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Night deliveries are increasingly used by motor carriers to cut costs, but many carriers struggle to secure night truck drivers because many drivers dislike night driving. Monetary incentives are offered to drivers to accept night loads, but the incentive system currently used in practice is inefficient, as it not only pays more incentives than necessary but also does not incentivize the right drivers, both of which increase costs. This paper develops a new incentive system that allows carriers to secure night drivers at lower costs. Based on the interviews conducted with seven motor carriers, as well as the analysis of large night delivery data, we propose a bi-level programming approach that (1) generates a unique incentive for each driver based on his/her night driving performance, and (2) implicitly aligns the incentive paid to each driver with his/her reservation price. Simulation experiments conducted with real-world data showed that by using our approach carriers can not only avoid over-incentivizing drivers, but also (1) incentive only the right set of drivers who can bring cost savings and (2) encourage other drivers to improve night driving. Results also showed that our approach may give cost savings of up to 2.5% over the current system. [ABSTRACT FROM AUTHOR]

In this paper, we take a mechanism design approach to optimal assignment problems with asymmetrically informed buyers. In addition, the surplus generated by an assignment of a buyer to a seller may be adversely affected by externalities generated by other assignments. The problem is complicated by several factors. Buyers know their own valuations and externality costs but do not know this same information for other buyers. Buyers also receive private signals correlated with the state and, consequently, the implementation problem exhibits interdependent valuations. This precludes a naive application of the VCG mechanism and to overcome this interdependency problem, we construct a two-stage mechanism. In the first stage, we exploit correlation in the firms signals about the state to induce truthful reporting of observed signals. Given that buyers are honest in stage 1, we then use a VCG-like mechanism in stage 2 that induces honest reporting of valuation and externality functions. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel solution to address the current challenges related to charging an Electric Vehicle (EV). The Power on the Go: Single-drop and Double-drop problems allow an EV to be charged at a convenient location, where a service vehicle (drone), which is launched from a nearby charging station, can bring a compatible power bank at the request of the driver through an app. The objective is to reduce the cumulative wait time between service requests and the start of charging. We present mathematical formulations and two order-first split-second-based heuristic approaches for both problems. While the mathematical formulations can generate optimal solutions for small instances in a reasonable amount of time, the heuristics are fast and perform very well, with gaps < 5% for up to 20 node instances. Moreover, the formulations highlight the mean savings in wait time (29.37%) when the power bank can charge two EVs consecutively before a replacement is needed. The implications of the proposed model can be extensive, as we seek to overcome the availability and technological challenges of EV charging while advocating its adoption. [ABSTRACT FROM AUTHOR]

We propose to use information regarding the fab's future state for Overhead Hoist Transport (OHT) dispatching, which is named as 'predictive dispatching' in this paper. Unlike conventional dispatching methods, two kinds of information are additionally considered in our proposed methods: the expected arrival time of jobs in the near future and the time needed for occupied vehicles to become idle. We firstly develop Basic Predictive Dispatching (BPD) under the assumption that job arrival time prediction is error-free. We demonstrate that BPD consistently surpasses conventional benchmark dispatching methods, even when job arrival time prediction contains a certain level of error. However, as the level of error increases, the performance of BPD deteriorates. To improve BPD's performance in the environment with prediction error, we take the certainty level of job arrival time prediction into consideration in our second method called Certainty Weighted Predictive Dispatching (CWPD). Both BPD and CWPD formulate the OHT dispatching problem as a linear assignment problem, but two different matching cost functions are employed separately. By conducting experiments on a sample semiconductor fab, we validate the effectiveness of our proposed approaches. The superiority of CWPD over BPD in the environment with prediction error is also verified. [ABSTRACT FROM AUTHOR]

Seminars are offered to students for education in various disciplines. The seminars may be limited in terms of the maximum number of participants, e.g., to have lively interactions. Due to capacity limitations, those seminars are often offered several times to serve the students' demands. Still, some seminars are more popular than others and it may not be possible to grant access to all interested students due to capacity limitations. In this paper, a simple, but efficient random selection using key objectives (SEKO) assignment strategy is proposed which achieves the following goals: (i) efficiency by utilizing all available seminar places, (ii) satisfying all students by trying to assign at least one seminar to each student, and (iii) fairness by considering the number of assigned seminars per student. We formulate various theoretical optimization models using integer linear programming (ILP) and compare their solutions to the SEKO assignment based on a real-world data set. The real-world data set is also used as the basis for generating large data sets to investigate the scalability in terms of demand and number of seminars. Furthermore, the first-in first-out (FIFO) assignment, as a typical implementation of fair assignments in practice, is compared to SEKO in terms of utilization and fairness. The results show that the FIFO assignment suffers in realworld situations regarding fairness, while the SEKO assignment is close to the optimum and scales regarding computational time in contrast to the ILP. [ABSTRACT FROM AUTHOR]

Jacobi's results on the computation of the order and of the normal forms of a differential system are translated in the formalism of differential algebra. In the quasi-regular case, we give complete proofs according to Jacobi's arguments. The main result is Jacobi's bound, still conjectural in the general case: the order of a differential system P 1 , ... , P n is not greater than the maximum O of the sums ∑ i = 1 n a i , σ (i) , for all permutations σ of the indices, where a i , j : = ord x j P i , viz. the tropical determinant of the matrix (a i , j) . The order is precisely equal to O iff Jacobi's truncated determinant does not vanish. Jacobi also gave a polynomial time algorithm to compute O , similar to Kuhn's "Hungarian method" and some variants of shortest path algorithms, related to the computation of integers ℓ i such that a normal form may be obtained, in the generic case, by differentiating ℓ i times equation P i . Fundamental results about changes of orderings and the various normal forms a system may have, including differential resolvents, are also provided. [ABSTRACT FROM AUTHOR]

Due to present condition, the expenses of allocating a job to a specific person or scheduling transport with a precise value may result in ambiguity. To deal with this, neutrosophic sets which is an extended form of fuzzy sets, appear alongside membership, non-membership and indeterminacy. The assignment problem in a trapezoidal neutrosophic environment with cost as the trapezoidal neutrosophic numbers is discussed in this work. The paper's motive is to convert the trapezoidal neutrosophic numbers into new interval arithmetic form and the efficiency of the same is shown by comparing the existing method with other assignment models using examples. [ABSTRACT FROM AUTHOR]

Great efforts have been made to develop precision medicine-based treatments using machine learning. In this field, where the goal is to provide the optimal treatment for each patient based on his/her medical history and genomic characteristics, it is not sufficient to make excellent predictions. The challenge is to understand and trust the model's decisions while also being able to easily implement it. However, one of the issues with machine learning algorithms—particularly deep learning—is their lack of interpretability. This review compares six different machine learning methods to provide guidance for defining interpretability by focusing on accuracy, multi-omics capability, explainability and implementability. Our selection of algorithms includes tree-, regression- and kernel-based methods, which we selected for their ease of interpretation for the clinician. We also included two novel explainable methods in the comparison. No significant differences in accuracy were observed when comparing the methods, but an improvement was observed when using gene expression instead of mutational status as input for these methods. We concentrated on the current intriguing challenge: model comprehension and ease of use. Our comparison suggests that the tree-based methods are the most interpretable of those tested. [ABSTRACT FROM AUTHOR]

The Assignment Problem (AP) can be stated as n activities to be assigned to n resources in such a way that the overall cost of assignment is minimized and each activity is assigned to one and only one resource. In real-life, the parameters of the AP are presented as uncertain numbers due to the lack of knowledge, experiences or any other (internal or external) factor. In this paper, the AP is considered under intuitionistic triangular fuzzy number and solved by the novel constructive heuristic Dhouib-Matrix-AP1 (DM-AP1) with a time complexity of O(n). Actually, this paper presents the first enhancement of the novel heuristic DM-AP1 to solve the AP under intuitionistic triangular fuzzy environment. DM-AP1 is composed of three simple steps: computing the total cost, selecting the highest value and finding the minimal element. These steps are repeated in n iterations with the use of a standard deviation statistical metric. Two case studies of AP under intuitionistic triangular fuzzy set are taken from the literature and a step-by-step application of the novel DM-AP1 heuristic is presented for more clarification. [ABSTRACT FROM AUTHOR]

The business continuity of services provided by Critical Infrastructures is vital in order to ensure the security, the economy and the public’s health of a nation. Delays and bad recovery strategies after disasters or failures can lead to impairing impacts in terms of injury to people, environmental pollution and loss of time, money and resources. In such a context, the adoption of a spatial Decision Support System (DSS) might play a crucial role in order to help operators to adopt the best recovery strategy in the shortest possible time frame. Current approaches do not consider the problem of assigning an intervention location to a maintenance crew and do not account for the effective time needed for emergency intervention. In this paper we develop a novel spatial multi-criteria DSS methodology for prioritizing repair interventions on power networks. The multi criteria strategy is solved by the adoption of Incomplete Analytic Hierarchy Process (AHP) which computes holistic assignment costs as the result of the combination of multiple and possibly conflicting metrics of cost. Then, we use the holistic costs as the basis for a task assignment phase that is based on the Hungarian algorithm. The proposed strategy has been implemented as a module in the Decision Support System, namely Critical Infrastructure Protection Risk Analysis and Forecast (CIPCast), whose outputs are represented on a web-based Geographic Information System (GIS) platform. The effectiveness of the proposed multi-criteria strategy has been validated via a real case study on the Rome City electrical distribution network.

An optimal configuration method of simulation parameters, including the solver and step size of each sub-model, is proposed to realize real-time virtual simulation. The content of the presented study is threefold: firstly, the simulation requirements of three simulation modes, including Model-Exchange, Co-Simulation, and Hybrid Co-Simulation, are analyzed; secondly, the mathematical descriptions of the three simulation configuration problems are constructed, which are classified as an inequality problem and two assignment problems, where the assignment problems are decoupled; finally, an optimal simulation configuration procedure is proposed, where the analysis method and corresponding design methods for configured simulation parameters of each sub-model are given. The configuration method is applied to configure the simulation parameters of an aeroengine control system model with 6 separate components, and the simulation results verify the effectiveness of the proposed method. Specifically, the feasibility analysis results of the sub-models reveal that 4 of them meet the requirements while 2 of them are numerically unstable, which are consistent with the verification results. Meanwhile, after redesigning the infeasible sub-models using the proposed design methods, all the sub-models can meet their simulation requirements. In addition, an optimal configuration of the simulation parameters as well as several comparative configurations are provided, and the simulation results show that the time consumption of the optimal configuration is minimal and it can achieve real-time performance.

This research article contributes to the advancement of the medical and wellness tourism supply chain through the development of a robust mathematical model aimed at optimizing profitability. Rooted in the principles of open innovation, our study delves into innovative avenues to enhance the economic sustainability of the sector. By strategically integrating diverse medical services including health assessments, dental care, beauty treatments, and spa services into the tourism framework, our model captures the intricate interplay among various stakeholders. Our findings underscore the current adequacy of supply chain capacities. However, a substantial challenge emerges in light of an anticipated 30% upswing in tourist volume, which necessitates a corresponding augmentation of medical facilities without commensurate increases in hotel and tourist route capacities. Rectifying this imbalance becomes pivotal in accommodating forthcoming demands effectively. The study identifies several pivotal factors—tourist numbers, medical center capacities, and resultant profits for supply chain participants—as key drivers of overall profitability. Embracing the tenets of open innovation empowers stakeholders to cultivate collaboration, shared knowledge, and collaborative solutions that optimize these factors, thereby fostering the economic viability of the broader ecosystem. This research offers insightful strategies for resource allocation optimization, operational efficiency enhancement, and sustainable economic growth within the realm of medical and wellness tourism. This contribution is intended to resonate with practitioners, policymakers, and industry stakeholders.

In this article, we focus on a periodic resource allocation problem applied on a dynamical system which comes from a biological system. More precisely, we consider a system with N$$ N $$ resources and N$$ N $$ activities, each activity use the allocated resource to evolve up to a given time T>0$$ T>0 $$ where a control (represented by a given permutation) will be applied on the system to reallocate the resources. The goal is to find the optimal control strategies which optimize the cost or the benefit of the system. This problem can be illustrated by an industrial biological application, namely, the optimization of a mixing strategy to enhance the growth rate in a microalgal raceway system. A mixing device, such as a paddle wheel, is considered to control the rearrangement of the depth of the algae cultures, hence the light perceived at each lap. We prove that if the dynamics of the system is periodic, then the period corresponds to one reallocation whatever the order of the involved permutation matrix is. A nonlinear optimization problem for one reallocation process is then introduced. Since N!$$ N! $$ permutations need to be tested in the general case, it can be numerically solved only for a limited number of N$$ N $$. To overcome this difficulty, we introduce a second optimization problem which provides a suboptimal solution of the initial problem, but whose solution can be determined explicitly. A sufficient condition to characterize cases where the two problems have the same solution is given. Some numerical experiments are performed to assess the benefit of optimal strategies in various settings. [ABSTRACT FROM AUTHOR]

Robotic Process Automation has emerged in recent years as an important field by allowing faster and more secure processes through a reduction in the risks or errors but also an increase in the productivity rates of many industries. In this specific paper, the RPA problem aims at assigning financial transactions to software robots to minimize the total costs, induced by the licenses and utilization time. The problem is represented as a bipartite graph and the effective resistance of the graph, which is analog to an electrical circuit, is used to order the edges of a heuristic method to assign the transactions to robots. Preliminary results, based on real data from a bank, are compared to the optimal solution obtained by a linear integer programming model. They show that the heuristic method allows to obtain results quicker and that they are near the optimal solution. [ABSTRACT FROM AUTHOR]

Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We introduce and consider in this work the "discovery" variant of the bipartite matching problem (or assignment problem) where edge weights are not provided as input but must be queried, requiring additional and costly computations. Hence, discovery algorithms are developed aiming to minimize the number of queried weights while providing guarantees on the computed solution. We show in this work the hardness of the underlying problem in general while providing several efficient algorithms that can make use of natural assumptions about the order in which the nodes are processed by the greedy algorithms. Our motivations for exploring this problem stem from finding practical solutions to maximum-weight matching in hypergraphs, a problem recently emerging in the formation of peer-to-peer energy sharing communities. [ABSTRACT FROM AUTHOR]

The assignment problem is one of the core combinatorial optimization problems in the optimization branch, and the theory and applications of fractional programming have made great strides in recent years. Usually, the possible coefficient values of linear fractional programming and real-world problems are frequently only known to the decision in vague or uncertain terms. Hence, it would be more acceptable to interpret the coefficients for as fuzzy numerical information. In this paper, a fuzzy bi-objective fractional assignment (FBOFAP) has been formulated. A problem has been defined. Here, triangular shapes are used to indicate the parameters. The fuzzy problem is turned into a typical crisp problem through α-cut using a fuzzy number and then the compromise solution is generated by fuzzy programming. [ABSTRACT FROM AUTHOR]

Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from everyday activities to large-scale industrial operations. In this study, a MOAP with fuzzy parameters is investigated, and the fuzziness is represented by a Type-2 fuzzy logic system. Because the T2FLS is more efficient in dealing with the uncertainty of a decision-making process, the current problem's many parameters are represented by Type-2 trapezoidal fuzzy numbers (T2TpFNs). T2TpFNs are first reduced to Type-1 fuzzy numbers, then to crisp numbers. Finally, the neutrosophic compromise programming technique (NCPT) is applied to produce a problem compromise solution. A numerical problem is used to demonstrate the validity and applicability of the NCPT for the current MOAP. Furthermore, a comparison of NCPT to other techniques such as FPT and IFPT shows its superiority.

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This paper proposes a probabilistic hill-climbing algorithm, called PH, for the single-source transportation problem (STP). PH is a tree search algorithm in which each node contains an assignment problem (AP) transformed from the STP being solved. The transformation converts each source's product units into product lots; a product lot equals multiple product units. The AP aims to find the optimal assignment of product lots to destinations to minimize the total assignment cost. PH uses the Hungarian method to find the optimal solution of the AP in every node, which is a solution of the STP. For the AP of the root node (as the initial current node), the number of each source's product lots is set to be small enough to guarantee the generation of a feasible solution for the STP. To generate every subsequent level, the current node is branched into multiple child nodes, in which the number of child nodes equals the number of sources in the STP. The AP of each child node is modified from the AP of the current node by adding one more product lot into a specific different source. Consequently, each child node provides a solution that is better than or the same as the current node's solution; however, some child nodes' solutions may be infeasible for the STP due to the insufficiency of a source's capacity. If all of the child nodes cannot find a better feasible solution than the current node's solution, PH stops its procedure. To diversify the search, PH selects one of the child nodes as the new current node in a probabilistic way, instead of always selecting the best child node. The experiment's results in this paper reveal the performance of the three variants of PH. [ABSTRACT FROM AUTHOR]

First- and last-mile trips are becoming increasingly expensive and detrimental to the environment, especially within dense cities. Thus, new micro-mobility transportation modes such as e-scooter sharing systems have been introduced to fill the gaps in the transportation network. Furthermore, some recent studies examined e-scooters as a green option from the standpoint of environmental sustainability. Currently, e-scooter charging is conducted by competitive freelancers who do not consider the negative environmental impact resulting from not optimizing the fuel efficiency of their charging trips. Several disputes have been recorded among freelance chargers, especially when simultaneously arriving at an e-scooters location. The paper aims to find the optimal tours for all chargers to pick up e-scooters in the form of routes, such that each route contains one charger, and each e-scooter is visited only once by the set of routes, which are typically called an E-Scooter-Chargers Allocation (ESCA) solution. This study develops a mathematical model for the assignment of e-scooters to freelance chargers and adapts a simulated annealing metaheuristic to determine a near-optimal solution. We evaluated the proposed approach using real-world instances and a benchmark-simulated dataset. Moreover, we compare the proposed model benchmark dataset to the baseline (i.e., state-of-practice). The results show a reduction of approximately 61–79% in the total distance traveled, leading to shorter charging trips. [ABSTRACT FROM AUTHOR]

Under just-in-time production, this paper studies a single machine common due-window (denoted by CONW) assignment scheduling problem with position-dependent weights and resource allocations. A job's actual processing time can be determined by the resource assigned to the job. A resource allocation model is divided into linear and convex resource allocations. Under the linear and convex resource allocation models, our goal is to find an optimal due-window location, job sequence and resource allocation. We prove that the weighted sum of scheduling cost (including general earliness–tardiness penalties with positional-dependent weights) and resource consumption cost minimization is polynomially solvable. In addition, under the convex resource allocation, we show that scheduling (resp. resource consumption) cost minimization is solvable in polynomial time subject to the resource consumption (resp. scheduling) cost being bounded. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel solution to address the current challenges related to charging an Electric Vehicle (EV). The Power on the Go: Single-drop and Double-drop problems allow an EV to be charged at a convenient location, where a service vehicle (drone), which is launched from a nearby charging station, can bring a compatible power bank at the request of the driver through an app. The objective is to reduce the cumulative wait time between service requests and the start of charging. We present mathematical formulations and two order-first split-second-based heuristic approaches for both problems. While the mathematical formulations can generate optimal solutions for small instances in a reasonable amount of time, the heuristics are fast and perform very well, with gaps < 5% for up to 20 node instances. Moreover, the formulations highlight the mean savings in wait time (29.37%) when the power bank can charge two EVs consecutively before a replacement is needed. The implications of the proposed model can be extensive, as we seek to overcome the availability and technological challenges of EV charging while advocating its adoption.

A central stability notion for allocation problems when there are private endowments is core: no coalition should be able to block the allocation. But, for an exchange economy of discrete resources, core can be empty. An alternative stability axiom is the bargaining set à la Aumann and Maschler (Advances in game theory, Annals of mathematics studies, Princeton University Press, Princeton, pp 443–476, 1964): a blocking by a coalition is justified only if there is no counter-objection to it and an allocation is in the bargaining set if there does not exist a justified blocking. Allowing for weak preferences, we prove that any allocation obtained by the well-known Top Trading Cycles class is in the bargaining set, but not all allocations in the bargaining set can be obtained by this class. [ABSTRACT FROM AUTHOR]

The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution, and scheduling problems. Showing such correlations is one of the aims of this paper. For some of the derived problems having exponential time complexity, the question arises of their solvability for larger instances. Instead of the traditional approach based on the use of approximate or stochastic heuristic methods, we focus here on the direct use of mixed integer programming models in the GAMS environment, which is now capable of solving instances much larger than in the past and does not require complex parameter settings or statistical evaluation of the results as in the case of stochastic heuristics because the computational core of software tools, nested in GAMS, is deterministic in nature. The source codes presented may be an aid because this tool is not yet as well known as the MATLAB Optimisation Toolbox. Benchmarks of the permutation flow shop scheduling problem with the informally derived MIP model and the traveling salesman problem are used to present the limits of the software's applicability. [ABSTRACT FROM AUTHOR]

We focus on a single-machine scheduling problem with common and slack due-window assignment methods. Both the job sequence and due-windows are decision variables to be determined by the decision maker. We consider the following performance criterion: the total weighted number of early and late jobs plus the total weighted of earliness, tardiness and due-window assignment cost, where the weights depend on the position in which a job is scheduled. Some properties are established, and it is shown that the problem can be solved in O (n 5) time, where n is the number of jobs. The extensions of the model are to cases of general position-dependent processing times and time-dependent processing times. [ABSTRACT FROM AUTHOR]

In this paper, we study the general restricted inverse assignment problems, in which we can only change the costs of some specific edges of an assignment problem as less as possible, so that a given assignment becomes the optimal one. Under l 1 norm, we formulate this problem as a linear programming. Then we mainly consider two cases. For the case when the specific edges are only belong to the given assignment, we show that this problem can be reduced to some variations of the minimum cost flow problems. For the case when every specific edge does not belong to the given assignment, we show that this problem can be solved by a minimum cost circulation problem. In both cases, we present some combinatorial algorithms which are strongly polynomial. We also study this problem under the l ∞ norm. We propose a binary search algorithm and prove that the optimal solution can be obtained in polynomial time. [ABSTRACT FROM AUTHOR]

Recently, many approaches were proposed to support human resource management in finding the best human resources for available jobs. However, existing solutions do not effectively evaluate employees’ skills, or they do only partially, neither provide mechanisms to describe subjects’ skills and desiderata. To face this issue, this paper proposes a decision model for assisting human resource management in effectively evaluating the degree of mutual satisfaction in job-employee assignments. In particular, the decision model has been devised with the following core characteristics: i) employees’ skills are modeled by combining hard skills (e.g.: academic training and competencies) and soft skills (e.g.: socio-relational experiences); ii) employees’ soft skills are self-evaluated, giving importance not so much to experiences possessed but rather how such skills have been applied over time; iii) employees and managers can self-evaluate their preferences to enable the achievement of the optimal allocation by maximizing the global mutual satisfaction iv) partial matches between characteristics and desires of both employees and jobs are measured through a set of tailored fuzzy metrics. The proposed decision model has been validated in a real case to support the allocation of newly hired employees among open job positions in a Public Administration. Results showed an adequate ability of the proposed model both to support the description of employees, skills, jobs and preferences, and to suggest the best allocation maximizing the global mutual satisfaction. Summarizing, a decision model for human resource management with innovative characteristics is proposed and used to support decisions for a real allocation problem.

Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from everyday activities to large-scale industrial operations. In this study, a MOAP with fuzzy parameters is investigated, and the fuzziness is represented by a Type-2 fuzzy logic system. Because the T2FLS is more efficient in dealing with the uncertainty of a decision-making process, the current problem's many parameters are represented by Type-2 trapezoidal fuzzy numbers (T2TpFNs). T2TpFNs are first reduced to Type-1 fuzzy numbers, then to crisp numbers. Finally, the neutrosophic compromise programming technique (NCPT) is applied to produce a problem compromise solution. A numerical problem is used to demonstrate the validity and applicability of the NCPT for the current MOAP. Furthermore, a comparison of NCPT to other techniques such as FPT and IFPT shows its superiority. [ABSTRACT FROM AUTHOR]

We generalize the well-known primal-dual algorithm proposed by Chambolle and Pock for saddle point problems and relax the condition for ensuring its convergence. The relaxed convergenceguaranteeing condition is effective for the generic convex setting of saddle point problems, and we show by the canonical convex programming problem with linear equality constraints that the relaxed condition is optimal. It also allows us to discern larger step sizes for the resulting subproblems, and thus provides a simple and universal way to improve numerical performance of the original primal-dual algorithm. In addition, we present a structure-exploring heuristic to further relax the convergence-guaranteeing condition for some specific saddle point problems, which could yield much larger step sizes and hence significantly better performance. Effectiveness of this heuristic is numerically illustrated by the classic assignment problem. [ABSTRACT FROM AUTHOR]

Assigning technicians to maintenance tasks at an aircraft maintenance base is challenging and needs to consider technician licences, fairness and such operational constraints as hangar capacity and work shifts. We formulate the problem as a bi-objective optimisation model, which minimises total cost while simultaneously achieving fairness in workload allocation among different technicians. A tabu-based heuristic algorithm is developed to obtain Pareto efficient solutions. The algorithm is shown to be effective through comparison with CPLEX. A case study from a major Chinese airline demonstrates that our optimisation-based approach is applicable and beneficial to the practice. Managerial issues on maintenance workforce management are examined as well. The results show that training technicians and upgrading their licences may not be better off, and increasing the number of technicians has both favourable and unfavourable effects. [ABSTRACT FROM PUBLISHER]

Abstract This article is concerned with the cost and time-effective scheduling of financial auditors with integer linear programming. The schedule optimization considers 13 different constraints, staff scarcity, frequent alterations of the input data with the need to minimize the changes in the generated schedule, and scaling issues. The delivered implementation reduced the time to the first schedule from 3 man-days to 1 h and the schedule update time from 1 man-day to 4 min.

In microfinance, with more loans, there is a high risk of increasing overdue loans by overloading the resources available to take actions on the repayment. So, three experiments were conducted to search for a distribution of the loans through the officers available to maximize the probability of recovery. Firstly, the relation between the loan and some characteristics of the officers was analyzed. The results were not that strong with F1 scores between 0 and 0.74, with a lot of variation in the scores of the good predictions. Secondly, the loan is classified as paid/unpaid based on what prediction could result of the analysis of the characteristics of the loan. The Support Vector Machine had potential to be a solution with a F1 score average of 0.625; however, when predicting the unpaid loans, it showed to be random with a score of 0.55. Finally, the experiment focused on segmentation of the overdue loans in different groups, from where it would be possible to know their prioritization. The visualization of three clusters in the data was clear through Principal Component Analysis. To reinforce this good visualization, the final silhouette score was 0.194, which reflects that is a model that can be trusted. This way, an implementation of clustering loans into three groups, and a respective prioritization scale would be the best strategy to organize and assign the loans to maximize recovery. [ABSTRACT FROM AUTHOR]

In a multi-agent system, multi-job assignment is an optimization problem that seeks to minimize total cost. This can be generalized as a complex problem in which several variations of vehicle routing problems are combined, and as an NP-hard problem. The parameters considered include the number of agents and jobs, the loading capacity, the speed of the agents, and the sequence of consecutive positions of jobs. In this study, a deep neural network (DNN) model was developed to solve the job assignment problem in a constant time regardless of the state of the parameters. To generate a large training dataset for the DNN, the planning domain definition language (PDDL) was used to describe the problem, and the optimal solution that was obtained using the PDDL solver was preprocessed into a sample of the dataset. A DNN was constructed by concatenating the fully-connected layers. The assignment solution obtained via DNN inference increased the average traveling time by up to 13% compared with the ground cost. As compared with the ground cost, which required hundreds of seconds, the DNN execution time was constant at approximately 20 ms regardless of the number of agents and jobs. [ABSTRACT FROM AUTHOR]

First, we give a detailed review of two algorithms that solve the minimization case of the assignment problem, the Bertsekas auction algorithm and the Goldberg & Kennedy algorithm. It was previously alluded that both algorithms are equivalent. We give a detailed proof that these algorithms are equivalent. Also, we perform experimental results comparing the performance of three algorithms for the assignment problem: the ϵ -scaling auction algorithm, the Hungarian algorithm and the FlowAssign algorithm. The experiment shows that the auction algorithm still performs and scales better in practice than the other algorithms which are harder to implement and have better theoretical time complexity. [ABSTRACT FROM AUTHOR]

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. We introduce a post-processing scheme in order to deal with rotation, sign and permutation invariance of the MCMC sample. The exact version of the contributed algorithm requires to solve 2 q assignment problems per (retained) MCMC iteration, where q denotes the number of factors of the fitted model. For large numbers of factors two approximate schemes based on simulated annealing are also discussed. We demonstrate that the proposed method leads to interpretable posterior distributions using synthetic and publicly available data from typical factor analytic models as well as mixtures of factor analyzers. An R package is available online at CRAN web-page. [ABSTRACT FROM AUTHOR]

The conventional assignment problem is unable to handle scenarios that may arise due to different working modes of machines leading to multiple cost and time entries corresponding to a job–machine pair. The present article deals with this problem and models it as a multi-choice bi-objective assignment problem, the two objectives being assignment cost and bottleneck time. Two different solution procedures are presented based on the Decision-Maker's (DM's) preference structure. First, when the DM provides his/her preference structure as goals, a solution methodology is proposed using goal programming and its different multi-choice variants. In the second case, when no preference is provided by the DM, a two-step approach is presented that iteratively solves a multi-choice cost-minimizing assignment problem to obtain all Pareto-optimal time–cost pairs and finally, based on the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), a single efficient pair is obtained. The algorithm is successfully implemented using the CPLEX ® optimization package and tested on various test problems. [ABSTRACT FROM AUTHOR]

A polynomial time algorithm for solving the minimum-cost network flow problem has been proposed in this paper. This algorithm is mainly based on the binary representation of capacities; it solves the minimum-cost flow problem in directed graph of n nodes and m directed arcs as a sequence of O(n2) shortest path problems on residual networks. The algorithm runs in O(n2mr) time, where r is the smallest integer greater than or equal to Log2B, and B is the largest arc capacity of the network. A generalization of this proposed algorithm has been also performed in order to solve the minimum-cost flow problem in a directed network subject to non-negative lower bound on the flow vector. A formulation of both the transportation and the assignment problems, as a minimal cost network flow problem has been also performed. A numerical example has been inserted to illustrate the use of the proposed method.

Estimation of solvent entropy from equilibrium molecular dynamics simulations is a long-standing problem in statistical mechanics. In recent years, methods that estimate entropy using k-th nearest neighbours (kNN) have been applied to internal degrees of freedom in biomolecular simulations, and for the rigorous computation of positional-orientational entropy of one and two molecules. The mutual information expansion (MIE) and the maximum information spanning tree (MIST) methods were proposed and used to deal with a large number of non-independent degrees of freedom, providing estimates or bounds on the global entropy, thus complementing the kNN method. The application of the combination of such methods to solvent molecules appears problematic because of the indistinguishability of molecules and of their symmetric parts. All indistiguishable molecules span the same global conformational volume, making application of MIE and MIST methods difficult. Here, we address the problem of indistinguishability by relabeling water molecules in such a way that each water molecule spans only a local region throughout the simulation. Then, we work out approximations and show how to compute the single-molecule entropy for the system of relabeled molecules. The results suggest that relabeling water molecules is promising for computation of solvation entropy.

The problem of virtual machine placement on physical servers in cloud data centers is considered. The resource management system has a two-level architecture consisting of global and local controllers. Local controllers analyze the state of physical servers on which they are located and determine possible underloading, overloading, and overheating states based on the forecast for the next observation window. The global controller gathers the information from local controllers and start the process of destination server selecting and virtual machines migrating. In this paper we propose to place virtual machines based on the criteria of minimum resource wastage and SLA-violation. The mathematical formulation of the optimization problem is given, which is equivalent to the known main assignment problem in terms of structure, necessary conditions, and the nature of variables. Reducing the assignment problem to a closed transport problem allowed us to effectively solve the problem of multicriteria virtual machine placement in real time. We could significantly increase its dimension compared to heuristic algorithms, which makes it possible to maintain the quality of cloud services in conditions of rapid resource demand growth of data centers. The developed mathematical formulation of the problem and the results of computational experiments can be included in the mathematical software of virtual machine live migration.

Under just-in-time production, this paper studies a single machine common due-window (denoted by CONW) assignment scheduling problem with position-dependent weights and resource allocations. A job’s actual processing time can be determined by the resource assigned to the job. A resource allocation model is divided into linear and convex resource allocations. Under the linear and convex resource allocation models, our goal is to find an optimal due-window location, job sequence and resource allocation. We prove that the weighted sum of scheduling cost (including general earliness–tardiness penalties with positional-dependent weights) and resource consumption cost minimization is polynomially solvable. In addition, under the convex resource allocation, we show that scheduling (resp. resource consumption) cost minimization is solvable in polynomial time subject to the resource consumption (resp. scheduling) cost being bounded.

Assignment problems (AP) are well-known topics in engineering and management science and are used frequently to analyze problems. A linear programming problem form was used in transforming assignment problem for crisp problem and in solving as per Hungarian methodology. Assigning n objects over m objects is an exciting problem that arises in different situations. Here we explore the optimal ways for assigning in n objects over m other objects. Numerous numerical applications are needed in production planning, Sales proportions, airline operators, etc. The existing Hungarian methods and maximized (or minimized) assignment methods have been solved using these methods. Entry details in the cost matrix are not always clear. This parameter is uncertain in many applications, and these uncertain parameters are represented by intervals. To solve interval linear assignment problems, we present interval Hungarian method and interval analysis concept. [ABSTRACT FROM AUTHOR]

Now a days Assignment problems were widely applied in the field of manufacturing sectors, production planning, etc to earn more profit with minimum inventory. Generally Fuzzy Numbers plays a vital role in many decision making problems. Here an optimal solution of the assignment problem had been derived from Hungarian method. The parameters were being given by using Heptagonal fuzzy numbers which are further decomposed into pentagonal fuzzy numbers. The fuzzy numbers were defuzzfied into real numbers by using pascal's graded mean technique. Numerical example had been given to illustrate the solution procedure. [ABSTRACT FROM AUTHOR]

Assignment problems were widely applied in the field of production planning, telecommunication VLSI design, economic etc. Generally Fuzzy Numbers plays a vital role in many decision making problems. Here an optimal solution of the assignment problem had been derived from Hungarian method. The parameters were being given by using pentagonal fuzzy numbers which are further decomposed into triangular fuzzy numbers. The fuzzy numbers were defuzzfied into real numbers by using pascal's graded mean technique. Numerical example had been given to illustrate the solution procedure. [ABSTRACT FROM AUTHOR]

Two-level priority based assignment problem (2PBAP) is an important optimization problem due to the timely delivery requirement in project management. Only four methods with deficiency are available in the literature to solve 2PBAP. In this paper, 2PBAP is reduced to a series of finding the feasible flow in a network with lower and upper arc capacities, and consequently two iterative algorithms are developed to solve 2PBAP. It is proved that both iterative algorithms find the optimal solution to 2PBAP in a strongly polynomial time. Owing to having fully utilized the network flow structural characteristic inherent to 2PBAP, both iterative algorithms have the advantages such as easy implementation on computer, no memory overflow in implementation on computer for large scale instances, high computational efficiency, and easy extension to the priority based assignment problem with priority level more than two, and successfully overcome the deficiency of existing approaches. Computational experiments validate that in terms of computational time, one of our proposed iterative algorithms has higher efficiency than the other, and rivals the existing best approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a collaborative model for the supplier selection for the purchasing activity in the supply chain. The problem addresses a set of firms that try to look for a cost saving configuration to optimise their ordering plans, given a set of suppliers with quantity discounts options. Possible collaborations between firms, modelled as a coalition formation, can be beneficial in the sense that the gathering of their orders generates a cost minimisation regarding the stand-alone situation. We propose the mathematical formulation of firms' collaborative ordering modelled as a cost-dependent assignment problem. The collaborative scenario is viewed as a two independent steps: the first step is based on game-theoretic approach to model possible coalitions of firms and to generate stable coalition structures according to the core concept. Once coalitions are formed, the second step consists mainly on the genetic algorithm is trigged to assign coalitions to shared suppliers. The assignment problem is solved using a specifically designed hybrid genetic algorithm. Experiments, driven on a large test-bed, highlight the effectiveness of the collaboration in handling the ordering activity within the supply chain and the usefulness of hybrid genetic algorithm in solving such supplier selection problems. We show that in all cases the collaborative scenario is more profitable regarding the stand-alone position. The obtained results show that the hybrid genetic algorithm is able to generate good quality solutions in a reasonable run time regarding Cplex results. [ABSTRACT FROM AUTHOR]

This work proposes metric learning for fast similarity-based scene retrieval of unstructured ensembles of trajectory data from large databases. We present a novel representation learning approach using Siamese Metric Learning that approximates a distance preserving low-dimensional representation and that learns to estimate reasonable solutions to the assignment problem. To this end, we employ a Temporal Convolutional Network architecture that we extend with a gating mechanism to enable learning from sparse data, leading to solutions to the assignment problem exhibiting varying degrees of sparsity. Our experimental results on professional soccer tracking data provides insights on learned features and embeddings, as well as on generalization, sensitivity, and network architectural considerations. Our low approximation errors for learned representations and the interactive performance with retrieval times several magnitudes smaller shows that we outperform previous state of the art. [ABSTRACT FROM AUTHOR]

One critical problem in Indonesia's national joint courses program, initiated by the ministry of education and culture of Indonesia, is the lecturer-course assignment problem. Although the lecturer-course assignment problem has been studied widely as part of the education timetabling problem, no existing lecturer-course assignment model suits this circumstance. The new cases in this program are as follows. First, this program is conducted online. Second, the participants are students and lecturers from different universities. Based on this problem, this work proposes a novel lecturer-course assignment model that suits this program. The lecturers' preferred courses and timeslots become hard constraints. The model has three objectives: (1) maximizing the educational quality, (2) maximizing the lecturers' time preference, and (3) minimizing the number of unserved classes. This model is developed by using integer linear programming and optimized by using cloud theory-based simulated annealing. This proposed model is then compared with the four previous lecturers-course assignment models. The first model concerns about minimizing the number of unserved classes, while the second model focuses on maximizing the education quality. The maximum number of classes per course for every lecturer is considered in the third model while balancing the lecturer’s load (teach, research, community service) is the feature of the fourth model. The research concludes that the proposed model is appropriate for lecture-course assignment in Indonesia’s national joint courses program compared to the previous models. Based on the simulation result, the proposed model performs moderately in education quality and several unserved classes. Meanwhile, the proposed model is the best in the timeslot preference aspect by creating a 25% to 28% higher total timeslot score than other previous models. [ABSTRACT FROM AUTHOR]

Problem definition: We consider an intermediary's problem of dynamically matching demand and supply of heterogeneous types in a periodic-review fashion. Specifically, there are two disjoint sets of demand and supply types, and a reward for each possible matching of a demand type and a supply type. In each period, demand and supply of various types arrive in random quantities. The platform decides on the optimal matching policy to maximize the expected total discounted rewards, given that unmatched demand and supply may incur waiting or holding costs, and will be fully or partially carried over to the next period. Academic/practical relevance: The problem is crucial to many intermediaries who manage matchings centrally in a sharing economy. Methodology: We formulate the problem as a dynamic program. We explore the structural properties of the optimal policy and propose heuristic policies. Results: We provide sufficient conditions on matching rewards such that the optimal matching policy follows a priority hierarchy among possible matching pairs. We show that those conditions are satisfied by vertically and unidirectionally horizontally differentiated types, for which quality and distance determine priority, respectively. Managerial implications: The priority property simplifies the matching decision within a period, and the trade-off reduces to a choice between matching in the current period and that in the future. Then the optimal matching policy has a match-down-to structure when considering a specific pair of demand and supply types in the priority hierarchy. [ABSTRACT FROM AUTHOR]