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This paper proposes an agent-based simulation model to study and analyse the performance of various procurement and production policies in the recycled paper industry. The proposed model includes the recycled pulp production process, as well as the waste paper inventory and procurement processes. A detailed simulation model developed in partnership with a large recycled pulp producer in North America was developed in order to emulate the procurement manager's behaviour. Therefore, based on the observed behaviour of the procurement manager, a procurement behaviour model, which takes both market price and inventory requirement into account, is introduced. This paper also introduces a waste paper market model that simulates a market price and enables the control of price forecast accuracy. Two series of experiments were carried out in order to study the performance of procurement and production policies in several productions contexts. Results show that production Volume Flexibility has a negative impact on costs, inventory and quality. However, it is possible to partially reduce these issues with the introduction of contracts with Volume Flexibility, although only a limited effect has been observed in our experiments. A more significant strategy to improve costs consists in reducing production rate to the minimum level required to meet demand.

We discuss cutting stock problems (CSPs) from the perspective of the paper industry and the financial impact they make. Exact solution approaches and heuristics have been used for decades to support cutting stock decisions in that industry. We have developed polylithic solution techniques integrated in our ERP system to solve a variety of cutting stock problems occurring in real world problems. Among them is the simultaneous minimization of the number of rolls and the number of patterns while not allowing any overproduction. For two cases, CSPs minimizing underproduction and CSPs with master rolls of different widths and availability, we have developed new column generation approaches. The methods are numerically tested using real world data instances. An assembly of current solved and unsolved standard and non-standard CSPs at the forefront of research are put in perspective.

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.

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.

In this paper we describe a container loading software package for a pulp and paper manufacturer. The program takes, as input, orders for paper products in sheets or reels. As output it produces precise order quantities, and stowage plans for shipping containers. The program includes a heuristic algorithm for two-dimensional stowing of reels of a common diameter, a bin packing algorithm for combining reels into stacks and a two-dimensional algorithm for stowing pallets of various sizes. Since the order sizes are usually greater than one container load all algorithms are designed for the multi-container case. The program is currently in use and has been effective in several decision situations including (a) good sizes for reel diameters (b) efficient stowage patterns, and (c) production quantities that are compatible with cost efficient shipping. It also reduces the time taken to produce stowage and shipping documents.

The paper addresses ranking of factors with a use of the pairwise comparison method in sense of the analytic hierarchy process (AHP). The aim of this study is to show that the logarithmic least squares method used to approximate judgement matrix in order to calculate the ranking of factors does not cause the reduction of weight of a new alternative as the eigenvector method does.

The great variety of project scheduling problems studied in the ever growing literature motivated the recent development of classification schemes. In a recent paper (European Journal of Operational Research 112 (1999) 3–41), Brucker et al. make the claim that, so far, no classification scheme exists which is compatible with what is commonly accepted in machine scheduling and introduce a new classification. In this note, we critically review major shortcomings of the suggested scheme which place heavy limitations on its potential use.

In a recently published article in EJOR, Christofides et al. (CAT) present a depth-first search, branch-and-bound solution procedure for the multiple-resource constrained, single project scheduling problem. While there are many important contributions in this paper, we show by counterexample that if the branching strategy described by the authors is used, the optimal solution might not result. Computational experience on a set of test problems appearing in the open literature is reported both with the original branching strategy suggested by the authors and a modified branching strategy that we propose. The modified strategy guarantees the determination of the optimal solution in all instances of the problem at the expense of an increase in node evaluations and average CPU time. Computational results using the revised procedure and a hybrid, breadth-first search procedure also investigated by CAT are reported.

The modelling process undertaken in order to evolve a continuous simulation model of the U.K. paper industry is outlined. The purpose in building the model was to produce a tool which could be used in investigating the effectiveness of a number of policies designed to reduce the impact of cyclical variations in demand on the industry. A series of experiments which was carried out in order to assess the effectiveness of the policies are described briefly, as are the results obtained from these experiments. The effect of the strategic and industry wide nature of the model on the investigations carried out with it is considered.

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time à la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton–Jacobi–Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand.

This paper studies a two-machine cross-docking flow shop scheduling problem in which a job at the second machine can be processed only after the processing of some jobs at the first machine has been completed. The objective is to minimize the makespan. We first show that the problem is strongly NP-hard. Some polynomially solvable special cases are provided. We then develop a polynomial approximation algorithm with an error-bound analysis. A branch-and-bound algorithm is also constructed. Computational results show that the branch-and-bound algorithm can optimally solve problems with up to 60 jobs within a reasonable amount of time.

In this paper, we consider single machine scheduling problem in which job processing times are controllable variables with linear costs. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time, total absolute differences in completion times and total compression cost; minimizing a cost function containing total waiting time, total absolute differences in waiting times and total compression cost. The problem is modelled as an assignment problem, and thus can be solved with the well-known algorithms. For the case where all the jobs have a common difference between normal and crash processing time and an equal unit compression penalty, we present an O(n log n) algorithm to obtain the optimal solution.

We study the supply chain problem of a large international pulp producer with five pulp mills located in Scandinavia. The company currently uses manual planning for most of its supply chain, which ...

In this paper, we consider the contextual variant of the MNL-Bandit problem. More specifically, we consider a dynamic set optimization problem, where a decision-maker offers a subset (assortment) of products to a consumer and observes the response in every round. Consumers purchase products to maximize their utility. We assume that a set of attributes describe the products, and the mean utility of a product is linear in the values of these attributes. We model consumer choice behavior using the widely used Multinomial Logit (MNL) model and consider the decision maker problem of dynamically learning the model parameters while optimizing cumulative revenue over the selling horizon $T$. Though this problem has attracted considerable attention in recent times, many existing methods often involve solving an intractable non-convex optimization problem. Their theoretical performance guarantees depend on a problem-dependent parameter which could be prohibitively large. In particular, existing algorithms for this problem have regret bounded by $O(\sqrt{\kappa d T})$, where $\kappa$ is a problem-dependent constant that can have an exponential dependency on the number of attributes. In this paper, we propose an optimistic algorithm and show that the regret is bounded by $O(\sqrt{dT} + \kappa)$, significantly improving the performance over existing methods. Further, we propose a convex relaxation of the optimization step, which allows for tractable decision-making while retaining the favourable regret guarantee., Comment: Accepted to be published at Elsevier European Journal of Operational Research (EJOR)

Urban on-demand transportation services are booming, in both passenger transportation and the transportation of goods. The types of service differ in timeliness and compensation and, until now, providers operate larger fleets separately for each type of service. While this may ensure sufficient resources for lucrative passenger transportation, the separation also leaves consolidation potentials untapped. In this paper, we propose combining both services in an anticipatory way that ensures high passenger service rates while simultaneously transporting a large number of goods. To this end, we introduce a dynamic priority policy that uses a time-dependent percentage of vehicles mainly to serve passengers. To find effective time-dependent parametrizations given a limited number of runtime-expensive simulations, we apply Bayesian Optimization. We show that our anticipatory policy increases revenue and service rates significantly while a myopic combination of service may actually lead to inferior performance compared to using two separate fleets., Working paper series, 2022, H. 6

In this special issue, 23 research papers are published focusing on COVID-19 and operational research solution techniques. First, we detail the process from advertising the call for papers to the point where the best papers are accepted. Then, we provide a summary of each paper focusing on applications, solution techniques and insights for practitioners and policy makers. To provide a holistic view for readers, we have clustered the papers into different groups: transmission, propagation and forecasting, non-pharmaceutical intervention, healthcare network configuration, healthcare resource allocation, hospital operations, vaccine and testing kits, and production and manufacturing. Then, we introduce other possible subjects that can be considered for future research.

Port terminals play a critical role in the context of world trade since they are the main nodes responsible for connecting sea and land transportation. There are several optimization problems arising in port terminals, and those involving berth allocation are among the most important ones. They constitute the first level of terminal planning operations. As a consequence, the corresponding decisions impact all the subsequent operations in the port terminals. Berth allocation decisions are often integrated with quay crane assignment and/or scheduling decisions. However, the quality of these decisions is greatly affected by unpredictable events that may occur frequently. Since 2006, different approaches have been proposed for solving general berth allocation problems under uncertainty. This paper provides an exhaustive survey of the works published in the literature addressing berth allocation and berth allocation and quay cranes assignment/scheduling problems under uncertainty. The publications are classified into three main classes of approaches: proactive, reactive, and proactive/reactive. An overview of the main methodologies proposed, including stochastic programming, robust optimization, fuzzy programming, and deterministic approaches, is provided. The common sources of uncertainty are identified, and the representation of the uncertain parameters is highlighted. The papers are also classified according to the main objectives to be optimized and the solution methods proposed. We identify several research trends, limitations in the current literature and future research directions. Fundação para a Ciência e a Tecnologia published

This paper aims to study a variant of the multi-manned assembly line balancing problem (MALBP), which considers the possibility of multiple workers simultaneously performing different tasks at the same workstation. In most cases it is assumed that task times are deterministic. This paper takes into account possible interferences between workers and deals with the MALBP with task times depending on the number of workers at the station. Different procedures are developed: resolutions on the basis of a mathematical model, two Relax-and-Fix procedures, a heuristic based on solving a partition problem with constraints (named “HEUR_PART”) and a set of other variants of the HEUR_PART procedure. The computational experiments indicate that HEUR_PART and the HEUR_PART_SGL variant are the proposals that perform best. Additionally, we show that they obtain better results than the ones published in the literature.

Copyright © 2022 The Authors. Differences in system boundaries and problem framings are unavoidable in multi-organisational decision-making. Unstructured problems, such as the grand challenges, are characterised by the existence of multiple actors with different perspectives and conflicting interests, and they require a coordinated effort from multiple organisations. Within this context, this paper aims to understand stakeholders’ perceptions of system boundaries and problem framings, and their potential effects on decision-making by systematically comparing different stakeholder groups’ causal maps around the same shared concern. Bridging notions from Operational Research, System Dynamics and Organisational Studies, the comparison is based on a novel type of thematic analysis of Causal Loop Diagrams (CLDs) built with each stakeholder group on their perceptions of a given system. The proposed integrated approach combines qualitative with quantitative analysis, such as the centrality of the variables and the structure of the CLDs. Such CLDs comparison provides an intuitive way to visualise differences and similarities of the thematic clusters of variables, underlining factors influencing the shared concern. This could be considered a starting point for more shared understanding as well as more integrated holistic perceptions of the system and, consequently, a more systemic decision-making. Furthermore, for the sake of replicability, this paper also presents a qualitative participatory System Dynamics modelling process aimed to define the key aspects of a problem for each group of stakeholders to support a collaborative multi-organisational decision-making process. The research is based on the activities carried out for an urban regeneration case study in Thamesmead, London, United Kingdom.

Ever since the times of Henry Ford up to today’s industry 4.0 era, flow-oriented assembly processes, where an assembly line conveys the workpieces from workstation to workstation, are very important for mass-producers in manifold branches of industry. Among the most elementary optimization problems in this context is the assembly line balancing problem, which decides on the division of labor among the stations of an assembly line. This paper surveys the scientific literature on assembly line balancing that has been published since the last major review papers have appeared in 2006 and 2007, respectively. We cover all essential stages of the decision making process: we address novel methods to efficiently gather the relevant (precedence graph) data, review especially new problem variants and models treated in the literature, and survey the most important algorithmic developments. Furthermore, we outline a possible research agenda for the next fifteen years.

This paper studies a machine scheduling problem that minimizes the worst-case total tardiness for unrelated parallel machines with sequence-dependent setup and uncertain processing times. We propose a robust optimization reformulation of the related machine scheduling problem and discuss several important properties of the mathematical model and the reformulation approach. The proposed model generalizes robust parallel machine scheduling problems by including sequence-dependent setup times and ellipsoidal uncertainty sets. Another key contribution of the paper is to show that scheduling problems usually have alternative optimal solutions for the worst-case tardiness objective, whose performance under nominal processing times may vary or vice a versa. This issue has been addressed by studying the Pareto efficient extensions of the proposed robust optimization models to provide solutions that are immune to changes in processing times. A branch-and-price algorithm has been developed to solve realistically sized instances in less than one hour, which a commercial solver cannot achieve. Numerical results show the effectiveness of the proposed approach since realistically sized instances such as (4 machines, 32 jobs) and (150 machines, 300 jobs) can be solved to optimality within the time limit, and the (average) objective function value improvement made by the robust approach can get as high as 56% compared with the (nominal) optimal solutions that ignore uncertainty in problem data.

This paper addresses the two-dimensional bin packing problem with guillotine constraints. The problem requires a set of rectangular items to be cut from larger rectangles, known as bins, while only making use of edge-to-edge (guillotine) cuts. The goal is to minimize the total bin area needed to cut all required items. This paper also addresses variants of the problem which permit 90 ∘ rotation of items and/or a heterogeneous set of bins. A novel heuristic is introduced which is based on the ruin and recreate paradigm combined with a goal-driven approach. When applying the proposed heuristic to benchmark instances from the literature, it outperforms the current state-of-the-art algorithms in terms of solution quality for all variants of the problem considered.

Consumers are increasingly concerned about pollution and are, at least in part, making their purchases accordingly. In this paper, we consider a supply chain where demand depends on the manufacturer’s environmental reputation, an asset that can only be built over time. We assume that this reputation depends on information emanating from the manufacturer itself about its environmental actions and on its objective environmental record when compared to an industry standard. In this paper, we look at the impact of consumers’ environmental concern on the strategies and outcomes of a supply chain. As the retailer has a direct influence on sales through its pricing policy, it seem more realistic to take a supply chain perspective instead of a single-firm one. Therefore, the contractual arrangement in the supply chain becomes a relevant issue. We model the supply chain as a two-player dynamic game and characterize and compare the equilibrium strategies and outcomes under wholesale-price and revenue-sharing contracts. We analyze the impact of the sharing parameter, the industry pollution standard and consumers’ degree of environmental sensitivity on the results, and in particular, on the region in the parameter space where a revenue-sharing contract is Pareto improving with respect to a wholesale-price contract. Also, we examine whether it is in the best interest of the retailer to behave myopically when setting its price.

Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g. decision making, image processing, machine learning for both classification, and regression. Tools for measure identification have been built. In short, as non-additive measures are more general than additive ones (i.e., than probabilities), they have better modeling capabilities allowing to model situations and problems that cannot be modeled by the latter. See e.g. the application of non-additive measures and the Choquet integral to model both Ellsberg paradox and Allais paradox. Because of that, there is an increasing need to analyze non-additive measures. The need for distances and similarities to compare them is no exception. Some work has been done for defining $f$-divergence for them. In this work we tackle the problem of defining the optimal transport problem for non-additive measures. Distances for pairs of probability distributions based on the optimal transport are extremely used in practical applications, and they are being studied extensively for their mathematical properties. We consider that it is necessary to provide appropriate definitions with a similar flavour, and that generalize the standard ones, for non-additive measures. We provide definitions based on the M\"obius transform, but also based on the $(\max, +)$-transform that we consider that has some advantages. We will discuss in this paper the problems that arise to define the transport problem for non-additive measures, and discuss ways to solve them. In this paper we provide the definitions of the optimal transport problem, and prove some properties.

Summarization: This paper presents a Cumulative Unmanned Aerial Vehicle Routing Problem (CUAVRP) approach to optimize Humanitarian Coverage Path Planning (HCPP). Coverage path planning consists of finding the route which covers every point of a certain area of interest. This paper considers a Search & Rescue mission, using a homogeneous fleet of Unmanned Aerial Vehicles (UAVs). In this scenario, the objective is to minimize the sum of arrival times at all points of the area of interest, thus, completing the search with minimum latency. The HCPP problem is transformed into a Vehicle Routing Problem by using an approximate cellular decomposition technique to discretize the area into a grid, where the rectangles represent the UAV sensor’s field of view. The center points of the formed rectangles, become the nodes used for a UAV routing problem. This approach uses the objective of minimizing the sum of arrival times at customers, found in the Cumulative Capacitated Vehicle Routing Problem (CCVRP), adjusted for the Search & Rescue Coverage Path Planning using UAVs. The Min-max objective is also implemented and tested. Three versions of a Parallel Weighted Greedy Randomized Adaptive Search Procedure - Variable Neighborhood Decent (GRASP-VND) algorithm is implemented to solve the Cumulative UAV Routing Problem for Humanitarian Coverage Path Planning. Presented on: European Journal of Operational Research

This paper focuses on the variance risk premium of project returns and its impacts on the real options to expand and to abandon a project. Variance risk premium measures the hedging costs associated with the time-varying variance of the returns. We find that the variance risk premium increases the real option value to expand and to abandon a project. Hence, the variance premium delays both abandoning and expanding the project. Our setting also enables us to study the multi-stage decisions with real options under the variance risk premium. For example, we consider when there is an abandonment or a re-expansion add-on attached to an expansion project, which is a reminiscence of how our framework facilitates modeling compound real option structures in the presence of the variance risk premium. We present two applications of our models that involve Ford Motor company and battery storage investments for electricity distribution networks. These cases demonstrate how the proposed framework in this paper can be applied to real world decisions, and, moreover, they establish a baseline for how much decisions can be improved when variance risk premium is included in the modeling.

This paper considers scheduling in a two-machine flow shop to maximize the total early work subject to a common due date. The early work of a job is a parameter defined as the total amount of the job that is processed before the specified due date. We mainly focus on the unweighted model in this paper, and propose a dynamic programming approach running in O ( n 2 d 2 ) time (compared with the previous result in O ( n 2 d 4 ) time for the weighted case discussed in the literature). Then we analyse the problem from an approximation point of view, in which we first show that Johnson’s algorithm, one of the most classical ones in flow shop scheduling, can only achieve the worst performance ratio for the considered problem (although it is an optimal one for makespan minimization). With the motivation of proposing better approximation algorithms, we further design a fully polynomial time approximation scheme (FPTAS). Finally, we point out that the approximation results also work for the weighted model - if a specific constraint is satisfied.

In this paper, we study an inventory model for an omnichannel retailer, that is, a retailer that sells items both via brick-and-mortar stores and online. Online items are delivered from a warehouse, which also replenishes the stores. When the inventory in a store drops below a certain level, the retailer offers customers a discount for purchasing online. In this way, the retailer can save items for customers who need the item immediately and thus avoid lost sales. For this model, we propose an approximation method for calculating the average inventory costs for one store and one warehouse and an optimization procedure for the case of more stores. Using extensive numerical experiments, we show that the approximations are very close to the performance measured via simulation. Finally, we show that by adopting the discounts policy proposed in this paper, the retailer can reduce its total cost, on average, by 8.5% compared to the no-discounts policy.

This paper introduces a complex real-world problem on a large scale that combines the split delivery heterogeneous vehicle routing problem with three-dimensional loading and considers new routing and loading constraints. The problem aims to find a set of routes with minimum transportation cost by satisfying the demand of all customers and loading constraints. We propose a column generation-based heuristic algorithm that employs three heuristic algorithms to solve the subproblem and a hybrid algorithm for loading. Computational experiments on the literature instances indicate that the proposed algorithm can produce very near solutions to the literature algorithm's solutions in significantly shorter running times. This paper introduces real-world instances with 230 to 850 customers, several times larger than the existing benchmarks. The results of the proposed algorithm for real-world instances are effective, and compared to the current situation, it leads to a reduction of 20% in the average total cost of transportation. Also, the average number of vehicles is reduced by 36%.

The maximum weighted submatrix coverage problem is a recently introduced problem with applications in data mining. It is concerned with selecting K submatrices of a given numerical matrix such that the sum of the matrix-entries, which occur in at least one of the selected submatrices, is maximized. In the paper introducing the problem, a problem-specific constraint programming approach was developed and embedded in a large neighborhood-search to obtain a heuristic. A compact integer linear programming formulation was also presented, but deemed inefficient due to its size. In this paper, we introduce new integer linear programming formulations for the problem, one of them is based on Benders decomposition. The obtained Benders decomposition-based formulation has a nice combinatorial structure, i.e., there is no need to solve linear programs to separate Benders cuts. We present preprocessing procedures and valid inequalities for all formulations. We also develop a greedy randomized adaptive search procedure for the problem, which is enhanced with a local search. A computational study using the instances from literature is done to evaluate the effectiveness of our new approaches. Our algorithms manage to find improved primal solutions for ten out of 17 real-world instances, and optimality is proven for two real-world instances. Moreover, for over 700 of 1617 large-scale synthetic instances, our algorithms find improved primal solutions compared to the heuristics from the literature.

In this paper, we extend the concept of quasidifferential to a new notion called semi-quasidifferential. This generalization is motivated by the convexificator notion. Some important properties of semi-quasidifferentials are established. The relationship between semi-quasidifferentials and the Clarke subdifferential is studied, and a mean value theorem in terms of semi-quasidifferentials is proved. It is shown that this notion is helpful to investigate nonsmooth optimization problems even when the objective and/or constraint functions are discontinuous. Considering a multiobjective optimization problem, a characterization of some cones related to the feasible set is provided. They are used for deriving necessary and sufficient optimality conditions. We close the paper by obtaining optimality conditions in multiobjective optimization in terms of semi-quasidifferentials. Some outcomes of the current work generalize the related results existing in the literature.