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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]

To address the issue of multiple closed circuits arising from applying the traditional Hungarian algorithm to the travelling salesman problem (TSP), a breaking mechanism was proposed, leading to the development of the Break-Cycle Hungarian Algorithm. By adopting the description method of the assignment problem for modeling the TSP and establishing the conversion relationship between them, it is demonstrated that a sufficient and necessary condition for a feasible solution to the TSP is that the feasible solution of the corresponding assignment problem, combined with auxiliary edges, contains only one cycle. The effectiveness of the algorithm was verified through testing and comparative analysis on six standard travelling salesmen, showing that the improved Hungarian algorithm can effectively solve the TSP across various datasets. [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]

Turkey's Aegean region is a very suitable region for fruit production in terms of climatic conditions and soil characteristics. Fruit and vegetable production in the Aegean region has an important position in terms of Turkey's agricultural economy. The fruit growing sector has a very important place in Turkey's agricultural economy. The aim of the study is to prevent unbalanced fruit production in the Aegean region and to ensure more efficient fruit growing. In the study, it was aimed to assign a balanced production of fruits grown under different conditions in provinces with different characteristics in the Aegean region. For the assignment problem, the conditions of the cities in the Aegean region and the growing conditions of the fruits are considered together. These conditions are altitude, temperature, soil quality, climate, humidity, labor and irrigation. Conditions for fruit production were analyzed with the AHP method and factor weights were calculated. ARAS and Fuzzy Logic methods were used to solve the assignment problem of fruits. These methods enable to reach the result by digitizing the non-computable features of a particular situation. Aydın, Manisa, Denizli and Afyonkarahisar provinces have been proposed, respectively, for the production of figs, grapes, thyme and cherries, which have high industrial value and export income. The study has shown that unbalanced production can be prevented by assigning fruits and vegetables in this way in every region of the country. As a result, the country's agricultural lands will be used effectively and the contribution of agriculture to the national economy will increase. [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]

Objectives . The problem of constructing the characteristics of the difference between test sequences is solved. Its relevance for generating controlled random tests and the complexity of finding measures of difference for symbolic tests are substantiated. The limitations of using the Hamming and Damerau – Levenshtein distances to obtain a measure of the difference between test sets are shown.Methods . Based on the characteristic of the interval used in the theory of the chain of successive events, a new measure of the difference between two symbolic test sets is determined. As a difference measure, the distance AD(Ti, Tk) between the test sets Ti and Tk is calculated using the interval characteristic, which is based on determining independent pairs of same (identical) symbols belonging to two sets and calculating the intervals between them.Results. The combinatorial nature of the calculation of the proposed difference measure for symbolic test sets of an arbitrary alphabet and dimension is shown. An example of calculating this measure for various types of test sets, including such as address test sets, is given. Possible modifications are shown and some properties and limitations are determined. The application of the measure of difference is considered for the case of repeated testing of storage devices based on address sequences pA with even p repetition of addresses. For the case p = 2, mathematical relations are given for calculating the intervals and distances AD(Ti, Tk) for address sequences 2A used for controlled random testing of storage devices. The main attention is paid to binary test sets, when the task of calculating given difference metric is reduced to the classical assignment problem using the Hungarian algorithm. The computational complexity of the Hungarian algorithm is estimated by the relation O(n4). As an alternative to the Hungarian algorithm, an algorithm for calculating the considered difference measure is proposed, the complexity of which is much less and has an estimate equal to O(n2). The experimental studies confirm the effectiveness of the proposed algorithm.Conclusion. The proposed difference measure extends the possibilities of generating test sequences when generating controlled random tests. It is shown that test sets, which are indistinguishable when Hamming distance is used as a measure of difference, have different values of AD(Ti, Tk) that allows to make more accurate classification of randomly generated sets as candidates for test sets.

The optimal strategy selection is an influential factor to enhance the efficiency of land reclamation projects. On the other hand, the process of desertification of the land during environmental degradation is the consequence of the interaction between various factors that make it challenging to select appropriate solutions. Therefore, this study aimed to provide systematic optimization strategies in the form of a group decision-making model in the Yazd-Khezrabad plain. The important strategies were identified using the Delphi model. Then, the alternative initial ranking was formed by Cook and Seiford method framework using the vote taken from the decision makers on strategies. Finally, by estimating the linear distance of each option and including the matrix of the intervals, the last priority of the strategies was obtained from solving the assignment problem. The results indicated that the strategies of "prevent land use inappropriate change" (A18) and "the regeneration of vegetation cover" (A23) with Value=1 and Reduced Cost=0, were identified as the most important combating-desertification strategies in the region, respectively. The results of this study help desert managers to utilize limited facilities and capital dedicated to controlling the desertification process efficiently and effectively.

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]