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The assignment problem (AP) is a discrete and combinatorial problem where agents are assigned to perform tasks for efficiency maximization or cost (time) minimization. AP is a part of human resource project management (HRPM). The AP optimization model, with deterministic parameters describing agent–task performance, can be easily solved, but it is characteristic of standard, well-known projects realized in a quiet environment. When considering new (innovation or innovative) projects or projects performed in very turbulent times, the parameter estimation becomes more complex (in extreme cases, even the use of the probability calculus is not recommended). Therefore, we suggest an algorithm combining binary programming with scenario planning and applying the optimism coefficient, which describes the manager’s nature (attitude towards risk). The procedure is designed for one-shot decisions (i.e., for situations where the selected alternative is performed only once) and pure strategies (the execution of a weighted combination of several decision variants is not possible).

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomised mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomised mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of e e - 1 . The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. By using a characterisation result of Bade, we show that any randomised mechanism that is a symmetrisation of a truthful, non-bossy and Pareto optimal mechanism has an improved lower bound of e e - 1 . Since our new mechanism is a symmetrisation of RSDM for strict preferences, it follows that this lower bound is tight. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomised strategy of the administrator who interviews the applicants. [ABSTRACT FROM AUTHOR]

Theory and applications of fractional programming have been significantly developed in the few last decades and assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization. Generally, in real world problems, the possible values of coefficients of a linear fractional programming problem are often only imprecisely or ambiguously known to the decision maker, therefore, it would be certainly more appropriate to interpret the coefficients as fuzzy numerical data. In this article, a fuzzy bi-objective fractional assignment problem has been formulated. Here the parameters are represented by triangular fuzzy numbers and the fuzzy problem is transformed into standard crisp problem through α -cut and then the compromise solution is derived by fuzzy programming. [ABSTRACT FROM AUTHOR]

In the classical secretary problem, multiple secretaries arrive one at a time to compete for a single position, and the goal is to choose the best secretary to the job while knowing the candidate's quality only with respect to the preceding candidates. In this paper we define and study a new variant of the secretary problem, in which there are multiple jobs. The applicants are ranked relatively upon arrival as usual, and, in addition, we assume that the jobs are also ranked. The main conceptual novelty in our model is that we evaluate a matching using the notion of blocking pairs from Gale and Shapley's stable matching theory. Specifically, our goal is to maximize the number of matched jobs (or applicants) that do not take part in a blocking pair. We study the cases where applicants arrive randomly or in adversarial order, and provide upper and lower bounds on the quality of the possible assignment assuming all jobs and applicants are totally ordered. Among other results, we show that when arrival is uniformly random, a constant fraction of the jobs can be satisfied in expectation, or a constant fraction of the applicants, but not a constant fraction of the matched pairs. [ABSTRACT FROM AUTHOR]

This paper sustains a sound mathematical and computing background. In this paper, the software-based approach for solving intuitionistic fuzzy solid assignment problem (IFSAP) is presented. The IFSAP is formulated and it is solved by using Lingo 17.0 software tool. Theorems related to IFSAP is proved. The IFSAP and its crisp solid assignment problem both are solved at a time and their optimal solution is obtained. In addition, the optimal objective values of both the IFSAP and its crisp solid assignment problem (SAP) are estimated with the help of substituting the optimal solution(s) to their respective decision variables in the objective functions. Some new and important results are proposed. To illustrate the efficiency of the proposed method the numerical example is presented. The reliability of the proposed results are verified by using the numerical example. Strengths and weakness of the paper is mentioned. The novelty of the analysis is given into a coherent, concise, and meaningful manner of analysis. Social issue (real-life problem) is converted into a mathematical model and it is solved by the proposed method. At the end, the advantages of the proposed algorithm is explained. [ABSTRACT FROM AUTHOR]

• Review of alternative methods to produce energy using poultry litter. • Use of an assignment model to allocate litter from poultry farms to electric reactors. • Solutions are obtained for single and multiple electric reactors. • Economic impact analysis show potential positive effects from building electric reactors. • An empirical model consists of real-world data from Louisiana, USA. Poultry litter has the potential to cause water quality problems if it is not applied properly to the land as a crop nutrient. Based on the data available from a survey of Louisiana poultry producers, we find that it is not cost effective to transport poultry litter farther than 38.6 km from the production facilities for crop nutrient purposes. This limited breakeven distance restricts the movement of poultry litter and points to a need to identify an alternative disposal method. We review common methods of producing electricity from poultry litter. We identify the minimum cost solution for assigning poultry litter when one large or three small electric reactors are chosen to be built for electricity production in the poultry production region. We calculate the cost-return analysis of building electric reactors and expand it to find the economic impact of starting such electric reactors to the local and regional economies. [ABSTRACT FROM AUTHOR]

This paper introduces a new distributed approach to solve multi-objective planning problem applied to multimodal transport network planning (MTNP) problem. In this problem, the commodities should be transported on the international network by at least two different transport modes. The main goal is to find the best multimodal transportation modes and itineraries. The aim of the new approach has assured us that a distributed optimization. We split the MTNP problem into two sub-problems. These sub-problems are the assignment and the planning problems. Each sub-problem is solved at a corresponding layer. Each layer is executed by an agent. These agents interact, collaborate and communicate together to solve the MTNP problem. In this paper, we contribute by introducing a multi-layer distributed approach to solve real case's problems. Firstly, we define the MTNP problem as a distributed constraint satisfaction multi-criteria optimization problem (DCSMOP). Secondly, we show that the split of the main problem reduces the computational complexity and the communication between the planner agent and the modes agents lead to faster convergence. The experimental results are proof of this work efficiently. This method proves their efficiency, according to the complexity of the problem and the exchange of information, the computational time and the solution quality. [ABSTRACT FROM AUTHOR]

We address, in this paper, a very recurring problem within hospitals that consists in assigning elective patients to a limited number of beds. Especially when dealing with patients requiring urgent intervention, this problem becomes more complex and the time factor becomes the most critical. In such situations, a set of patients are to be examined and their clinical states are to be well specified in order to decide whether they need admission and hospitalization or not. In case of hospitalization, the hospital staff should assign patients to beds while taking into account beds availability in terms of specialization and patient needs. All these actions should be well planned in order to maximize the quality of service in the hospitals. This challenging problem can be modeled as an assignment problem that handles a set of patients to be assigned to a set of beds over a given time horizon, while taking into account availability constraints expressed in terms of beds, medical necessity and patient demands. Due to its NP -hardness, the problem is mainly solved using approximate approaches, especially for large-scaled instances. We propose a hybrid simulated annealing approach, combining both advantages of simulated annealing (SA), that provides a local search, and genetic algorithm, that provides a global search, to enhance the performance of SA. The experimental results show that the proposed metaheuristic generates high-quality solutions for several benchmark instances from the literature with regards to the basic simulated annealing approach. [ABSTRACT FROM AUTHOR]

Cross-docks serve as distribution centers where shipments from different vendors are first consolidated according to their destinations, and then delivered to the retailers directly, with little or no storage in between. A critical problem encountered in the operation of cross-docks is the assignment of receiving and shipping doors, which greatly influences the labor or machinery cost of transferring the shipments between inbound and outbound transports. We show that the cross-dock door assignment problem (CDAP) is strictly non-deterministic polynomial-time complete. Although some deterministic algorithms have been reported to handle small-scale problems, the solutions to the middle- and large-scale CDAPs progressed at a slow pace. In this paper, we develop a nature-inspired dual-colony ant algorithm for CDAP, in which the two colonies of ants cooperatively search the optimal assignments of receiving and shipping doors to minimize the transferring costs of shipments. A collaborative local search strategy is designed and incorporated into the algorithm to enhance the search efficiency. Experiments have been conducted on a number of problem instances with different cross-dock sizes and freight flow patterns. The results show that the proposed algorithm is very competitive and can provide better solutions than the state-of-the-art heuristic algorithms. [ABSTRACT FROM AUTHOR]

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We deal with the classical problem of testing two simple statistical hypotheses but, as a new element, it is assumed that the data vector is observed after an unknown permutation of its entries. What is the fundamental limit for the detection performance in this case? How much information for detection is contained in the entry values and how much in their positions? In the first part of this paper, we answer these questions. In the second part, we focus on practical algorithms. A low-complexity detector solves the detection problem without attempting to estimate the permutation. A modified version of the auction algorithm is then considered, and two greedy algorithms with affordable worst case complexity are presented. The detection operational characteristics of these detectors are investigated by computer experiments. The problem we address is referred to as unlabeled detection and is motivated by large sensor network applications, but applications are also foreseen in different fields, including image processing, social sensing, genome research, and molecular communication. [ABSTRACT FROM AUTHOR]

We describe an extensive channel-measurement campaign, including 325 unique transmitter–receiver configurations, conducted in a lecture room with our 3-D double-directional 60 GHz channel sounder. The receiver was mounted on a mobile robot, with 40 cm spacing between channel acquisitions, enabling the tracking of clustered multipath components in the multidimensional delay-angle space. To mitigate against angle-estimation error and multipath blockage, we introduce a robust tracking algorithm based on the Assignment Problem. For the purpose of validation, the clusters were transformed from the delay-angle space onto a 2-D map of the environment and compared against the locations of cluster-generating reflectors, such as walls and tables. The location errors were typically within 30–50 cm. The clusters identified were then reduced to a stochastic map-based channel model, including reflection loss and dispersion characteristics such as the Ricean K-factor and angular spread. Given the 0.5 ns delay resolution of the channel sounder and angle-estimation error around 2°, the parameters were reported with high fidelity. [ABSTRACT FROM AUTHOR]

We consider a one-to-one assignment problem consisting of matching n objects with n agents. Any matching leads to a utility vector whose n components measure the satisfaction of the various agents. We want to find an assignment maximizing a global utility defined as an ordered weighted average (OWA) of the n individual utilities. OWA weights are assumed to be non-increasing with ranks of satisfaction so as to include an idea of fairness in the definition of social utility. We first prove that the problem is NP-hard; then we propose a polynomial algorithm under some restrictions on the set of admissible weight vectors, proving that the problem belongs to XP. [ABSTRACT FROM AUTHOR]

The mission of an earth observation satellite (EOS) is to acquire images of specified areas of the Earth surface related to observation requests from customers. This paper proposes an optimization approach for the daily photograph selection problem (DPSP) of EOSs. DPSP is related to operational management of EOSs and about the scheduling of observations for an EOS. Each photograph related to a customer order generates a profit but not all of the requests can be satisfied due to some physical and technological constraints. Then the problem is to select a subset of requests of maximal profit. The proposed algorithm inherits the hyper-cube framework of ant colony optimization (ACO) metaheuristic. Realistic instances are used as benchmark problems. Computational results demonstrate that the proposed algorithm is capable of generating competitive and promising solutions. [ABSTRACT FROM AUTHOR]

A shortage of large power system data sets, as well as the frequent restrictions on sharing such models, have led to newfound interest in creating synthetic data that can be easily shared among researchers. This paper considers the problem of forming a power system test case from the constituent parts of realistic power grid samples. Starting from a topology, and samples of generation, load, and branches, we assemble systems while respecting the constraints imposed by a typical Optimal Power Flow problem. Expressed in this manner, the problem involves solving for permutations of the input data. Since permutations matrices are binary, the problem is linearized, allowing for a Mixed Integer Linear Problem formulation. The problem is further decomposed using the Alternating Direction Method of Multipliers as well as an Evolutionary Algorithm to facilitate scaling to larger system sizes. A post processing step is used to add shunt elements for reactive power planning. The resulting systems demonstrate statistically similar power flow behavior to reference systems. Finally, new analysis avenues, opened by synthesizing test cases according to the proposed method, are briefly introduced by creating fictitious systems with different topology models and examining how these affect power flow behavior. [ABSTRACT FROM AUTHOR]

In this paper, the object of the study is multistage systems, at the input of which comes a stream of requests that require executing a set of serial-parallel jobs for their support. The subject of the research is the optimization of the problem of assigning jobs to executors in such a system. As a result, a formalization of the problem is proposed, including a nonlinear objective function and recursive constraints. [ABSTRACT FROM AUTHOR]

A sonobuoy is an underwater acoustic sensor primarily deployed by airdrop. An acoustic sensor plays a significant role in conducting anti-submarine warfare for detecting underwater sounds. As a future underwater acoustic sensor, sonobuoy is expected to have an ability of self-movement, i.e., autonomous sonobuoy. In this study, we consider an optimal linear array deployment of autonomous sonobuoys when detecting an unknown underwater sound, assuming that the initial locations of sonobuoys are random in a specified operational area. Deploying sonobuoys from the initial locations onto a specific line requires to first determine the line and positions on that line. Under the interval equivalence between two adjacent sonobuoys, we propose two lines, one that is perpendicular from the underwater sound source location and the other based on the linear regression analysis using the initial locations of sonobuoys. With these two lines onto which sonobuoys will be deployed, we provide two optimization models, total distance minimization and maximum distance minimization, which turn out to be assignment and bottleneck assignment problems, respectively, with nonlinear cost coefficients in the objectives. Due to non-convexity of the objectives, we solve these problems for a fixed interval repetitively as a linear program and integer program, respectively. Computational results show that regression-based line provides higher solution qualities for both problems. Finally, we suggest an approximate interval in a heuristic manner, which guarantees a highly near-optimality as the number of sonobuoys increases. Our results may support a decision-making and provide practitioners with insight on more variety of effective use of autonomous sonobuoys. [ABSTRACT FROM AUTHOR]

Abstract Many technical systems like manufacturing plants or software applications generate large event sequences. Knowing the temporal relationship between events is important for gaining insights into the status and behavior of the system. This paper proposes a novel approach for identifying the time lag between different event types. This identification task is formulated as a binary integer optimization problem that can be solved efficiently and close to optimality by means of a linear programming approximation. The performance of the proposed approach is demonstrated on synthetic and real-world event sequences. [ABSTRACT FROM AUTHOR]

Abstract Several studies have found that students' academic achievement is as much determined by the socioeconomic composition of their school as their own socioeconomic status. In this paper we provide a methodology for assigning students to schools so as to balance the socioeconomic compositions of the schools while taking into consideration the total travel distance. Our technique utilizes a biobjective general 0–1 fractional program that is linearized into a mixed 0–1 linear program that can be submitted directly to a standard optimization package. We show how a parametrized model could be utilized to provide a spectrum of different possible assignments so that a decision maker can decide how to balance socioeconomic factors with transportation costs. As a test case for our approach we analyze data from the Greenville County School District in Greenville, South Carolina. [ABSTRACT FROM AUTHOR]

Abstract: A new algorithmic approach to the synthesis of economically optimum multistage heat exchange network in the design and reconstruction of chemical-technological units has been considered. The problem was proposed to be solved based on the assignment problem and decomposition principle of fixation of variables. The efficiency of the approach was shown on the example of solving a number of typical problems on heat integration. [ABSTRACT FROM AUTHOR]

The layout design for storage vessels is an important issue to keep safe process plants, since the accidents originated in storage areas are almost one-third of all reported accidents. In order to reduce fire and explosion damages different mathematical approaches have been proposed; however, most of them are not suitable for real storage facilities design. In this work, a MILP approach has been developed to find the optimal layout of storage vessels, seeking to minimize the cost associated with potential damage of fire and explosion. This approach allows allocation of suitable sites for storage vessels, reducing accidents propagation, and domino effect while keeping safety as much as possible the plant assets. In this way, the optimization approach provides substantial support for decision-makers during the design stage. The study case used to test the mathematical model considers 19 vessels, six buildings, five process facilities and 25 possible scenarios, which includes 16 fires and 9 explosions. [ABSTRACT FROM AUTHOR]

The assembly process is extremely complex for aircraft and its management requires to address numerous optimization problems related to the assignment of tasks to workstations, staffing problem for each workstation and finally the assignment of tasks to operators at each workstation. This paper treats the latter problem dealing with the assignment of tasks to operators under ergonomic constraints. The problem of optimal tasks scheduling in aircraft assembly line is modelled as Resource-Constrained Project Scheduling Problem (RCPSP). The objective of this research is to assign tasks to operators and to find an optimal schedule of task processing under economic and ergonomic constraints. Two different models to solve this problem are presented and evaluated on an industrial case study. [ABSTRACT FROM AUTHOR]

The general assignment problem is a classical NP-hard (non-deterministic polynomial-time) problem. In a warehouse, the constraints on the equipment and the characteristics of consecutive processes make it even more complicated. To overcome the difficulty in calculating the benefit of an assignment and in finding the optimal assignment plan, a simulation-based optimization method is introduced. We first built a simulation model of the warehouse with the object-oriented discrete-event simulation (O2DES) framework, and then implemented a random neighborhood search method utilizing the simulation output. With this method, the throughput and service level of the warehouse can be improved, while keeping the number of workers constant. Numerical results with real data demonstrate the reduction of discrepancy between inbound and outbound service level performance. With a less than 10% reduction in inbound service level, we can achieve an over 30% increase in outbound service level. The proposed decision support tool assists the warehouse manager in dealing with warehouse worker allocation problem under conditions of random daily workload.

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. [ABSTRACT FROM AUTHOR]

The spectral matching algorithm is a classic method for finding correspondences between two graphs, a fundamental task in pattern recognition. It has a time complexity of O (n 4) and a space complexity of O (n 4) , where n is the number of nodes. However, such complexity limits its applicability to large-scale graph matching tasks. This paper proposes a redesign of the algorithm by transforming the graph matching problem into a one-dimensional linear assignment problem. This transformation enables efficient solving by sorting two n × 1 vectors. The resulting algorithm is named the Lightning Spectral Assignment Method (LiSA), which enjoys a complexity of O (n 2). Numerical experiments demonstrate the efficiency of LiSA, supported by theoretical analysis. [ABSTRACT FROM AUTHOR]

We address the correspondence problem which arises when applying empirical mode decomposition (EMD) to multi-trial and multi-subject data. EMD decomposes a signal into a set of narrow-band components named intrinsic mode functions (IMFs). The number of IMFs and their signal properties can be different between trials, channels and subjects. In order to assign IMFs with similar characteristics to each other, we compare two assignment methods, unbalanced assignment and k-cardinality assignment and two clustering algorithms, namely hierarchical clustering and density-based spatial clustering of applications with noise based on heart rate variability data of children with temporal lobe epilepsy.

Aim: This article presents a theoretical model that enables achievement of macroeconomic efficiency of the legal aid system by means of adjusting supply to the pre-determined demand.Results: Main deterministic components of aggregate demand for legal aid are defined using a shift-share type framework. The knowledge of its parameters makes it possible to estimate expected demand for legal aid in response to various formulae of possible reforms of the system.Motivation: Estimates of demand serve to compute legal aid supply that minimizes social costs of legal aid provision. This task is accomplished by means of the so called assignment problem originating the field of operational research. Providers are divided in line with their average productivities in solving appropriate legal cases and the aggregate personal costs of legal aid provision are subject to minimization.

This study constructs a practical fuzzy three-dimensional axial assignment model, and proposes two efficient algorithms to solve the model. In our case, the model is applied to team performance management in a company to promote the performance of all members in a team. Two algorithms, namely the index-based branch and bound (B&B) algorithm and the f-g trade-off algorithm, which is a hybrid of the trade-off and B&B concepts, are proposed. A numerical example is presented to illustrate these two algorithms. The computational results show that the proposed algorithms are sufficiently efficient and accurate. Two special cases are also discussed.

This paper proposes a DEA model for evaluating arc efficiency in the presence of multiple weights on arcs in a network. Thereafter, a multi-criteria assignment problem is formulated based on the efficiency of the arcs. Appraisal is given to some parts of the proposed DEA-model used for solving multi-criteria network flow problems and provide some examples. Finally, a numerical example is used to illustrate the applicability of the approach.

This paper presents a new multiple criteria optimization model of an assignment problem with imprecise coefficients. Besides, minimizing the total cost, total time of finishing jobs, and maximization of the overall achieved quality, we introduce a new criterion that minimizes the number of workers employed to finish all jobs. It contributes significantly in multi-job assignment to adjust the number of workers assigned to at least one job for balancing work allocation among the workers. Furthermore, we employ new diversification constraints to obtain a reasonable tradeoff between the number of workers employed and number of jobs assigned. A new interactive possibilistic programming approach is developed for trapezoidal possibility distributions, which uses $\alpha$ -level sets to incorporate confidence levels of the decision maker in his fuzzy judgments leading to $\alpha$ -efficient solutions. Numerical experiments are conducted using data coming from a manpower planning problem to demonstrate working of the proposed multiple criteria assignment model and effectiveness of the fuzzy interactive approach. [ABSTRACT FROM AUTHOR]

Motivated by the growth of ridesourcing services and the expected advent of fully-autonomous vehicles (AVs), this paper defines, models, and compares assignment strategies for a shared-use AV mobility service (SAMS). Specifically, the paper presents the on-demand SAMS with no shared rides , defined as a fleet of AVs, controlled by a central operator, that provides direct origin-to-destination service to travelers who request rides via a mobile application and expect to be picked up within a few minutes. The underlying operational problem associated with the on-demand SAMS with no shared rides is a sequential (i.e. dynamic or time-dependent) stochastic control problem. The AV fleet operator must assign AVs to open traveler requests in real-time as traveler requests enter the system dynamically and stochastically. As there is likely no optimal policy for this sequential stochastic control problem, this paper presents and compares six AV-traveler assignment strategies (i.e. control policies). An agent-based simulation tool is employed to model the dynamic system of AVs, travelers, and the intelligent SAMS fleet operator, as well as, to compare assignment strategies across various scenarios. The results show that optimization-based AV-traveler assignment strategies, strategies that allow en-route pickup AVs to be diverted to new traveler requests, and strategies that incorporate en-route drop-off AVs in the assignment problem, reduce fleet miles and decrease traveler wait times. The more-sophisticated AV-traveler assignment strategies significantly improve operational efficiency when fleet utilization is high (e.g. during the morning or evening peak); conversely, when fleet utilization is low, simply assigning traveler requests sequentially to the nearest idle AV is comparable to more-advanced strategies. Simulation results also indicate that the spatial distribution of traveler requests significantly impacts the empty fleet miles generated by the on-demand SAMS. [ABSTRACT FROM AUTHOR]

In order to implement the human-centric manufacturing and sustainability concepts in industry, an important effort should be done in order to model working conditions for human operators and improve them. Several studies have been conducted for mass production assembly lines where short cycle times make the work content highly repetitive. However, the case of low-volume production with long cycle times and different impacts on human operators has been rarely considered in the literature. In this paper, we develop a model to take into account the associated ergonomic risks in assembly lines with long cycle times. An optimization method is also developed in order to schedule tasks and assign the required tasks to a set of human operators taking into account the existing ergonomic risks. [ABSTRACT FROM AUTHOR]

This paper proposes an uncertain random assignment problem in which random variables coexist with uncertain variables. Critical values of uncertain random variables are used to rank uncertain random variables. An uncertain random simulation algorithm is developed in order to obtain chance distributions and critical values of uncertain random variables. An α -optimistic model is presented. A combined optimization approach is designed to solve the α -optimistic model. This approach incorporates uncertain random simulation into branch and bound algorithm. Finally, an example application of the approach is presented. [ABSTRACT FROM AUTHOR]

Smart objects represent appliances enhanced by digital and interconnectable functionality, which are intended to support users in everyday life. By embedding sensors, these objects become input resp. interaction devices that stimulate the actuators of their own or other smart objects. However, due to a large number of objects to be expected, there also exist a number of challenges for the usability of such devices. In addition to the invisible nature of embedded digital functionality, wireless interconnections and possible changes in connectivity depending on the context, it is often not possible for users to explore the complete functionality of a smart object and interconnect them appropriately. In this paper, we present a dynamic approach for the automated interconnection of smart objects input and output capabilities with reference to the assignment problem. In addition to a formal definition, we present an evaluation of a naive approach and familiar algorithms for this problem. [ABSTRACT FROM AUTHOR]

We show how auction algorithms, originally developed for the assignment problem, can be utilized in Merriman, Bence, and Osher's threshold dynamics scheme to simulate multi-phase motion by mean curvature in the presence of equality and inequality volume constraints on the individual phases. The resulting algorithms are highly efficient and robust, and can be used in simulations ranging from minimal partition problems in Euclidean space to semi-supervised machine learning via clustering on graphs. In the case of the latter application, numerous experimental results on benchmark machine learning datasets show that our approach exceeds the performance of current state-of-the-art methods, while requiring a fraction of the computation time. [ABSTRACT FROM AUTHOR]

In this study we consider the Minimum Cost Bipartite Perfect Matching Problem with Conflict Pair Constraints (MCBPMPC) on bipartite graphs. Given a bipartite graph G with a cost associated with each edge and a conflict set of edge pairs, the MCBPMPC consists of finding a perfect matching with the lowest total cost such that no more than one edge is selected from each pair in the conflict set. A specially tailored branch-and-bound (B&B) algorithm is introduced. Computational experiments are performed on randomly generated instances. According to the extensive experiments, the suggested B&B algorithm yields promising results compared to a state-of-the-art mixed integer linear programming solver. [ABSTRACT FROM AUTHOR]

This paper introduces a variant of the well-known Multi-Depot Periodic Vehicle Routing Problem, which is inspired by a real situation of a distribution company. The problem consists in determining the number of extra vehicles to rent, the assignment of vehicles to plants, and the routes between plants and distribution centers, while the transportation cost is minimized. We propose a mixed integer linear formulation and a Reactive Greedy Randomized Adaptive Search Procedure to solve the problem. Extensive computational results show that the proposed procedure provides high-quality solutions with an average gap lower than 2.5% from the computed lower bound. [ABSTRACT FROM AUTHOR]

We consider combinatorial algorithms for the minimum-cost flow problem on networks with unit capacities, and special cases of the problem. Historically, researchers have developed special-purpose algorithms that exploit unit capacities. In contrast, for the maximum flow problem, the classical blocking flow and push-relabel algorithms for the general case also have the best bounds known for the special case of unit capacities. In this paper we show that the classical blocking flow push-relabel cost-scaling algorithms of Goldberg and Tarjan (Math. Oper. Res. 15, 430-466, 1990) for general minimum-cost flow problems achieve the best known bounds for unit-capacity problems as well. We also develop a cycle-canceling algorithm that extends Goldberg's shortest path algorithm (Goldberg SIAM J. Comput. 24, 494-504, 1995) to minimum-cost, unit-capacity flow problems. Finally, we combine our ideas to obtain an algorithm that solves the minimum-cost bipartite matching problem in $O(r^{1/2} m \log C)$ time, where m is the number of edges, C is the largest arc cost (assumed to be greater than 1), and r is the number of vertices on the small side of the vertex bipartition. This result generalizes (and simplifies) a result of Duan et al. (2011) and solves an open problem of Ramshaw and Tarjan (2012). [ABSTRACT FROM AUTHOR]