Department of Management, Information and Production Engineering, University of Bergamo, via 7 Pasubio 7b, Dalmine (BG) 24044, Italy (b) Sloan School of Management, Massachusetts Institute of Technology, 100 Main St, Cambridge, MA 02142, USA * Corresponding author. Article History: Received 28 October 2022; Accepted 23 February 2023 Byline: Sebastian Birolini [sebastian.birolini@unibg.it] (a), Alexandre Jacquillat [alexjacq@mit.edu] (*,b)

Keywords Scheduling; Staff rostering; Task assignment; Integration; Clique Highlights * Shift-based model outperforms the task- and roster-based models to solve the integrated staff rostering and task assignment (ISRTA) problem. * Shift-based ISRTA model is extended to six operational considerations, i.e., shift flexibility, qualification, travel time, contractual rules, task connection preference, and fairness, which ensure the applicability of the result schedule. * A clique-based aggregated reformulation is proposed to enhance the performance of the shift-based ISRTA model. Two heuristics, i.e., rolling horizon algorithm and iterative shift selection algorithm, are also proposed to speed up the solution process. Abstract Due to the computational complexity, the staff scheduling problem is generally decomposed into two subproblems, i.e. staff rostering and task assignment problems. Very often, this could result in suboptimal solutions. Thus, we study an integrated staff rostering and task assignment (ISRTA) problem in this paper. Previous studies formulate this problem as task- and roster-based ISRTA models, which can only solve small-scale problems. To overcome this limitation, this paper proposes a novel shift-based ISRTA model, which exhibits less symmetry and greatly reduces the number of variables and constraints. We extend the shift-based ISRTA model to six real-world requirements, i.e., shift flexibility, qualification, travel time, contractual rules, task connection preference, and fairness, which ensure the applicability of the result schedule. To efficiently solve the shift-based ISRTA model, we propose a clique-based aggregated model that enhances the performance of the basic shift model. Further, two heuristics, i.e., rolling horizon algorithm and iterative shift selection algorithm, are proposed to speed up the solution process. Based on randomly generated 24 benchmark instances and 16 real-world instances from a major airline, computational results show that the shift-based ISRTA model outperforms the task- and roster-based ISRTA models. For small- and mid-scale problems, the shift-based ISRTA model can be solved optimally or near-optimally directly using a commercial solver, and the rolling horizon algorithm and iterative shift selection algorithm can solve large-scale problems and obtain high-quality solutions. Author Affiliation: (a) School of Economics and Management, Tongji University, Shanghai 200092, China (b) China Eastern Aircateting Co. Ltd., Shanghai 201202, China (c) SILC Business School, Shanghai University, Shanghai, China * Corresponding author. Article History: Received 22 November 2021; Accepted 27 February 2023 Byline: Wenshu Wang [2010083@tongji.edu.cn] (a), Kexin Xie [2110079@tongji.edu.cn] (a), Siqi Guo [2110078@tongji.edu.cn] (a), Weixing Li [lwx@ceair.com] (b), Fan Xiao [xiaofan@tongji.edu.cn] (c,*), Zhe Liang [liangzhe@tongji.edu.cn] (a)

Keywords Scheduling; Parallel batch machines; Non-identical capacities; Total completion time; Ant colony optimization Highlights * A parallel batch scheduling problem with non-identical capacities is considered. * The objective of scheduling is to minimize the total completion time. * A modified elite ant system algorithm with the local search is proposed. Abstract This paper considers the problem of scheduling a group of jobs with arbitrary release times, non-identical sizes, and different processing times on non-identical parallel batch processing machines to minimize the total completion time. A mixed-integer programming (MIP) model is firstly constructed in this paper to solve this problem. Then since the studied problem is strongly NP-hard, a modified elite ant system algorithm with the local search (MEASL) is also proposed to solve it, which is compared with several meta-heuristic algorithms and the commercial optimization solver (Gurobi) through extensive simulation experiments. Finally, the experimental results verify the effectiveness of the proposed algorithm. Author Affiliation: (a) School of Management, Hefei University of Technology, Hefei 230009, PR China (b) Key Laboratory of Process Optimization and Intelligent Decision-Making, Ministry of Education, Hefei 230009, PR China (c) School of Computer Science and Technology, Anhui University, Hefei 230039, PR China (d) School of Economics & Management, Fuzhou University, Fuzhou 350116, PR China (e) Université Gustave-Eiffel, ESIEE Paris, COSYS-GRETTIA, Marne-la-Vallée F-77454, France * Corresponding author at: School of Management, Hefei University of Technology, Hefei 230009, PR China. Article History: Received 29 May 2022; Accepted 13 February 2023 Byline: Han Zhang [hanzhang3411@outlook.com] (a), Kai Li [hfutlk@139.com] (*,a,b), Zhao-hong Jia [zhjia@mail.ustc.edu.cn] (c), Chengbin Chu [chengbin.chu@univ-eiffel.fr] (d,e)

Keywords Combinatorial optimization; Machine learning; Column generation; Branch-and-price Highlights * Adaptive solution prediction is proposed for heuristic search, based on an offline-trained ML model to predict the optimal solution iteratively. * Information is extracted from improved solutions in online sampling and used as features in an ML model, enabling adaptive solution prediction. * Adaptive solution prediction benefits from both online and offline learning, hence it can find heuristic solutions effectively and efficiently. * Adaptive solution prediction can find many high-quality solutions, making it advantageous for heuristic pricing in branch-and-price. Abstract This paper aims to predict optimal solutions for combinatorial optimization problems (COPs) via machine learning (ML). To find high-quality solutions efficiently, existing work uses a ML prediction of the optimal solution to guide heuristic search, where the ML model is trained offline under the supervision of solved problem instances with known optimal solutions. To predict the optimal solution with sufficient accuracy, it is critical to provide a ML model with adequate features that can effectively characterize decision variables. However, acquiring such features is challenging due to the high complexity of COPs. This paper proposes a framework that can better characterize decision variables by harnessing feedback from a heuristic search over several iterative steps, enabling an offline-trained ML model to predict the optimal solution in an adaptive manner. We refer to this approach as adaptive solution prediction (ASP). Specifically, we employ a set of statistical measures as features, which can extract useful information from feasible solutions found by a heuristic search and inform the ML model as to which value a decision variable is likely to take in high-quality solutions. Our experiments on three NP-hard COPs show that ASP substantially improves the prediction quality of an offline-trained ML model and achieves competitive results compared to several heuristic methods in terms of solution quality. Furthermore, we demonstrate that ASP can be used as a heuristic-pricing method for column generation, to boost an exact branch-and-price algorithm for solving the graph coloring problem. Author Affiliation: (a) School of Computing Technologies, RMIT University, Melbourne, Australia (b) La Trobe Business School, La Trobe University, Melbourne, Australia (c) School of Science, RMIT University, Melbourne, Australia (d) School of Mathematics, Monash University, Melbourne, Australia * Corresponding author. Article History: Received 28 February 2022; Accepted 25 January 2023 Byline: Yunzhuang Shen [s3640365@student.rmit.edu.au] (*,a), Yuan Sun [yuan.sun@latrobe.edu.au] (b), Xiaodong Li [xiaodong.li@rmit.edu.au] (a), Andrew Eberhard [andy.eberhard@rmit.edu.au] (c), Andreas Ernst [andreas.ernst@monash.edu] (d)

Keywords Transportation; Routing; Set orienteering; Matheuristic Highlights * The paper proposes an adaptive memory matheuristic for the set orienteering problem. * Local search is equipped with mathematical programming components. * Solution reconstruction mechanisms exploit high-quality node sequences stored in an adaptive memory structure. * The algorithm outperforms the results of the state-of-the-art methodologies. * New very large-scale test problems are introduced and solved for the first time. Abstract This paper proposes a novel matheuristic algorithm for the Set Orienteering Problem (SOP). The set orienteering problem generalizes the Orienteering Problem (OP) by considering customers to be divided into mutually exclusive clusters. The profit associated with each cluster is collected by visiting at least one of the customers belonging to this cluster. The problem calls for the determination of the closed route that maximizes the collected profit without violating a given maximum route duration. We propose a matheuristic algorithm based on local search. The proposed algorithm is equipped with mathematical programming components for dealing with various subproblems, as well as an adaptive memory structure for producing high-quality starting solutions. Promising and diverse solutions are collected and multiple solution reconstruction mechanisms are presented. Extensive computational experiments are conducted for parameter tuning, and for evaluating the contribution of the mathematical programming components and the adaptive memory mechanism. The proposed solution approach is compared against previously published SOP algorithms. It produces the best solutions for 98.20% of the instances of the classic SOP benchmark data set. For 102 of the total 612 instances a new best solution is obtained. In addition, a new large data set of 304 instances is introduced with instances of up to 3162 customers and 634 clusters to evaluate the scalability of the proposed algorithm, and the effectiveness of the various adaptive memory schemes. The proposed algorithm manages to outperform or match the best-known solution for 281 out of 304 instances when compared with a state-of-the-art open source SOP algorithm. Author Affiliation: Department of Management Science and Technology, School of Business, Athens University of Economics and Business, Athens, Greece * Corresponding author. Article History: Received 12 March 2022; Accepted 7 February 2023 Byline: Michael Dontas [mdontas@aueb.gr], Georgios Sideris [geosideris@aueb.gr], Eleftherios G. Manousakis [lmanousakis@aueb.gr] (*), Emmanouil E. Zachariadis [ezach@aueb.gr]

Keywords Multiple criteria analysis; Evolutionary multi-criterion optimization; Multi-criteria decision making; NIMBUS; Self-organizing maps Highlights * Utilizes trade-off and other information visually through iSOM within the NIMBUS method for an informed decision-making. * Assists decision-makers to comprehend better about various properties of preferred solutions. * Visually assists decision-makers to avoid infeasible or least preferred solutions and aids in choosing the most preferred solutions. * Illustrates iSOM-NIMBUS integrated approach on multi-objective optimization problems with 3 to 10 objectives. * Enables extension of the proposed method to the other popular MCDM methods. Abstract In multi-criterion optimization, decision-makers (DMs) are not often interested in the complete Pareto-optimal front. Instead, they have preferences favoring specific parts of the front. Multi-criterion decision-making (MCDM) literature provides a plethora of approaches for introducing DM's preference information in an interactive manner to solve multi-criterion optimization problems. Interactions with DMs can be aided with a user-friendly visualization method or by using special data analysis procedures. An earlier study has indicated the use of self-organizing maps (SOM) as a tool for analyzing Pareto-optimal solutions. In this paper, we demonstrate how a specific MCDM method -- NIMBUS -- can be executed with the interpretable SOM (iSOM) approach iteratively to arrive at one or more preferred solutions. A visual illustration of the entire high-dimensional search space into multiple reduced two-dimensional spaces allows DMs to have a better understanding of the interactions of the objectives and constraints independently, and execute the NIMBUS decision-making procedure with a more wholistic approach. The paper demonstrates the proposed method on a number of multi- and many-objective numerical and engineering problems. The approach is now ready to be integrated with other popular MCDM methods. Author Affiliation: (a) Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600 036, India (b) Department of Electrical and Computer Engineering, Michigan State University, East Lansing, USA * Corresponding author. Article History: Received 26 July 2022; Accepted 31 January 2023 Byline: Deepanshu Yadav [deepanshu.yadav380@gmail.com] (*,a), Deepak Nagar (a), Palaniappan Ramu [https://ed.iitm.ac.in/~palramu/] (a), Kalyanmoy Deb [https://www.egr.msu.edu/~kdeb/] (b)

Keywords Problem structuring methods; Climate adaptation; Community operational research; OR in developing countries; OR in government Highlights * Climate adaptation can be impeded by disconnects between different stakeholders group. * This is especially problematic when working across local-to-national policy levels. * A multi-level integrated planning and implementation (MIPI) process is presented. * Enhanced trust and mutual understanding enable integrative systemic analysis. * A trial of the MIPI process in Ghana successfully overcame problematic disconnects. Abstract Adaptation to climate change is impacted by a range of interrelated processes operating from local to global levels. There are often significant disconnects between different people's perceptions of responsibilities, capabilities and motivations, and divergent understandings of how the system works across actors, sectors and levels of governance. This results in misalignments of policies and practices, plus ineffective flows of resources and knowledge across the network of climate adaptation actors. As these disconnects are rooted in deep misunderstandings of the grounded realities of different actors, an experiential process of mutual discovery is required to build shared understanding and mutual respect. While it is common in the literature for people to talk about multi-level governance, most existing planning processes involve the production of separate plans at each individual level, based on the often-mistaken assumption that they will aggregate into an effective multi-level approach. This paper presents a new, multi-level integrated planning and implementation (MIPI) process, bringing together diverse actors from community, district, regional and national levels in the same workshop. The MIPI process creates a safe space that allows participants to interact directly in conducting systemic, cross-level analyses, as well as the multi-level integration of policies, plans and programs. The paper describes how the MIPI process was designed and facilitated in Ghana to address climate change, agricultural development and food security. This methodology has potential for much broader applicability to complex, multi-level planning and implementation processes. Author Affiliation: (a) Department of the Premier and Cabinet, Government of South Australia, Adelaide, Australia (b) Collaborative Futures, Australia (c) Centre for Systems Studies, Faculty of Business, Law and Politics, University of Hull, Hull, UK (d) Department of Informatics, Faculty of Technology, Linnaeus University, Växjö, Sweden (e) School of Innovation, Design and Engineering, Mälardalen University, Eskilstuna, Sweden (f) Victoria Business School, Victoria University of Wellington, Wellington, New Zealand (g) School of Political and Social Sciences, University of Canterbury, Christchurch, New Zealand (h) School of Agriculture and Food Sciences, University of Queensland, Brisbane, Queensland, Australia (i) Saïd Business School, University of Oxford, Oxford, UK (j) Copernicus Institute of Sustainable Development, Utrecht University, Utrecht, the Netherlands (k) World Food Program, Center for Strategic and International Studies, Washington DC, USA (l) MaRS Discovery District, Toronto, Canada * Corresponding author. Article History: Received 15 November 2019; Accepted 24 January 2023 Byline: Ariella Helfgott (a,b), Gerald Midgley [g.r.midgley@hull.ac.uk] (c,d,e,f,g,h,*), Abrar Chaudhury (i), Joost Vervoort (j), Chase Sova (k), Alex Ryan (l)

Keywords Data envelopment analysis; Network production process; Two-stage efficiency measurement; Second order conic programming; Nonconvex optimisation Abstract In two recent papers, [Guo, C., Wei, F., & Chen, Y. (2017). A note on second order cone programming approach to two-stage network data envelopment analysis. European Journal of Operational Research, 263(2), 733--735; and Chen, K., & Zhu, J. (2017). Second order cone programming approach to two-stage network data envelopment analysis. European Journal of Operational Research, 262(1), 231238] converted the general multiplicative two-stage DEA (data envelopment analysis) network model into a parametric/single second order conic programming (SOCP) problem. In this paper, we (i) note that the proposed transformation cannot result in an equivalent mathematical program in view of the fact that the general multiplicative two-stage DEA model is basically a nonconvex optimisation problem, possibly with several local and global optimums, whereas a single SOCP is a convex optimisation; (ii) demonstrate that there is a subtle technical error contained in the main transformation process proposed in both papers; (iii) illustrate, by providing a numerical counterexample, that the optimal solution obtained from the resulting single SOCP problem might be substantially different from the original model's optimum; and (iv) offer some computational remark for solving the multiplicative/additive two-stage DEA model. Author Affiliation: (a) Department of Basic Sciences, Semnan Branch, Islamic Azad University, Semnan, Iran (b) School of Business, Faculty of Business and Law, University of Wollongong, Wollongong, Australia (c) Department of Accounting and Finance, The University of Auckland, Auckland, New Zealand * Corresponding author. Article History: Received 31 January 2023; Accepted 16 February 2023 Byline: Israfil Roshdi [i.roshdi@semnaniau.ac.ir] (a,*), Mahdi Mahdiloo (b), Amir Arjomandi (b), Dimitris Margaritis (c)

Keywords E-commerce; Live-streaming; Agency selling; Reselling; Price discount strategy; Game theory Highlights * We introduce a new decision problem arising in the live-streaming commerce. * We consider the selling format selection and discount rate decision issues in the paper. * We study two regular price schemes. * We extend the assumption of exogenous commission fee charged by the live streamer and examine the negotiated commission fee problem. Abstract This paper analytically investigates the channel choice problem and price discount strategy of a supply chain under the live-streaming context. In the existing literature of traditional e-commerce, it is assumed that a manufacturer sells through the retailer's reselling or agency selling format. As live-streaming services developed, firms leverage the influence of Internet celebrities and discount strategies in the live-streaming channel to attract new consumers who are never aware of the firms' offerings. However, it is unclear that how the unique characteristics of live-streaming commerce affect the choice of selling formats and the optimal price discount strategy. We develop a game-theoretical model with two price schemes (i.e., committed price scheme and dynamic price scheme) where the decision-maker only decides on the live channel introduction in the first period. We first provide the thresholds at which decision-makers decide to adopt live-streaming selling. Second, we offer the optimal price discount rate and equilibrium outcomes for each selling format. The optimal price discount rate mainly depends on the uninformed consumers' (UCs) valuation and informed consumers' (ICs) proportion. Third, we solve the optimal selection of selling format for the retailer. The introduction of a live-streaming channel reduces the threshold that the retailer selects the agency selling format. Fourth, we compare the results of the committed price scheme and the dynamic price scheme. Findings show that decision-makers are more likely to offer a live channel promotion and raise the price of the traditional online channel under the dynamic price scheme. However, under the dynamic regular scheme, decision-makers tend to provide a deeper discount rate in the live channel, leading to a lower retail price in the live channel. Finally, we extend our model by considering a negotiated commission fee between the decision-maker and the third-party live streamer under different selling formats. Our study provides useful insights to managers to make the live-streaming channel adoption decision and make price discount decisions in supply chains with manufacturers selling through online retail. Author Affiliation: School of Management, Xiamen University, 422 South Siming Road, Xiamen 361005, China * Corresponding author. Article History: Received 18 August 2021; Accepted 18 January 2023 Byline: Guojun Ji, Tianyu Fu [futianyuabc123@163.com] (*), Shuhao Li

Keywords Inventory; Trade credit; Over-ordering; Financially constrained; Newsvendor Highlights * Study inventory in a supply chain where supplier issues trade credit to retailer. * Examine the role of return policies to control over-ordering in trade credit. * Analyze generalizable return policies to develop managerial insights. * Quantify impact of key parameters on the supply chain partners' decision variables. Abstract This paper explores the role of return policies on trade credit offered by suppliers to retailers. Traditional trade credit agreements, wherein a supplier extends a short-term loan to a retailer, can lead to over-ordering by the retailer even though she is financially constrained (FC), and this can affect supply chain efficiency. With ever-increasing product-handling costs, such over-ordering can have a severe impact on the supply chain profit. Motivated by our work with an industry partner, we design a game-theoretic model to evaluate optimal stocking decisions and wholesale prices in an FC supply chain, analyze the traditional trade credit model, and establish the reasons for over-ordering by the retailer when trade credit is deployed. We then examine how product returns, prevalent in the industry, can be used to control over-ordering. We design three different mechanisms incorporating returns in a trade credit model: quantity-limit-based returns, partial refund based returns, and marginal refund based returns. We find that returns-based policies improve profits for all members of the supply chain by driving inventory reduction and reducing over-ordering when trade credit is used. We also perform numerical analysis to quantify the impact of key parameters on the optimal decision variables. Our paper contributes by suggesting easy-to-implement mechanisms for improving trade credit deployment in supply chains and provides useful insights to decision makers to incorporate returns in trade credit policies. Author Affiliation: (a) Operations Management Area, Indian Institute of Management (IIM) Raipur, Atal Nagar, P. O. - Kurru (Abhanpur), Raipur, Chattisgarh 493661, India (b) Department of Information Systems, Supply Chain & Decision Making, NEOMA Business School, 1 Rue du Maréchal Juin, Mont-Saint-Aignan 76130, France (c) Department of Information and Operations Management, Mays Business School, Wehner Building, Texas A&M University, 4113 TAMU | 210 Olsen Blvd, USA (d) Research Chair Professor, IIM Udaipur, Balicha Campus, Udaipur, Rajasthan, 313001, India * Corresponding author. Article History: Received 23 July 2022; Accepted 7 January 2023 Byline: Bhawna Priya [bpriya@iimraipur.ac.in] (*,a), Indranil Biswas [indranil.biswas@neoma-bs.fr] (b), Anupam Agrawal [anupam.agrawal@iimu.ac.in] (c,d)

Keywords Game theory; Community operational research; Participatory modelling; Design framework; Learning Highlights * A design framework for participatory game theory interventions with stakeholders. * Decision-support needs of participating stakeholders are mapped to learning levels. * Structured learning about strategic problems through game theory-based interventions. * Framework specifies facilitator's role and design choices for each learning level. * Potential to extend framework for design of other participatory OR interventions. Abstract Game theory provides a valuable conceptual framework for developing strategic insight into complex, multi-actor situations and is well-suited for addressing real-world problems. Participatory game theory involves model construction and analysis with stakeholders guided by a facilitator with the aim of examining strategic interactions within real-world problems. Previous work in this field focused often on the analytical insights from game theory models whereas guidance on the design and implementation process of participatory game theory interventions remains under researched. This paper addresses this gap by providing a framework to assist in the design of game theory-based interventions. Here, stakeholders' decision-support needs are designed according to specific learning levels, as defined by Bloom's taxonomy and triple-loop learning, that the intervention will target. The framework further specifies the design choices for each learning level by comparing the design choices from two case studies of game theory-based interventions in Dutch railway and Bangladesh drinking water contexts. The former involved stakeholders using a game concept identification tool while the latter used game theory-based role-playing games with community and local government stakeholders. This paper describes the value of this framework for structured learning through game theory-based interventions. It includes the facilitator's role and design choices for each learning level related to the knowledge capabilities and activity focus to achieve that learning outcome. Future work will incorporate design inputs from additional learning theories, behavioural game theory and will explore the framework's potential for evaluating game theory-based interventions. Author Affiliation: (a) Radboud University Nijmegen, School of Management, Department of Methodology, Heyendaalseweg, 141, 6525 AJ Nijmegen, the Netherlands (b) Leiden University, Faculty Governance and Global Affairs, Institute of Public Administration, Turfmarkt, 99, 2511 DP the Hague, the Netherlands * Corresponding author. Article History: Received 23 June 2022; Accepted 25 January 2023 Byline: Femke Bekius [femke.bekius@ru.nl] (a,*), Sharlene L. Gomes [s.l.gomes@fgga.leidenuniv.nl] (b)

Keywords OR in medicine; Covid-19 pandemic; Epidemic model; Networks; Simulation Highlights * We model the spread of an epidemic in its early stage using the network-based approach. * We compare the network-based approach with the equation-based approach using simulation. * The empirical data of spread of Covid-19 from eight countries is considered for validation. * Partial curve mapping is used to compare simulated results with the empirical data. * The network-based approach matches the empirical data better than the equation-based approach. Abstract The spread of epidemics is a common societal problem across the world. Can operational research be used to predict such outbreaks? While equation-based approaches are used to model the trajectory of epidemics, can a network-based approach also be used? This paper presents an innovative application of epidemic modelling through the design of both approaches and compares between the two. The network-based approach proposed in this paper allows implementing heterogeneity at the level of individuals and incorporates flexibility in the variety of situations the model can be applied to. In contrast to the equation-based approach, the network-based approach can address the role of individual differences, network properties, and patterns of social contacts responsible for the spread of epidemics but are much more complex to implement. In this paper, we simulated the spread of infection at the beginning of Covid-19 (Coronavirus disease 2019) using both approaches. The results are showcased using empirical data for eight countries. Sophisticated measures, including partial curve mapping, are used to compare the simulated results with the actual number of infections. We find that the plots generated by the network-based approach match the empirical data better than the equation-based approach. While both approaches can be used to predict the spread of infections, we conclusively show that the proposed network-based approach is better suited with its ability to model the spread of epidemics at the level of an individual. Hence, this can be a model of choice for epidemiologists who are interested to model the spread of an epidemic. Author Affiliation: (a) Indian Institute of Management Calcutta, Diamond Harbour Road, Joka, Kolkata 700104, India (b) Indian Institute of Management Ahmedabad, Vastrapur, Ahmedabad 380015, India * Corresponding author. Article History: Received 1 March 2022; Accepted 13 January 2023 Byline: Saikat Das (a), Indranil Bose [indranil_bose@yahoo.com] (b,*), Uttam Kumar Sarkar (a)

Keywords Multiple criteria analysis; Composite indicator; Multi-attribute value theory (MAVT); Robustness and validation analyses; Deck of cards method Highlights * An impact assessment indicator of COVID-19 pandemic in Portugal. * Multi-attribute value theory (MAVT) tools for designing composite indicators, in a sociotechnical and co-constructive perspective. * Behavioural decision-making and the deck of cards method for assessing experts' judgments and for constructing a MAVT model. * Monte Carlo simulation and robustness analysis in multiple criteria decision aiding. Abstract The COVID-19 pandemic has caused major damage and disruption to social, economic, and health systems (among others). In addition, it has posed unprecedented challenges to public health and policy/decision-makers who have been responsible for designing and implementing measures to mitigate its strong negative impact. The Portuguese health authorities have used decision analysis techniques to assess the impact of the pandemic and implemented measures for counties, regions, or across the entire country. These decision tools have been subject to some criticism and many stakeholders requested novel approaches. In particular, those which considered the dynamic changes in the pandemic's behaviour due to new virus variants and vaccines. A multidisciplinary team formed by researchers from the COVID-19 Committee of Instituto Superior Técnico at the University of Lisbon (CCIST analyst team) and physicians from the Crisis Office of the Portuguese Medical Association (GCOM expert team) collaborated to create a new tool to help politicians and decision-makers to fight the pandemic. This paper presents the main steps that led to the building of a pandemic impact assessment composite indicator applied to the specific case of COVID-19 in Portugal. A multiple criteria approach based on an additive multi-attribute value theory aggregation model was used to build the pandemic assessment composite indicator. The parameters of the additive model were devised based on an interactive socio-technical and co-constructive process between the CCIST and GCOM team members. The deck of cards method was the adopted technical tool to assist in the assessment the value functions as well as in the assessment of the criteria weights. The final tool was presented at a press conference and had a powerful impact on the Portuguese media and on the main health decision-making stakeholders in the country. In this paper, a completed mathematical and graphical description of this tool is presented. Author Affiliation: (a) CEGIST, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, Lisboa 1049-001, Portugal (b) CAMGSD, Instituto Superior Técnico, Universidade de Lisboa, Portugal (c) CQE, Instituto Superior Técnico, Universidade de Lisboa, Portugal (d) IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Portugal (e) GCOM, Ordem dos Médicos, Portugal * Corresponding author. Article History: Received 23 September 2021; Accepted 14 January 2023 Byline: José Rui Figueira [figueira@tecnico.ulisboa.pt] (*,a), Henrique M. Oliveira (b), Ana Paula Serro (c), Rogério Colaço (d), Filipe Froes (e), Carlos Robalo Cordeiro (e), António Diniz (e), Miguel Guimarães (e)

Keywords OR in societal problem analysis; Human trafficking; Operations research; Analytics; Responsible research Highlights * Human trafficking, a prevalent global crime, harms communities' health and economics. * OR and Analytics can support trafficking prevention and intervention efforts. * The paper informs practitioners by highlighting key features of this illicit activity. * Avenues for future work are suggested. Abstract Human trafficking, the commercial exploitation of individuals, is a gross violation of human rights; harming societies, economies, health and development. The related disciplines of Operations Research (OR) and Analytics are uniquely positioned to support trafficking prevention and intervention efforts by efficiently evaluating a plethora of decision alternatives and providing quantitative, actionable insights. As operations and analytical efforts in the counter-trafficking field emerge, it is imperative to grasp subtle, yet distinctive, nuances associated with human trafficking. This paper is intended to inform those practitioners working in the Operations and Analytics fields by highlighting key features of human trafficking activity. We grouped ten themes around two broad categories: (1) representation of human trafficking and (2) consideration of survivors and communities. These insights are derived from our collective experience in working in this area and substantiated by domain expertise. Based on these areas, we then suggest avenues for future work. Author Affiliation: (a) School of Business, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA (b) Department of Mechanical and Industrial Engineering, Northeastern University, 360 Huntington Ave, Boston, MA 02115, USA (c) Data Science Program, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA * Corresponding author. Article History: Received 1 April 2021; Accepted 19 December 2022 Byline: Renata A. Konrad [rkonrad@wpi.edu] (*,a), Kayse Lee Maass [k.maass@northeastern.edu] (b), Geri L. Dimas [gldimas@wpi.edu] (c), Andrew C. Trapp [atrapp@wpi.edu] (a,c)

Keywords Supply chain management; Sharing economy; Channel structure choice; Sharing channel; Sales reward contract Highlights * This paper studies whether and when a manufacturer should establish a direct sharing channel. * It analyzes the possible interaction between the manufacturer and its independent retailer. * It shows the manufacturer will benefit from the sharing channel only if the operating cost of sharing channel is low. * It shows a sales reward contract can be designed to benefit both firms from adding the sharing channel. Abstract With the rapid development of sharing economy, the manufacturer has begun to establish direct sharing channels in addition to their existing distribution channels via independent retailers. Motivated by this business practice, this paper aims to answer the following questions: whether and when should a manufacturer establish a direct sharing channel? To this end, we first analyze a supply chain where a manufacturer distributes her product only through a retailer (the M-S Model), where we obtain the optimal retail price. Next, we consider the scenario where the manufacturer sets up a direct sharing channel in addition to the retail channel (the MR-S Model), where we obtain the optimal rental price and retail price. We then study the manufacturer's channel structure choice between the M-S and the MR-S models. Our main findings include the followings. First, the manufacturer may not always benefit from establishing a new sharing channel. The manufacturer will benefit only if the operating cost of sharing channel is low. However, when the operating cost of sharing channel is below a threshold, adding the sharing channel will decrease the profit at the retail channel, resulting in channel conflict. Second, only if the operating cost of sharing channel falls into a certain interval, the manufacturer's sharing channel will decrease the retailer's profit but increase the total supply chain profit. To avoid channel conflict, the two firms can adopt an appropriate sales reward contract so that both can benefit from the sharing channel. Lastly, when both the operating cost of sharing channel and the simultaneous rental rate of consumers are low, the manufacturer even needs to produce less if she establishes a new sharing channel. Author Affiliation: (a) Business School, Yangzhou University, Yangzhou 225127, PR China (b) Jiangsu Modern Logistics Research Base, Yangzhou University, Yangzhou 225127, PR China (c) Lazaridis School of Business and Economics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada (d) School of Management Science and Engineering, Anhui University of Technology, Ma'anshan 243002, PR China (e) School of Accounting, Southwestern University of Finance and Economics, Chengdu 610074, PR China * Corresponding author. Article History: Received 18 July 2021; Accepted 16 December 2022 Byline: Peng Zhang (a,b), Victor Shi (c), Lingzhi Shao (d), Yang Liu [yang.liu@swufe.edu.cn] (e,*)

Keywords Logistics; Container stacking; Dynamic programming; Self-attention-based neural network; Rollout algorithm Highlights * A new bay representation is proposed, leading to the new dynamic programming model. * Two neural network algorithms are learnt from optimal solutions to tackle large-scale instances. * A data-driven rollout algorithm is proposed. * The proposed models and algorithms are validated through benchmark data. Abstract In this paper, we investigate the stacking problem of outbound containers. It focuses on developing an optimal stacking strategy to allocate the arriving containers in a preassigned yard bay, with the aim of reducing extra rehandles during later retrieval. Some studies employ dynamic programming models to tackle the problem, which can offer exact solutions. Following this line of research, we propose an alternative dynamic programming model by redefining the bay representation and adjusting the formulations accordingly. The results show that the new model strikes a good balance between stacking quality and computational time. Considering that the dynamic programming model encounters difficulty in solving large-scale instances, we design two neural network algorithms that adopt a self-attention mechanism to enhance the fitting ability of the network. The neural network algorithms learn the decision patterns from the optimal results for small-scale instances obtained by dynamic programming and then are applied to solve large-scale instances. In addition, we propose a data-driven rollout algorithm by integrating the branching strategy and the aforementioned neural network algorithms to prevent the myopic drawback of using solely the neural network. To the best of our knowledge, this is the first paper that integrates the optimization method and machine learning techniques to tackle the container stacking problem. Finally, extensive computational experiments are performed to verify the effectiveness of the proposed models and algorithms. Author Affiliation: Research Center for Modern Logistics, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China * Corresponding author. Article History: Received 25 August 2021; Accepted 2 December 2022 Byline: Canrong Zhang [crzhang@sz.tsinghua.edu.cn] (*), Qi Wang, Guoping Yuan

Keywords OR in banking; Bayesian joint models; Discrete time; Autoregressive process Highlights * This paper proposes a joint model with autoregressive terms in the longitudinal outcome. * A discrete time framework is applied to credit scoring. * We analyse 10,399 mortgage loans originated in the US. * Our proposal increases the discrimination performance of traditional survival models. Abstract The inclusion of time-varying covariates into survival analysis has led to better predictions of the time to default in behavioural credit scoring models. However, when these time-varying covariates are endogenous, there are two major problems: estimation bias of the survival model and lack of a prediction framework for future values of both the event and the endogenous time-varying covariates. Joint models for longitudinal and survival data is an appropriate framework to model the mutual evolution of the survival time and the endogenous time-varying covariates. To the best of our knowledge, this paper explores for the first time the application of discrete-time joint models to credit scoring. Moreover, we propose a novel extension to the joint model literature by including autoregressive terms in modelling the endogenous time-varying covariates. We present the method via simulations and by applying it to US mortgage loans. The empirical analysis shows, first, that discrete joint models can increase the discrimination performance compared to survival models. Second, when an autoregressive term is included, this performance can be further improved. Author Affiliation: (a) Business School, University of Edinburgh, United Kingdom (b) School of Mathematics, University of Edinburgh, United Kingdom * Corresponding author. Article History: Received 22 December 2020; Accepted 12 October 2022 Byline: Victor Medina-Olivares [victor.medina@ed.ac.uk] (*,a), Raffaella Calabrese (a), Jonathan Crook (a), Finn Lindgren (b)

Keywords Scheduling; Warehousing; Parts-to-picker; Synchronization Highlights * Processing multiple orders demanding the same products jointly is treated. * We provide a classification scheme of the resulting synchronization problems. * Complexity results for the vast majority of problem settings are obtained. * We gain insight on suited system setups. * We benchmark the gains of synchronization with alternative decision tasks. Abstract Triggered by the great success of e-commerce, today's warehouses more and more evolve to fully-automated fulfillment factories. Many of them follow the parts-to-picker paradigm and employ shelf-lifting mobile robots or conveyors to deliver stock keeping units (SKUs) to stationary pickers operating in picking workstations. This paper aims to structure and review the family of synchronization problems that arise in this environment: If multiple orders demanding the same SKU can be serviced jointly, then a more efficient picking process and a relief of the bin supply system can be achieved. This paper classifies the family of slightly varying synchronization problems arising with different workstation setups in alternative warehouses. This classification scheme is applied to analyze computational complexity, to systematically quantify the gains of alternative workstation setups, and to benchmark the performance gains of synchronization with those of other well-established decision tasks. Our results show that the right workstation setup can greatly improve throughput performance, so that the gains of synchronization can outreach those promised by other well-researched decision tasks. Author Affiliation: (a) Friedrich-Schiller-Universität Jena, Lehrstuhl für Operations Management, Carl-Zeiß-Straße 3, Jena 07743, Germany (b) Friedrich-Schiller-Universität Jena, Lehrstuhl für Management Science, Carl-Zeiß-Straße 3, Jena 07743, Germany * Corresponding author. Article History: Received 7 June 2021; Accepted 25 September 2022 Byline: Nils Boysen [http://www.om.uni-jena.de] (*,a), Stefan Schwerdfeger [https://www.mansci.uni-jena.de] (a,b), Konrad Stephan [konrad.stephan@uni-jena.de] (a)

Keywords Maintenance policy; Greenhouse gas emissions; Condition-based monitoring; Two time scales; Integer nonlinear programming Highlights * The paper considers the greenhouse gas emission of a system as a degradation process. * It also considers the failure process due to other causes. * It proposes two methods to model the bivariate stochastic process. * Maintenance policies are proposed to optimise the expected cost rate. Abstract Greenhouse gases (GHG) from human activities are the main contributor to climate change since the mid-20th century. Reducing the release of GHG emissions is becoming a thematic research topic in many research disciplines. In the reliability research community, there are research papers relating to reliability and maintenance for systems in power generation farms such as offshore farms. Nevertheless, there is sparse research that aims to optimise maintenance policies for reducing the GHG emissions from systems such as automotive vehicles or building service systems. To fill up this gap, this paper optimises replacement policies for systems that age and degrade and that produce GHG emissions (i.e., exhaust emissions) including the initial manufacturing GHG emissions produced during the manufacturing stage and the emissions generated during the operational stage. Both the exhaust emissions process and the failure process are considered as functions of two time scales (i.e., age and accumulated usage), respectively. Other factors that may affect the two processes such as ambient temperature and road conditions are depicted as random effects. Under these settings, the decision problem is a nonlinear programming problem subject to several constraints. Replacement policies are then developed. Numerical examples are provided to illustrate the proposed methods. Author Affiliation: (a) Kent Business School, University of Kent, Canterbury, Kent CT2 7PE, United Kingdom (b) School of Management, Xi'an Jiaotong University, Xian, China (c) School of Economics and Management, Beijing University of Technology, Beijing 100124, China * Corresponding author. Article History: Received 3 November 2021; Accepted 3 October 2022 Byline: Shaomin Wu [s.m.wu@kent.ac.uk] (a,*), Di Wu (b), Rui Peng (c)

Keywords Problem structuring; Facts and values; Multi-methodology; SCA; ANP Highlights * A multi-methodology that focuses on OR interventions in socio-technical terms. * The paper considers Latour's 'collective' as a potential description of the decision-making process. * The research proposes a combination of SCA and ANP to facilitate dealing with 'facts' and 'values'. Abstract The paper proposes a new multi-methodological framework combining a Problem Structuring Method and a Multi-Criteria Decision Analysis to address the problem of composing facts and values in the decision-making process of policy making. We position our work theoretically in relation to Latour's concept of the 'collective' as a potential description of the decision-making process, with its conflicts and negotiations, openings and closures. With Latour, we can say that there are no 'separate chambers' in which facts (i.e., the use of public resources, different time horizons) and values (i.e., the values of different stakeholders, the legitimacy of public decisions) are discussed; rather, all these aspects are considered together in a cycle that encompasses them, progressively expanding and contracting to arrive at a tangible result: a decision. In the paper we illustrate the transposition of the concept of this cycle in our multi-methodology, the proposal of the combination of the Strategic Choice Approach (SCA) and the Analytic Network Process (ANP)--which is absent in the literature--and we then empirically test this theoretical contribution with a case study, the repurposing of a former hospital in Italy. Author Affiliation: Interuniversity Department of Regional and Urban Studies and Planning, Politecnico di Torino. Viale Mattioli 39, 10125 Turin, Italy * Corresponding author. Article History: Received 11 March 2021; Accepted 15 October 2022 Byline: Isabella M. Lami [isabella.lami@polito.it] (*), Elena Todella [elena.todella@polito.it]

Keywords Transportation; Variable-echelon vehicle routing; Mobile satellites; Cargo bikes; Open routes Highlights * A novel multi-modal variable-echelon last-mile delivery system is introduced. * The problem is formulated as a mixed integer programming model. * A fast heuristic is proposed which combines biased-randomisation and local search. * Experiments demonstrate the efficiency of the heuristic and benefits of the proposed delivery system. * Customer density and parcels sizes are shown to be critical factors effecting fleet composition. Abstract This paper proposes a last-mile logistics delivery system which makes use of multiple localised storage depots and multi-modal delivery options. Multiple localised storage depots facilitate express and instant delivery services. Multi-modal delivery allows for use of alternative green vehicle types for performing deliveries where there may also be vehicle access restrictions. Additionally, when demand density is sufficiently high and parcel sizes small, utilising alternative delivery modes, such as electric cargo bike and porters, can be cost effective in their own right. The proposed model allows for vehicles to rendezvous at kerbside locations (mobile satellites) where parcels can be transferred between vehicles, a feature that is shown to reduce depot stem costs. For the purpose of generality and the potential for higher quality solutions, no fixed echelon or hierarchical structure is placed on the sequence of vehicles transporting any parcel, that is, the problem is one of variable-echelon. The last-mile delivery system described in the paper gives rise to a multi-modal delivery problem using a heterogeneous fleet of vehicles and with synchronisation constraints. The paper presents a mathematical formulation of the problem and a heuristic algorithm. Computational results are presented that validate the mathematical model and the heuristic on a set of benchmark instances, some of which are based on the literature. The paper also describes a new set of benchmark instances derived from real sales data in London, whose results demonstrate potential benefits from using the proposed delivery concept. Author Affiliation: (a) Operations and Supply Chain Management, University of Liverpool Management School, Liverpool, Chatham Street, L69 7ZH, UK (b) Darwin Evolution Technologies, UK * Corresponding author. Article History: Received 20 January 2022; Accepted 27 August 2022 Byline: Christopher Bayliss [christopher.bayliss@liverpool.ac.uk] (*,a), Tolga Bektas [t.bektas@liverpool.ac.uk] (a), Vernon Tjon-Soei-Len [vernon@bezos.ai] (b), Remo Rohner [remo@bezos.ai] (b)

Keywords OR in maritime industry; Disruption management; Vessel schedule recovery; Greenhouse gas emissions; Crowd-learning particle swarm optimization Highlights * Develops novel MIPP model and heuristic to solve the large-scale instances in liner shipping. * Explores the blockage of the Suez Canal versus rerouting through the Cape of Good Hope. * Results show that adjusting vessel speed and/or skipping call-ports mitigates costly disruptions. * Examines temporary cargo storage and accounts for GHG increased from vessel speeding. * Conducts extensive computations to validate and analyze the model. Abstract Disruptions often occur in liner shipping networks, and they are costly. When they occur, freight companies evaluate their effects on freightage in the pipeline and take the appropriate recovery actions by balancing customer service levels and increases in fuel consumption while accounting for environmental impact (greenhouse gas (GHG) emissions). The paper, therefore, develops an integrated mixed-integer programming problem (MIPP) that jointly minimizes the total voyage and transshipment costs and penalty charges for emitting GHG excess amounts beyond what is allowed. It does so by recovering a pre-established schedule of disrupted containerships. The solution to the MIPP suggests how to reconfigure the liner shipping network when skipping one or more call ports and determines the optimal velocity on assigned routes. The paper also develops and proposes a new and efficient algorithm based on the Crowd-Learning Particle Swarm Optimization (CLPSO) to solve this large-scale problem and shows the CLPSO to be superior to the potential ones in the literature. Computational experiments, based on data from a maritime shipping company, demonstrate the effectiveness of both the MIPP and CLPSO using several comparative metrics with suitable assumptions. The numerical results show that the developed MIPP has a potential application in practice. Author Affiliation: (a) Department of Industrial Engineering, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada (b) Department of Mechanical and Industrial Engineering, Toronto Metropolitan University 1 Toronto, ON M5B 2K3, Canada (c) Department of Industrial Engineering and Management Systems, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran (d) Rennes School of Business, 2 Rue Robert d...Arbrissel, 35065, Rennes, France * Corresponding author. Article History: Received 5 November 2021; Accepted 26 August 2022 (footnote)1 Formerly Ryerson University. Byline: Mohammad Asghari (a), Mohamad Y. Jaber [mjaber@ryerson.ca] (b,*), S.M.J. Mirzapour Al-e-hashem (c,d)

Keywords Group decisions and negotiationst; Minimum cost consensus; Consensus principle; Tolerance level; Feedback regulation mechanism Highlights * The concept and constraint of consensus principle are proposed. * The definitions of tolerance level and consensus level are proposed. * The minimum cost consensus model based on the consensus principle is constructed. * The minimum cost consensus models with feedback regulation mechanism are constructed. Abstract Since the hard consensus is difficult and costly to achieve in group decision making (GDM), it is reasonable and necessary for decision makers (DMs) to reach a soft consensus within a certain level of tolerance and consensus. To achieve this purpose, the concepts and definitions of consensus principle, tolerance level and consensus level are proposed in this paper. The consensus principle keeps the consensus reaching process (CRP) always moving in a better direction, and the tolerance level characterizes the individual's psychological receptivity, while the consensus level guarantees the quality of consensus results, then the minimum cost consensus models (MCCMs) based on these three points are proposed. Thereafter, we add a feedback regulation mechanism based on tolerance threshold rewards to the proposed MCCMs, the mechanism connects individual weight with tolerance threshold, avoiding the subjective disadvantage caused by the two values need to be given in advance. Meanwhile, the framework and specific algorithm of CRP under the tolerance threshold reward feedback regulation mechanism are given, providing a precise method for solving the realistic consensus problems. Finally, the consensus reaching case of the carbon emission benchmark shows the reasonable effectiveness of the two different models proposed in this paper, and the comparative analysis shows the differences and applicability of the two models. Author Affiliation: (a) School of Business Administration, South China University of Technology, Guangzhou 510641, China (b) School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China (c) College of Management, Shenzhen University, Shenzhen, 518055, China (d) School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China * Corresponding author. Article History: Received 12 October 2021; Accepted 24 August 2022 Byline: Weiwei Guo [guowwwhh@163.com] (a), Zaiwu Gong [zwgong26@163.com] (b), Wei-Guo Zhang [wgzhang@scut.edu.cn] (*,a,c), Yanxin Xu [yanxinxuxu@163.com] (d)

Keywords Stochastic programming; Scenario tree generation; Recursive algorithms; Model error; Distributionally robust solutions HIGHLIGHTS * This is an elaboration of the semiplenary talk I held in Athens at EURO 2021. * The paper summarizes some earlier work, a new aspect is however included by emphasizing the recursive structure of data structures and algorithms. * The role of the ambiguity radius as a tradeoff between model information and efficiency of the optimal decisions is elaborated for several informative examples. Abstract Stochastic multistage decision problems appear in many - if not all - application areas of Operations Research. While to define such problems is easy, to solve them is quite difficult, since they are of infinite dimension. Numerical solution can only be found by solving an approximate, easier problem. In this paper, we show good approximations can be found, where we emphasize the recursive structure of the involved algorithms and data structures. In a second part, the problem of coping with the model error of approximations is discussed. We present algorithms for finding distributionally robust solutions for the model error problem. We also review some application cases of such situations from the literature. Author Affiliation: Faculty of Economics and Statistics, University of Vienna, Wien Oskar-Morgenstern Platz, Vienna A-1090, Austria Article History: Received 6 December 2021; Revised 20 March 2022; Accepted 2 April 2022 (footnote)[white star] This paper is an elaboration of a semiplenary talk held at the EURO21 conference in Athens Byline: Georg Ch. Pflug [georg.pflug@univie.ac.at]

Keywords OR in health services; Implementation Abstract This paper is based on the keynote address given by the paper's first author at EURO 2021. We draw on our experience over more than three decades to define the critical challenges of healthcare implementation. We do not address issues pertaining to technical quality of a solution. Rather, we focus on five general characteristics of the problem that should be carefully considered for any healthcare project that requires implementation. The problem needs an internal Champion; there should be a current Critical Issue; one must understand and adapt to the Cultural dynamics of the organization; appropriate Data exists; and we need to manage Expectations. We illustrate each with examples of our successes, failures, and mixed results. Finally, we summarize what short and long-term steps we believe the operational research community can take that will lead to improvement in each of these areas. Author Affiliation: Department of Mechanical & Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, ON, M5S 3G8, Canada * Corresponding author. Article History: Received 30 November 2021; Revised 11 April 2022; Accepted 16 April 2022 Byline: Michael W. Carter [mike.carter@utoronto.ca] (*), Carolyn R. Busby

Keywords Multiple objective programming; ESG in investing; Efficient frontiers; ESG integration; Tri-criterion portfolio selection Highlights * The paper provides a framework for solving the three-objective Markowitz problem where sustainability in the form of ESG is the third objective. * With no clear definition of ESG integration in the literature, we provide a crisp definition of what it is and is not. * A new technique called non-contour efficient fronts is presented for searching tri-criterion efficient surfaces for most preferred portfolios. * While current methods leave ESG on the table, the non-contour methodology leads to portfolios with significantly greater ESG content. * We develop an ESG integration index that is able to assess the degree to which ESG has been integrated into a portfolio. Abstract The paper focuses on investors whose strength of interest in sustainability issues (such as environmental, social, and governance) causes ESG to become a third criterion alongside risk and return in portfolio selection. This causes the efficient frontier to become an efficient surface. This means that an investor's optimal portfolio is no longer the point of most preferred risk/return tradeoff on the mean-variance (M-V) efficient frontier, but is the point of most preferred risk/return/ESG tradeoff on the investor's M-V-ESG efficient surface. However, to find such a point requires non-trivial ESG integration which is the name given to the process of integrating ESG into the portfolio construction process after screening. With the third objective transporting the problem into 3D-space, it is difficult to search the efficient surface in any kind of comprehensive fashion using M-V based or other bi-criterion techniques as this is akin to a 2-dimensional being trying to view a 3-dimensional object. To remedy the situation, the paper proposes a tri-criterion approach that computes efficient surfaces and special non-contour curves (called NC-efficient fronts in the paper) that are stretched across the efficient surface so as to dragnet it for the points of best ESG integration within it. Using the methodology and data from the S&P500, the paper conducts computational tests on problems with up to 500 securities and under different constraint conditions so as to know what to expect from the new approach over a range of situations. Author Affiliation: (a) University of Georgia, Department of Finance, Athens, Georgia 30602, USA (b) University of Augsburg, Faculty of Business Administration and Economics and Centre for Climate Resilience, Universitaetsstrasse 12, 86159 Augsburg, Germany * Corresponding author. Article History: Received 30 November 2021; Accepted 5 August 2022 Byline: Ralph E. Steuer [rsteuer@uga.edu] (*,a), Sebastian Utz [sebastian.utz@uni-a.de] (b)

Keywords Behavioural or; System dynamics; Intervention Highlights * Critically evaluates the 'behavioural turn' in OR and re-visits the core ideas. * Applies to system dynamics the behavioural perspective of biases and deviations from rationality. * Presents a new framework for system dynamics studies which reveals a range of behavioural effects. * Proposes five 'Behavioural SD' axioms involving interdisciplinarity and experiments. * Makes the case that 'Behavioural SD' can explain behavioural phenomena and improve model-based interventions. Abstract Attempts to examine so-called 'behavioural effects' have reached into many different fields and are in full sway across OR. This paper considers whether this can be applied to System Dynamics modelling in a useful way. The idea is that humans frequently do not employ strict rationality in their daily lives but make errors and are subject to fallacies. This can shed light on the cognitive and human interaction aspects of the process and outcomes of modelling. The paper first raises concerns about the current state of 'Behavioural OR' -- BOR. To refocus the underlying ideas it then returns to the Decision Theory roots, takes a broader view using an illustration from the history of science and then builds on work which first proposed a link to System Dynamics (SD). The core of the paper then explores in depth how behavioural ideas apply to SD. This is done using examples dealing with complex systems in a 'naïve' versus a 'sophisticated' way, and then using a mind map. It then offers a new and detailed framework of the stages of an SD-based intervention, indicating the presence of behavioural effects and providing a fine-grained discussion of those effects as they apply to SD. It builds on this by proposing a definition of 'Behavioural System Dynamics' (BehSD) in terms of its perspective on phenomena, five new, constitutive axioms, and its potential for improving practice. The paper closes by reprising the nature and potential of 'BehSD' and by sketching how research that adopts this perspective might go forward. Author Affiliation: (a) Henley Business School, University of Reading, Reading, RG6 6UD, United Kingdom (b) Institute for Management Research, Radboud University, P.O. Box 9108, 6500, HK, Nijmegen, The Netherlands * Corresponding author. Article History: Received 18 November 2020; Accepted 12 August 2022 Byline: David C. Lane (a), Etiënne A.J.A. Rouwette [Etienne.Rouwette@ru.nl] (b,*)

Keywords Data envelopment analysis; Corporate social responsibility; Dynamic data envelopment analysis; Fuzzy data envelopment analysis Highlights * A new method for inefficiency evaluation is proposed. * The method accounts for firms' CSR activities. * The method considers the vagueness of CSR data through fuzzy DEA. * The method allows for dynamics of firms' production decisions through adjustment costs. * Dynamic fuzzy methodology adds some value to the standard crisp approach. Abstract This paper contributes to research on the corporate social responsibility (CSR) field and the inefficiency measurement of firms by proposing a new method for evaluating inefficiency accounting for firms' CSR activities. The new approach considers the imprecise nature of CSR data through the fuzzy data envelopment analysis (FDEA) method and further extends it by allowing for the dynamic interdependence of firms' production decisions through adjustment costs, related to firms investments. In addition, the new method deals with zero or negative values for inputs and/or outputs of the data. The empirical application used in this paper considers a dataset of CSR activities of European firms for three industries (capital, consumption, and other) over the period 2014--2016. Two main results are found with this data. First, the study shows that fuzzy dynamic inefficiencies tend to be lower than these obtained from the conventional crisp evaluation of inefficiency. Second, the study finds some differences in dynamic inefficiencies at distinct levels of fuzziness. Overall, the results seem to confirm that the usage of dynamic fuzzy methodology adds some value to the standard crisp approach. Author Affiliation: (a) Center of Operations Research (CIO), Miguel Hernandez University of Elche (UMH), Elche, Alicante, Spain (b) Department of Logistics, Wroclaw University of Economics and Business, ul. Komandorska 118/120, Wroclaw 53-345, Poland * Corresponding author. Article History: Received 1 February 2021; Accepted 4 September 2022 Byline: Juan Aparicio (a), Magdalena Kapelko [magdalena.kapelko@ue.wroc.pl] (b,*), Lidia Ortiz (a)

Keywords OR in environment and climate change; Multistage distributionally robust optimization; Phi-divergences; Water resources; Nested benders decomposition Highlights * Multistage distributionally robust optimization (MDRO) with [phi]-divergences is studied. * A nested Benders decomposition algorithm is proposed and its properties are examined. * The approach is applied to allocate water under climate uncertainties in Tucson, AZ. * Water allocation and infrastructure planning via MDRO helps reduce extreme shortages. Abstract This paper investigates a Multistage Distributionally Robust Optimization (MDRO) approach to water allocation under climate uncertainty. The MDRO is formed by creating sets of conditional distributions (called conditional ambiguity sets) on a finite scenario tree. The distributions in the conditional ambiguity sets remain close to a nominal conditional distribution according a [phi]-divergence (e.g., Kullback-Leibler divergence, Hellinger distance, Burg entropy, etc.). The paper discusses a decomposition algorithm to solve the resulting MDRO with [phi]-divergences, which uses the dual formulation and solves only linear subproblems instead of convex ones. Some properties of the algorithm such as generating feasible policies and valid upper/lower bounds are established. The paper then applies the modeling and solution techniques to allocate water in a rapidly-developing area of Tucson, Arizona. Tucson, like many arid and semi-arid regions around the world, faces considerable uncertainty in its ability to provide water for its citizens in the future. The primary sources of uncertainty in the Tucson region include (1) unpredictable population growth, (2) the availability of water from the Colorado River, and (3) the effects of climate variability on water consumption. This paper integrates forecasts for all these sources of uncertainty into a single optimization model for robust and sustainable water allocation. Then, it uses this model to analyze the value of constructing additional treatment facilities to reduce future water shortages. The results indicate that the MDRO approach can be very valuable for water managers by providing insights to minimize their risks and help them plan for the future. Author Affiliation: (a) Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley CA 94720, USA (b) Department of Integrated Systems Engineering, The Ohio State University, Columbus OH 43210, USA * Corresponding author. Article History: Received 21 November 2019; Accepted 24 June 2022 Byline: Jangho Park [janghopark.1814@gmail.com] (a), Güzin Bayraksan [bayraksan.1@osu.edu] (*,b)

Keywords Logistics; Sorting operations; Express parcel delivery; Robust optimization Highlights * We introduce robust optimization models for express parcel sort planning. * We explicitly model demand uncertainty in arrival quantities and arrival times. * We demonstrate models' computational viability on instances using industry data. * We show models' value in generating plans trading-off sorting cost and robustness. Abstract Parcel logistics services play a vital and growing role in economies worldwide, with customers demanding faster delivery of nearly everything to their homes. To move larger volumes more cost effectively, express carriers use sort technologies to consolidate parcels that share similar geographic and service characteristics for reduced per-unit handling and transportation costs. This paper focuses on an operational planning problem that arises in two-stage sort systems operating within parcel transportation networks. In this context, primary sorters perform an initial grouping of parcels into 'piles' that are subsequently dispatched when necessary to secondary sorters; there, each pile's parcels are fine-sorted based on their final destinations and service class for packing into outbound transportation vehicles. Such systems must be designed to handle a high degree of uncertainty in the quantity and timing of arriving parcels, yet must also group and sort the parcels to meet tight departure deadlines. Thus motivated, this paper presents robust planning models that assign parcels to sort equipment while protecting against different sources of demand uncertainty commonly faced by parcel carriers. We demonstrate the computational viability of the proposed models using realistic-sized instances based on industry data, and show their value in providing sort plan alternatives that trade off operational costs and levels of robustness. Author Affiliation: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA * Corresponding author. Article History: Received 15 March 2021; Accepted 13 July 2022 Byline: Reem Khir [reem.khir@gatech.edu] (*), Alan Erera, Alejandro Toriello

Keywords Logistics; Pickup and delivery; Transshipments; Time windows; Mixed-integer linear programming Highlights * This paper addresses the pickup and delivery problem with transshipments (PDP-T) and the pickup and delivery problem with time windows and transshipments (PDPTW-T). * We make revisions and modifications to two state-of-the-art models. * We present a new model and generate several benchmarks for future comparison. * The solvable scale is increased significantly by using the new model. * Computational time is reduced by 96% and 40% for PDP-T and PDPTW-T, respectively. Abstract The pickup and delivery problem with transshipments (PDP-T) is generalized from the classical pickup and delivery problem (PDP) by allowing the transfer of requests between vehicles. After considering the time window constraints, the PDP-T is further generalized to the pickup and delivery problem with time windows and transshipments (PDPTW-T). In this paper, we review two state-of-the-art models for the PDP-T and PDPTW-T. We point out the possible issues existing in the models and provide our revisions. In addition, we develop a new mixed-integer linear programming formulation to solve the PDP-T and PDPTW-T. The performance of the proposed model is evaluated by solving 340 generated PDP-T instances and 360 open-access PDPTW-T instances. Computational results show that the proposed model outperforms the existing models in terms of solution quality and computing time. PTP-T instances with up to 25 requests and 2 transfer stations are solved to optimality by using the proposed model. As a comparison, the best-known benchmarks in the literature are instances with 5 requests and 1 transfer station. In addition, the computing time is significantly reduced. In our experiments, the average computational time for solving PDP-T is reduced by 96%. For PDPTW-T instances, the solvable scale is increased from 3 requests and 4 transfer stations to 5 requests and 4 transfer stations. The average computing time is reduced by 40%. Author Affiliation: Department of Industrial and Systems Engineering, The University of Tennessee, Knoxville, Knoxville, TN 37996, United States * Corresponding author. Article History: Received 16 September 2021; Accepted 31 May 2022 Byline: Zefeng Lyu, Andrew Junfang Yu [ajyu@utk.edu] (*)

Keywords Supply chain management; Private labels; National brands; e-tailer; Sourcing strategy Highlights * This paper fills a research gap by thoroughly studying whether an e-tailer should introduce a private label (PL) product. * If yes, when should the e-tailer manufacture it in-house or outsource if from a national brand (NB) or another third-party manufacturer? * It shows the e-tailer would charge the highest agency fee and provide the highest service level when sourcing from the NB manufacturer * It shows that there is always a sourcing strategy that can benefit the NB manufacturer and the e-tailer. * It shows the robustness of the analytic findings by considering model extensions. Abstract Many electronic retailers (e-tailers) have introduced private labels (PLs). Although there is a vast literature on modeling pricing and e-tailers' operational issues, research on PL sourcing has been lacking. This paper seeks to fill this gap by investigating an e-tailer (she) who can manufacture her PL in-house or source it from an external third-party manufacturer or a national brand manufacturer (he). The e-tailer simultaneously sells the PL directly and the product of the national brand (NB) manufacturer with agency selling. Furthermore, she provides consumer service for both products. Our analysis leads to the following major results. First, the e-tailer would charge the highest agency fee and provide the highest service level when sourcing from the NB manufacturer. Second, the PL sourcing preference of the e-tailer mainly depends on the production cost and consumer service sensitivity. In contrast, the profit of the NB manufacturer is influenced primarily by the consumer preference for PL and the sourcing strategy of the e-tailer. Third, there is always a PL sourcing strategy that can benefit the NB manufacturer and the e-tailer. Our model extensions explore how price elasticity, product quality, consumer loyalty, and exogenous fees affect our main results, which are shown to be robust. Author Affiliation: (a) School of Economic and Management, University of Electronic Science and Technology of China, China (b) School of Business Administration, Faculty of Business Administration, Southwestern University of Finance and Economics, China (c) Lazaridis School of Business and Economics, Wilfrid Laurier University, Canada * Corresponding author. Article History: Received 8 November 2021; Accepted 12 May 2022 Byline: Hengyu Li (a), Huangen Chen (b), Junwu Chai [chaijw@uestc.edu.cn] (a,*), Victor Shi (c)

Keywords Data envelopment analysis; Business partnerships; Inverse DEA; Strategic alliances; Decision making units Highlights * Defines various types of strategic alliances and partnerships between different decision making units. * Develops novel data envelopment analysis models for business partnerships. * Guides partners on how redistributing inputs and outputs could improve their efficiency score. * Helps partners to use each other's resources in order to reach target efficiency. Abstract Strategic alliances and partnerships including mergers and acquisitions have been a growing trend in many industries in the past decades. There are many studies in the literature emphasizing the importance of business partnerships. However, literature on partnership optimization is quite limited. This paper defines various types of strategic alliance collaborations and partnerships between different decision making units (DMUs) and develops data envelopment analysis (DEA) models to guide partners on how redistributing their inputs and outputs could enhance their performance. The results of this study are useful for companies considering strategic alliances and partnerships to improve competitiveness. An application in banking is used to highlight the advantages of the proposed method in this paper. Author Affiliation: Faculty of Business, University of New Brunswick, Saint John NB E2K 5E2, Canada * Corresponding author. Article History: Received 30 October 2021; Accepted 17 May 2022 (miscellaneous) Edited by Prof. Mike Yearworth Byline: Gholam R. Amin [gamin@unb.ca] (*), Mustapha Ibn Boamah [mboamah@unb.ca]