Assignment Problem Research Papers - Academia.edu (original) (raw)

2025, Reno: University of Nevada

Abstract—With the growth of the Internet, Internet Service Providers (ISPs) try to meet the increasing traffic demand with new technology and improved utilization of existing resources. Routing of data packets can affect network utilization. Packets are sent along network paths from source to destination following a protocol. Open Shortest Path First (OSPF) is the most commonly used intra-domain Internet routing protocol (IRP). Traffic flow is routed along shortest paths, splitting flow at nodes with several outgoing links on a ...

2025, Lecture Notes in Computer Science

We investigate the problem of enumerating schedules, consisting of course-section assignments, in increasing order of the number of conflicts they contain. We define the problem formally, and then present an algorithm that systematically enumerates solutions for it. The algorithm uses backtracking to perform a depth-first search of the implicit search space defined by the problem, pruning the search space when possible. We derive a mathematical formula for the algorithm's average-case time complexity using a probabilistic approach, and also give a brief overview of its implementation in a WEB application.

2025

Assumption 1 can be made with a loss of (1+ )-factor in the competitive ratio. If pi′,j pi,j ≥ m for some j ∈ J, i, i′ ∈Mj , we can change pi′,j to∞. If the job j is assigned to i′ in the optimum solution, we assign it to the machine i∗ with the minimum pi∗,j instead. Thus, the processing time of j is decreased by at least a factor of m . We apply the operation for all violations of the assumption. Then the makespan of a machine i will be increased by at most (m−1)T m/ ≤ T . This holds since the total processing time of machines other than i in the optimum solution is at most (m − 1)T . We also remark the procedure that guarantees the assumption can run online, as jobs are handled separately in the procedure.

2025

Within a cross-dock, the assignment of trucks to dock-doors and the scheduling of trucks to be processed are two major operational decisions. Conventionally, assignment and scheduling decisions are made sequentially. However, solving the two problems sequentially can lead to sub-optimal solutions because the objectives of the two problems are in conflict with each other. To gain further insights, we create an integrated model which is capable of simultaneously scheduling and assigning trucks at cross-docks. We contrast the integrated model with a sequential model which first schedules trucks for processing and then assigns them to dock-doors. Experiments demonstrate that the integrated model can produce superior solutions, despite that it is computationally more expensive. concern the use of a temporary storage area and the determination of the amount of personnel and equipment that need to be available at the cross-dock. At the operational level, the assignment of trucks to dock-doors and the scheduling of trucks to be processed at the dock-doors are the two major decisions. In the assignment problem, trucks are assigned to specific dock-doors with the objective to minimize the internal travel distances within the facility . This is an important objective because cross-docks can be large with significant distances between dock-doors. The reduction of travel distances has a positive impact on productivity by reducing labor and equipment usage, and it increases customer service by reducing the time required to complete the transshipment processes [3]. The assignment of trucks to dock-doors can also be done at a tactical level. In such a case, all trucks originating from or destined to certain locations are assigned to the same dock-door throughout the tactical planning period. In this paper, we only refer to assignment decisions at the operational level. Cross-dock scheduling involves the sequencing of trucks for processing when the number of trucks is larger than the number of dock-doors. In contrast to the assignment problem, internal travel distances within the cross-dock are not considered in the scheduling problem. Schedules can be created with the objective to minimize delayed shipments [6], lost shipments [17], makespan [2], [8], [21], [25], temporary storage [12], temporary storage and tardiness of outbound trucks [4], or to maximize throughput [18]. The scheduling of inbound and outbound trucks without considering the assignment of trucks to dock-doors would suffice for small cross-dock facilities. This is because the travel times between dock-doors are small. Consequently, the sum of the travel distances from solutions to the assignment problem might not differ much compared to the total travel distance when trucks are assigned to dock-doors on a first-come-first-assigned basis. However, in larger cross-dock facilities with a high truck-to-dock-door ratio, it could be beneficial to solve the scheduling and assignment problem of trucks in an integrated manner. By doing so, inbound and outbound truck pairs can be docked closer to each other which leads to lower internal travel distances without compromising scheduling objectives. Scheduling and assignment problems have mostly been tackled sequentially within the cross-docking context because of the inherent complexity in each of the two problems. However, significant gains may be realized by integrating both problems. We develop two models to evaluate the differences between solving the integrated scheduling and assignment problem versus the sequential approach. The first model considers the scheduling and assignment problem in an integrated manner. While, the second model first schedules inbound and outbound trucks and then assigns them to dock-doors. Both models aim to minimize internal travel distances within the cross-dock, delays of outbound trucks, and usage of temporary storage. In addition, we compare both models extensively on randomly generated instances to gain insights into the trade-offs between the integrated and sequential model.

2025

Orthogonal Variable Spreading Factor (OVSF) CDMA code consists of an infinite number of codewords with variable rates, in contrast to the conventional orthogonal fixed-spreadingfactor CDMA code. Thus, it provides a means of supporting of variable rate data service at low hardware cost. However, assigning OVSF-CDMA codes to wireless ad hoc nodes posts a new challenge since not every pair of OVSF-CDMA codewords are orthogonal to each other. In an OVSF-CDMA wireless ad hoc network, a code assignment has to be conflict-free, i.e., two nodes can be assigned the same codeword or two non-orthogonal codewords if and only if their transmission will not interfere with each other. The throughput (resp., bottleneck) of a code assignment is the sum (resp., minimum) of the rates of the assigned codewords. The maxthroughput (resp., max-bottleneck) conflict-free code assignment problem seeks a conflict-free code assignment which achieves the maximum throughput (resp., bottleneck). In this paper, we present several efficient methods for conflict-free code assignment in OVSF-CDMA wireless ad hoc networks. Each method is proved to be either a constant-approximation for max-throughput conflict-free code assignment problem, or a constant-approximation for max-bottleneck conflictfree code assignment problem, or constant-approximations for both problems simultaneously.

2025, International Mathematics Research Notices

Z. Rudnick and P. Sarnak have proved that the pair correlation for the fractional parts of n 2 α is Poissonian for almost all α. However, they were not able to find a specific α for which it holds. We show that the problem is related to the problem of determining the number of (a, b, r) ∈ N 3 such that a ≤ M , b ≤ N , r ≤ K and pab ≡ r(q) for p and q coprime. With suitable assumptions on the relative size of K, M , N and q one should expect there to be KM N/q such triples asymptotically and we will show that this holds on average. as N → ∞ uniformly in M , K, q and ρ. The rate of convergence may depend on η, δ, C 1 and C 2 . Conjecture 1.2 has applications to the pair correlation problem at hand. We will show that:

2025, arXiv (Cornell University)

2025, International Mathematics Research Notices

2025, ACTES du Congrès International de l'Arganier

This contribution aims to highlight the cultural and social par-ticularity of the Argan forest in some areas of the Western An-ti-Atlas. In this regard, considers a set of cultural and social patterns, where knowledge, cultural practices,... more

2025, Graph-Theoretic Concepts in Computer Science

In this paper we use arc tolerances, instead of arc costs, to improve Branch-and-Bound type algorithms for the Asymmetric Traveling Salesman Problem (ATSP). We derive new tighter lower bounds based on exact and approximate bottleneck upper tolerance values of the Assignment Problem (AP). It is shown that branching by tolerances provides a more rational branching process than branching by costs. Among others, we show that branching on an arc with the bottleneck upper tolerance value is the best choice, while such an arc appears quite often in a shortest cycle of the current AP relaxation. This fact shows why branching on shortest cycles was always found as a best choice. Computational experiments confirm our theoretical results.

2025

We present a branch and cut algorithm that yields in finite time, a globally -optimal solution (with respect to feasibility and optimality) of the nonconvex quadratically constrained quadratic programming problem. The idea is to estimate all quadratic terms by successive linearizations within a branching tree using Reformulation-Linearization Techniques (RLT). To do so, four classes of linearizations (cuts), depending on one to three parameters, are detailed. For each class, we show how to select the best member with respect to a precise criterion. The cuts introduced at any node of the tree are valid in the whole tree, and not only within the subtree rooted at that node. In order to enhance the computational speed, the structure created at any node of the tree is flexible enough to be used at other nodes. Computational results are reported that include standard test problems taken from the literature. Some of these problems are solved for the first time with a proof of global optimality.

2025

Multiagent Systems. These protocols use the paradigm of economic models to define the coordination mechanisms in agent communities. Specifically, in this work we use auction and tender economical models. We propose an adaptive Metascheduler for GRID platforms using these ideas. According to the number of available resources one of these models is used to coordinate the assignment of resources.

2025, WSEAS Transactions on Computers

1 Introduction The GRID intends to satisfy computational environment's necessities that the traditional systems have not been able to do, as it is to share the great capacity of calculate and storage, dispersed geographically [1, 2,... more

2025, Journal of Combinatorial Optimization

With the growth of the Internet, Internet Service Providers (ISPs) try to meet the increasing traffic demand with new technology and improved utilization of existing resources. Routing of data packets can affect network utilization. Packets are sent along network paths from source to destination following a protocol. Open Shortest Path First (OSPF) is the most commonly used intra-domain Internet routing protocol (IRP). Traffic flow is routed along shortest paths, splitting flow at nodes with several outgoing links on a shortest path to the destination IP address. Link weights are assigned by the network operator. A path length is the sum of the weights of the links in the path. The OSPF weight setting (OSPFWS) problem seeks a set of weights that optimizes network performance. We study the problem of optimizing OSPF weights, given a set of projected demands, with the objective of minimizing network congestion. The weight assignment problem is NP-hard. We present a genetic algorithm (GA) to solve the OSPFWS problem. We compare our results with the best known and commonly used heuristics for OSPF weight setting, as well as with a lower bound of the optimal multi-commodity flow routing, which is a linear programming relaxation of the OSPFWS problem. Computational experiments are made on the AT&T Worldnet backbone with projected demands, and on twelve instances of synthetic networks.

2025, European Journal of Operational Research

Analysis of random instances of optimization problems is instrumental for understanding of the behavior and properties of problem's solutions, feasible region, optimal values, especially in large-scale cases. A class of problems that have been studied extensively in the literature using the methods of probabilistic analysis is represented by the assignment problems, and many important problems in operations research and computer science can be formulated as assignment problems. This paper presents an overview of the recent results and developments in the area of probabilistic assignment problems, including the linear and multidimensional assignment problems, quadratic assignment problem, etc.

2025, Available online: www. public research. att. com/~ mgcr/doc/kstrap. pdf

ABSTRACT. We consider the problem of interconnecting a set of customer sites using SONET rings of equal capacity, which can be defined as follows: Given an undirected graph G=(V, E) with nonnegative edge weight duv,(u, v)∈ E, and two integers k and B, find a partition of the nodes of G into k subsets so that the total weight of the edges connecting the nodes in different subsets of the partition is minimized and the total weight of the edges incident to any subset of the partition is at most B. This problem, called the k-SONET Ring ...

2025, Journal of Applied Probability

We consider several versions of the job assignment problem for an M/M/m queue with servers of different speeds. When there are two classes of customers, primary and secondary, the number of secondary customers is infinite, and idling is not permitted, we develop an intuitive proof that the optimal policy that minimizes the mean waiting time has a threshold structure. That is, for each server, there is a server-dependent threshold such that a primary customer will be assigned to that server if and only if the queue length of primary customers meets or exceeds the threshold. Our key argument can be generalized to extend the structural result to models with impatient customers, discounted waiting time, batch arrivals and services, geometrically distributed service times, and a random environment. We show how to compute the optimal thresholds, and study the impact of heterogeneity in server speeds on mean waiting times. We also apply the same machinery to the classical slow-server probl...

2025, TheScientificWorldJournal

2025

We show that the problem of finding a perfect matching satisfying a single equality constraint with a 0-1 coefficients in an n ×n incomplete bipartite graph, polynomially reduces to a special case of the same peoblem called the partitioned case. Finding a solution matching for the partitioned case in the incomlpete bipartite graph, is equivalent to minimizing a partial sum of the variables over Q n,r 1 n 1 ,n 2 = the convex hull of incidence vectors of solution matchings for the partitioned case in the complete bipartite graph. An important strategy to solve this minimization problem is to develop a polyhedral characterization of Q n,r 1 n 1 ,n 2 . Towards this effort, we present two large classes of valid inequalities for Q n,r 1 n 1 ,n 2 , which are proved to be facet inducing using a facet lifting scheme.

2025, Artificial Life and Robotics

This article focuses on the techniques of evolutionary computation for generating players performing tasks cooperatively. However, in using evolutionary computation for generating players performing tasks cooperatively, one faces fundamental and difficult decisions, including the one regarding the so-called credit assignment problem. We believe that there are some correlations among design decisions, and therefore a comprehensive evaluation of them is essential. We first list three fundamental decisions and possible options in each decision in designing methods for evolving a cooperative team. We find that there are 18 typical combinations available. Then we describe the ultimately simplified soccer game played on a one-dimensional field as a testbed for a comprehensive evaluation for these 18 candidate methods. It has been shown that some methods perform well, while there are complex correlations among design decisions. Also, further analysis has shown that cooperative behavior can be evolved, and is a necessary requirement for the teams to perform well even in such a simple game.

2025, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium

Distributed Virtual Environments (DVEs) are distributed systems that allow multiple geographically distributed clients (users) to interact simultaneously in a computer-generated, shared virtual world. Applications of DVEs can be seen in many areas nowadays, such as online games, military simulations, collaborative designs, etc. To support large-scale DVEs with real-time interactions among thousands or more distributed clients, a geographically distributed server architecture (GDSA) is generally needed, and the virtual world can be partitioned into many distinct zones to distribute the load among the servers. Due to the geographic distributions of clients and servers in such architectures, it is essential to efficiently assign the participating clients to servers to enhance users' experience in interacting within the DVE. This problem is termed the client assignment problem. In this paper, we propose a two-phase approach, consisting of an initial assignment phase and a refined assignment phase to address this problem. Both phases are shown to be NP-hard, and several heuristic assignment algorithms are then devised based on this two-phase approach. Via extensive simulation studies with realistic settings, we evaluate these algorithms in terms of their performances in enhancing interactivity of the DVE.

2025

We study agents who are more likely to remember some experiences than others, but who update their beliefs as if the experiences they remember are the only ones that occurred. To characterize their long-run behavior, we introduce the concept of selective memory equilibrium, where people choose actions that maximize their payoff given their distorted recollection of the outcome distribution. Selective memory equilibrium can explain why people are persistently overconfident, and can capture the long-run effects of “underinference,” where all experiences are remembered but some are given too little weight. When the expected number of recalled experiences is bounded, the long-run distribution of actions corresponds to a stochastic memory equilibrium. We use this to study the effect of “rehearsal,” where once an experience is recalled it is more likely to be recalled again. We also study the implications of agents who are only partially näıve about their selective memory. ∗We thank Ian B...

2025, Journal of Combinatorial Optimization

Graphs that arise from the finite element or finite difference methods often include geometric information such as the coordinates of the nodes of the graph. The geometric separator algorithm of Miller, Teng, Thurston, aad Vavasis uses some of the available geometric information to find small node separators of graphs. The algorithm utilizes a random sampling technique based on the uniform distribution to find a good separator. We show that sampling from an elliptic distribution based on the inertia matrix of the graph can significantly improve the quality of the separator. More generally, given a cost functionf on the unit d-sphere (/d, we caa define aa elliptic distribution based on the second moments off. The expectation of f with respect to the elliptic distribution is less than or equal to the expectation with respect to the uniform distribution, with equality only in degenerate cases. We also present experimental results that demonstrate the significant benefit gained by use of the additional geometric information. Some previous algorithms have used the moments of inertia heuristically, and suffer from extremely poor worst case performance. This is the first result, to our knowledge, that incorporates the moments of inertia into a provably good strategy. 1 Introduction Many problems in computational science and engineering are based on unstructured meshes of points in two or three dimensions. The meshes can be quite large, often containing millions of points. Typically, the size of the mesh is limited by the size of the machine available to solve the problem, even though, in many problems, the accuracy of the solution is related to the size of the mesh. As a result, methods for solving problems on large meshes are becoming increasingly important. Mesh partitioning is the process of decomposing a mesh into two or more pieces of roughly equal size. A mesh consists of nodes (vertices) and undirected edges connecting the nodes. In some cases, additional information in the form of the geometric coordinates of the vertices may also be available. Meshes are special cases of graphs, and mesh partitioning is a special case of the more general problem of graph partitioning.

2025, Social Science Research Network

Many authors have described search techniques for the satisficing assignment problem: the problem of finding an interpretation for a set of discrete variables that satisfies a given set of constraints. In this paper we present a formal specification of dependency directed backtracking as applied to this problem. We also generalize the satisficing assignment problem to include limited resource constraints that arise in operations research and industrial engineering. We discuss several new search heuristics that can be applied to this generalized problem, and give some empirical results on the performance of these heuristics.

2025

This paper presents a new branching strategy that is applied on the cost of a subproblem during the solution of a large-scale linear program by a column generation technique. This branch and cut strategy has been used to improve the solution time for the preferential bidding problems encountered in the airline industry. Moreover, it is shown that this strategy can also be applied to other problems with particular structures. Nous proposons une stratégie de type branchement et coupe intervenant au niveau des sous-problèmes dans le cadre de la procédure de génération de colonnes. L'application de cette stratégie pour la résolution des problèmes de fabrication des horaires personnalisés avec priorités chez Air Canada présentant un grand gap d'intégrité a permis d'améliorer le temps de calcul et de générer de meilleurs horaires pour un bon nombre de pilotes. La taille et la profondeur de l'arbre de branchement ont été réduites de façon très significative. Nous avons discuté de l'extension de la stratégie pour la résolution d'autres classes de problèmes. Plusieurs applications connues dans la littérature sont présentées.

2025

We present an exact, constructive deterministic algorithm that, for each integer n ≥ 2, solves the Quadratic Assignment Problem (QAP) in Ω(n^{O(1)}) time and Ω(n^{O(1)}) space.

2025, Symposium on Discrete Algorithms

In this paper we present a strategy to route unknown duration virtual circuits in a highspeed communication network. Previous work on virtual circuit routing concentrated on the case where the call duration is known in advance. We show that by allowing O(logn) reroutes per call, we can achieve O(logn) competitive ratio with respect to the maximum load (congestion) for the unknown duration case, were n is the number of nodes in the network. This is in contrast to the ( 4 p n) lower bound on the competitive ratio for this case if no rerouting is allowed 3]. Our routing algorithm can be also applied in the context of machine load balancing of tasks with unknown duration. We present an algorithm that makes O(log n) reassignments per task and achieves O(logn) competitive ratio with respect to the load, where n is the number of parallel machines. For a special case of unit load tasks we design a constant competitive algorithm. The previously known algorithms that achieve up to polylogarithmic competitive ratio for load balancing of tasks with unknown duration dealt only with special cases of related machines case and unit-load tasks with restricted assignment 4, 11].

2025, International Journal of Fuzzy System Applications

In today's era, managerial decision making has become a very momentous component due to the leverage of attention on achieving organizational goal i.e. enhancing effective utilization of input assets, satisfying customers' demand and minimizing loss (maximize profit). The evaluation of the most appropriate Computer Numerical Control (CNC) machine tool has become one of the key factors for sustaining the organization/manufacturing sectors/production units at competitive global market place. Productivity, precision and accuracy etc. are the most important issues behind adaptation/exploration of CNC machine tools. So, in such a cases, subjective indices are considered beside the objective indices and complexity of the CNC machine tool evaluation decision problems is solved via subjective assessments (judgment) of expert panel, also called the decision-making group. In this reporting, TOPSIS (technique for order preference by similarity to ideal solution) based Multi-Criteria De...

2025, IEEE Transactions on Robotics and Automation

In recent years, the hybrid control framework has received much attention from the research community. Several variations of this control framework are available. In this paper, an actual industrial warehouse order picking problem where goods are stored at multiple locations and the pick location of goods can be selected dynamically in near real time, is considered. A hybrid intelligent agent based scheduling and control system architecture is presented for the order picking problem. The need for a higher level optimizer and communication between higher and lower level controllers is demonstrated. The presented architecture includes a higher level optimizer, a middle level guide agent, and lower level negotiation agents. A mathematical model and a genetic algorithm for the resource assignment problem are presented. Simulation results demonstrating efficiency of the new approach are also presented.

2025, 2006 9th International Conference on Information Fusion

all object tracking scheme are provided. Overall, the approach demonstrates that well established data association methods developed for "point" multitarget tracking can, after appropriate adaptation, be very useful for tracking rigid... more

2025, Http Www Theses Fr

Thèse acceptée le 3 Février 2012 RÉSUMÉ Les problèmes d'optimisation discrète sont pour beaucoup difficiles à résoudre, de par leur nature combinatoire. Citons par exemple les problèmes de programmation linéaire en nombres entiers. Une approche couramment employée pour les résoudre exactement est l'approche de Séparation et Évaluation Progressive. Une approche différente appelée « Resolution Search » a été proposée par Chvátal en 1997 pour résoudre exactement des problèmes d'optimisation à variables 0-1, mais elle reste mal connue et n'a été que peu appliquée depuis. Cette thèse tente de remédier à cela, avec un succès partiel. Une première contribution consiste en la généralisation de Resolution Search à tout problème d'optimisation discrète, tout en introduisant de nouveaux concepts et définitions. Ensuite, afin de confirmer l'intérêt de cette approche, nous avons essayé de l'appliquer en pratique pour résoudre efficacement des problèmes bien connus. Bien que notre recherche n'ait pas abouti sur ce point, elle nous a amené à de nouvelles méthodes pour résoudre exactement les problèmes d'affectation généralisée et de localisation simple. Après avoir présenté ces méthodes, la thèse conclut avec un bilan et des perspectives sur l'application pratique de Resolution Search.

2025, Computer Science and Information Technologies

Ports are essential for international trade, connecting production areas to consumer markets. However, port operations often face delays, disrupting supply chains and increasing transit times. To address this, mathematical modeling, particularly through genetic algorithms, offers a solution for optimizing processes like container unloading. This paper presents a model predicting and optimizing unloading times by considering factors such as crane types, schedules, and environmental conditions. Focusing on the Casablanca port, the model addresses scheduling for two gantry and two mobile cranes, treating each bay as a unique task handled by one crane type to avoid conflicts. Using genetic algorithms, the goal is to create efficient schedules that minimize waiting times and maximize crane utilization. The expected outcome is a detailed timetable enabling effective gantry crane use or simultaneous multi-crane operations, enhancing unloading efficiency. This approach can be adapted to other ports with similar challenges, highlighting the model's broader applicability.

2025

Message sequencing and channel assignment are two important issues that need to be addressed in scheduling vuriable-length messages in a Wavelength Division Multiplexing (WDM) network. Channel assignment addresses the problem of choosing an appropriate data channel via which a message is transmitted to a node. This problem has been addressed extensively in the literature. On the other hand, message sequencing which addresses the order in which messages are sent, has rarely been addressed. In this papel; we propose a set of scheduling techniques for single-hop WDM passive star networks which address both the sequencing aspect and the assignment aspect of the problem. In particulal; we develop two priority schemes for sequencing messages in a WDM network in order to increase the overall performance of the network. We evaluate the proposed algorithms, using analytical modeling and discreteevent simulations, by comparing their performance with state-of the-art scheduling algorithms that only address the assignment problem. We find that signijkant improvement in perj5ormance can be achieved using our scheduling algorithms where message sequencing and channel assignment are simultaneously taken into consideration.

2025, RePEc: Research Papers in Economics

When the trading process is characterized by search frictions, traders may be rationed so markets need not clear. We build a general equilibrium model with transferable utility where the uncertainty arising from rationing is incorporated in the definition of a commodity, in the spirit of the Arrow-Debreu theory. Prices of commodities then depend not only on their physical characteristics, but also on the probability that their trade is rationed. The standard definition of competitive equilibrium is extended by replacing market clearing with a matching condition which describes a trading technology that is not frictionless. This condition relates the rationing probabilities of buyers and sellers to ratio of buyers to sellers in the market via an exogenous matching function with constant returns, as in standard search-theoretic models. When search frictions vanish, our model is equivalent to the competitive assignment model of . We adopt their approach, which uses linear programming techniques and duality theory, to derive the welfare and existence theorems in our search environment. Our competitive equilibrium notion is equivalent to that of directed (or competitive) search. The strength of our formulation and the linear programming approach is that they allow us to generalize the constrained efficiency and existence results in the directed search literature to a much broader class of economies. Our framework also opens the door to the use of linear programming algorithms for computing equilibria.

2025

Column Generation (CG) algorithms are instrumental in many areas of applied optimization, where Linear Programs with an enormous number of columns need to be solved. Although succesfully used in many aplication, the standard CG algorithm suffers from wellknown "instability" issues that somewhat limit its efficiency and usability. Building on the theory developed for NonDifferantiable Optimization algorithm, we propose a large class of Stabilized Column Generation (SCG) algorithms which avoid the instability problems of the standard approach by using an explicit stabilizing term in the dual; this amounts at considering a (generalized) Augmented Lagrangian of the primal Master Problem. Since the theory allows for a great degree of flexibility in the choice and in the management of the stabilizing term, we can use piecewise-linear functions that can be efficiently dealt with off-the-shelf LP technology, as well as being related in interesting ways with some previous attempt at stabilizing the CG algorithm. The effectiveness in practice of this approach is demonstrated by extensive computational experiments on large-scale Multi-Depot Vehicle Scheduling problems and simultaneous Vehicle and Crew Scheduling problems.

2025, ITEGAM-JETIA

This case study addresses the staffing challenges faced by a hospital's porter service, which is currently insufficient to meet patient needs effectively. Due to the lack of a systematic task assignment mechanism, the head of the porters' center has had to manage patient transport manually, leading to unequal workload distribution among porters. This research aims to rectify this operational issue by developing a mathematical model and a userfriendly program for optimizing porter assignments. The methodology includes extensive data collection on existing protocols and factors affecting operations. A mathematical model is formulated with the objective of minimizing monthly workload deviations among porters. The model is executed using Excel Solver, producing an optimal assignment solution. Additionally, Visual Basic for Applications (VBA) in Excel is utilized to create a practical program for real-world application. A quantitative comparison of the standard deviation in cumulative workload from September 2022 reveals a significant improvement: the proposed program reduced the standard deviation by 5,907 seconds, or 76.17%. This outcome highlights the effectiveness of the new solution in achieving a more balanced distribution of porter assignments, thereby enhancing operational efficiency.

2025, Annali di Matematica Pura ed Applicata

EzIo lg~CHI (Campinas, Brasil) -P~BLO TA~AZAG~ (San Luis, Argentina)(**) Summary. -In this paper we generalize the assignment problem in higher dimensions, referring at to another study by the authors. The hide-and-seek game, which is intimately related to the assignment problem, is extended, and an elegant result due to K. Han about extrema is generalized. Let N~=N= (!, 2, ... , n} be a se~, for i=l, 2,...,k. We define the general hide-and-seek game in k-dimension as a zero-sum-two-person game k (*) Entrata in Redazione il 4 ottobre 1978.

2025, Annals of Operations Research

Teamwork has increasingly become more popular in educational environments. With the also increasing mobility trends in the educational sector, internationalization and other diversity features have gained importance in the structure of teams. In this paper, we discuss an assignment problem arising in the allocation of students to business projects in a master program in Norway. Among other problem features, the students state their preferences on the projects they most want to conduct. There are also requirements from the companies that propose the projects and from the program administration. We develop a bi-objective approach to consider efficiency and fairness criteria in this assignment problem. We test the model using real data of 2017 and 2018, in joint collaboration with the administrative staff of the program. In light of the good results, our proposed solutions have been implemented in practice in 2019 and 2020. The implementation of these solutions have been beneficial for...

2025

In this research, the problem addressed involves sets of practical case studies relating to a third-party logistics firm that mainly provides services to a big industrial estate in Thailand. This study considers constraints consisting of time windows, multiple trips, multi-product deliveries, a limited number of drivers and mixed fleets with limited and unlimited numbers of available vehicles. An adapted genetic algorithm hybridizes three inter-route search operators, i.e. relocation, exchange and elimination are developed and used to determine the best solution to a heterogeneous fleet vehicle routing problem with various constraints as mentioned previously. The benchmark problem sets do not exactly fit the addressed unique problem; therefore, the performance of the proposed method is evaluated against a branch-and-bound algorithm as a built-in solver. Due to the limitations of the solver for solving large-scale problems, percentage deviations of the solutions with respect to the b...

2025, Lecture Notes in Computer Science

We propose combining advanced statistical approaches with data mining techniques to build classifiers to enhance decision-making models for the job assignment problem. Adaptive Generalized Estimation Equation (AGEE) approaches with Gibbs sampling under Bayesian framework and adaptive Bayes classifiers based on the estimations of AGEE models which uses modified Naive Bayes algorithm are proposed. The proposed classifiers have several important features. Firstly, it accounts for the correlation among the outputs and the indeterministic subjective noise into the estimation of parameters. Secondly, it reduces the number of attributes used to predict the class. Moreover, it drops the assumption of independence made by the Naive Bayes classifier. We apply our techniques to the problem of assigning jobs to Navy officers, with the goal of enhancing happiness for both the Navy and the officers. The classification results were compared with nearest neighbor, Multi-Layer Perceptron and Support Vector Machine approaches.

2025, Transportation Research Part B-methodological

An analysis of the continuous-time dynamics of a route-swap adjustment process is presented, which is a natural adaptation of that which was presented in Smith (1984) for deterministic choice problems, for a case in which drivers are assumed to make perceptual errors in their evaluations of travel cost, according to a Random Utility Model. We show that stationary points of this system are stochastic user equilibria. A Lyapnuov function is developed for this system under the assumption of monotone, continuously differentiable and bounded cost-flow functions and a logit-based decision rule, establishing convergence and stability of trajectories of such a dynamical system with respect to a stochastic user equilibrium solution.

2025

This paper was written during a visit of the second author to the University of Leeds, partially funded by EPSRC grant GR/M79493. The support of Advanced Fellowship AF/1997 from the UK Engineering and Physical Sciences Research Council is... more

2025

2025, Transportation Research Part B: Methodological

2025, Mathematical Social Sciences

Inspired by Roth and Sotomayor we make a deeper mathematical study of the assortative matching markets defined by Becker, finding explicit results on stability and fairness. We note that in the limit, when the size of the market tends to infinity, we obtain the continuous model of Sattinger and retrieve his characterization of the core of the game in this limit case. We also find that the most egalitarian core solution for employees is the employer-optimal assignment.

2025

We are developing AUREMOL 1 (www.auremol.de), which goal is the reliable and automatic structure determination of biological macro molecules such as proteins from NMR data. For a fully automatic sequential NOESY assignment the tool ASSIGN 2 has been developed. The required input consists of a homologous structure for a NOESY spectrum simulation and the experimental NOESY spectrum. ASSIGN fits the simulated NOE signals to the experimental spectrum. The fit quality given by a probability depends on the line shapes and volumes of the signals. The assignment is varied by moving or swapping spin system assignments using a Monte Carlo approach. A threshold accepting algorithm (TA 3 ) is employed to find the maximum of accordance.

2025, Journal of Modern Applied Statistical Methods

A new model for the weighted method of goal programming is proposed based on minimizing the distances between ideal objectives to feasible objective space. It provides the best compromised solution for Multi Objective Linear Programming Problems (MOLPP). The proposed model tackles MOLPP by solving a series of single objective subproblems, where the objectives are transformed into constraints. The compromise solution so obtained may be improved by defining priorities in terms of the weight. A criterion is also proposed for deciding the best compromise solution. Applications of the algorithm are discussed for transportation and assignment problems involving multiple and conflicting objectives. Numerical illustrations are given for the proposed model.

2025

Delta Air Lines flies over 2,500 domestic flight legs every day, using about 450 aircraft from 10 different fleets. The fleet as-signment problem is to match aircraft to flight legs so that seats are fllled with paying passengers. Recent advances in mathe-matical programming algorithms and computer hardv^are make it possible to solve optimization problems of this scope for the first time. Delta is the first airline to solve to completion one of the largest and most difficult problems in this industry. Use of the Coldstart model is expected to save Delta Air Lines $300 million over the next three years. D elta Air Lines has over 2,500 domes- It has been said that an airline seat is the tic flight departures every day. This most perishable commodity in the world, includes flights to Canada and Mexico but Each time an airliner takes off with an excludes the other international routes. empty seat, a revenue opportunity is lost Delta has about 450 aircraft available to fly forever. So th...

2025, DIMACS Series in Discrete Mathematics and Theoretical Computer Science

2025

Software development teams consist of developers with varying expertise and levels of productivity. With reported productivity variation of up to 1:20, the quality of assignment of developers to tasks can have a huge impact on project performance. Developers are characterized according to a defined core set of technical competence areas. The objective is to find a feasible assignment, which minimizes the total time needed to fix all given bugs. In this paper, the modeling of the developer’s assignment to bugs is given. Subsequently, a genetic algorithm called GA@DAB (Genetic Algorithm for Developer’s Assignment to Bugs) is proposed and empirically evaluated. The performance of GA@DAB was evaluated for 2040 bugs of 19 open-source milestone projects from the Eclipse platform. As part of that, a comparative analysis was done with a previously developed approach using K-Greedy search. Our results and analysis shows that GA@DAB performs statistically significantly better than K-greedy se...