Assignment Problem Research Articles

A new mathematical model and meta-heuristic algorithm for order batching, depot selection, and assignment problem with multiple depots and pickers

The ‘order picking problem’ involves the efficient and organized retrieval of items from shelves to fulfill customer orders. In this study, we consider a new configuration of warehouse system with multiple pickers and depots (m-pickers & n-depots) for manually operated ‘picker-to-parts’ warehouses. The efficiency of the process is measured based on two metrics: i- total order picking distance of each picker ii- total number of pickers assigned to each of depots. The handled problem is called as ‘Order Batching, Depot Selection and Assignment Problem with Multiple Depots and Multiple Pickers (OBDSAPMDMP)11OBDSAPMDMP = Order Batching, Depot Selection, and Assignment Problem with Multiple Depots and Multiple Pickers.’. To solve this complex problem, a new bi-objective Mixed-Integer Linear Programming (MILP) formulation for small-sized problems and a meta-heuristic called ‘Dependent Harmony Search (DHS)22DHS = Dependent Harmony Search.’ for large-sized problems are proposed. The performance of DHS algorithm is evaluated by comparing the optimal results attained by MILP model. For the problem size of 10 orders, the average gap (%) in distance between the solution of DHS and MILP is 4.22%, although in some experiments DHS can find the optimal solution in a very short time. Also, in related analysis, it is seen that constructing multiple depots instead of one left-most located depot decreases total order picking distance by 7.11% on average.

Mapping the landscape of social behavior.

Social interaction is integral to animal behavior. However, we lack tools to describe it with quantitative rigor, limiting our understanding of its principles and neuropsychiatric disorders, like autism, that perturb it. Here, we present a technique for high-resolution 3D tracking of postural dynamics and social touch in freely interacting animals, solving the challenging subject occlusion and part assignment problems using 3D geometric reasoning, graph neural networks, and semi-supervised learning. We collected over 140 million 3D postures in interacting rodents, featuring new monogenic autism rat lines lacking reports of social behavioral phenotypes. Using a novel multi-scale embedding approach, we identified a rich landscape of stereotyped actions, interactions, synchrony, and body contact. This enhanced phenotyping revealed a spectrum of changes in autism models and in response to amphetamine that were inaccessible to conventional measurements. Our framework and large library of interactions will greatly facilitate studies of social behaviors and their neurobiological underpinnings.

A time-driven simulation–optimization framework for the dynamic heterogeneous order-courier assignment problem for instant deliveries

In recent years, instant delivery services have become very popular for transporting meals to urban areas, with an extensive range of products now available to order. The platforms that offer these services rely on crowdsourced couriers who utilize their personal vehicles, resulting in heterogeneous fleets. Furthermore, the competition among companies to retain both customers and couriers is very intense, which underscores the importance of developing superior decision support systems. These systems must generate real-time assignments that meet the expectations of service providers, customers, and couriers. In this study, we designed a time-driven simulation–optimization framework that addresses the dynamic heterogeneous order-courier assignment problem and incorporates order-vehicle restrictions. The framework efficiently manages real-time order arrivals, courier movements, and positional updates while considering dynamic factors such as traffic congestion and regional speed limits for various vehicle types. Extensive testing using literature instances demonstrated the framework’s ability to satisfactorily address the defined problem. Additionally, the time-driven simulation–optimization framework was applied to a realistic case study, resulting in an approximately 4.5% reduction in the total delivery times (from the submission of the order until the delivery to the client) for all orders when compared to the original assignment.

Dynamic soft-kill weapon-target assignment in naval environments

One of the most significant threats faced by ships is anti-ship missiles. Nowadays, these missiles, equipped with diverse guidance systems, can locate their trajectory and attack the ship. Consequently, ships need to utilize their weapons to attempt to neutralize these threats. This article aims to develop dynamic assignment algorithms to assign a ship’s defensive soft-kill weapons to a set of incoming missiles, to minimize the average damage inflicted on the ship. To this end, initially, a binary linear programming model is developed to solve the static weapon-target assignment problem. Subsequently, a simulation–optimization algorithm and a reinforcement learning-based approach, grounded in the value iteration algorithm, are developed to solve the dynamic weapon-target assignment problem. To compare and evaluate the performance of the developed solution methods, we employ a set of randomly generated test instances. Computational results indicate that the reinforcement learning approach, due to its inherent foresight, outperforms the simulation–optimization approach in reducing the inflicted damages. However, in terms of CPU run time, the simulation–optimization approach is more efficient.

Strategic manipulation of preferences in the rank minimization mechanism

We consider one-sided matching problems, where agents are allocated items based on stated preferences. Posing this as an assignment problem, the average rank of obtained matchings can be minimized using the rank minimization (RM) mechanism. RM matchings can have significantly better rank distributions than matchings obtained by mechanisms with random priority, such as Random Serial Dictatorship. However, these matchings are sensitive to preference manipulation from strategic agents. In this work we consider a scenario where agents aim to be matched to their top-n preferred items using the RM mechanism, and strategically manipulate their preferences to achieve this. We derive a best response strategy for an agent to be assigned to their n most preferred items using the Hungarian algorithm, under a simplified cost function. This strategy is then extended to a first-order heuristic strategy for being matched to the top-n items in a setup that minimizes the average rank. Based on this finding, an empirical study is conducted examining the impact of the first-order heuristic strategy. The study utilizes data from both simulated markets and real-world matching markets in Amsterdam, taking into account variations in item popularity, fractions of strategic agents, and the preferences for the n most favored items. For most scenarios, RM yields more rank efficient matches than Random Serial Dictatorship, even when agents apply the first-order heuristic strategy. However, although highly market dependent, the matching performance can become worse when 50% of agents or more want to be matched to their top-1 or top-2 preferred items and apply the first-order heuristic strategy to achieve this.

Algorithm Portfolios for Solving the Quadratic Assignment Problem

Introduction. The quadratic assignment problem is a well-established NP-hard problem in combinatorial optimization with applications in diverse fields like economics, archaeology, and chemistry. Due to its complexity, research on efficient solution methods remains active, including efforts for parallelization on multiprocessor computing systems. However, effective parallel algorithms are crucial to fully leverage these computational resources. In this context, algorithm unions (portfolios and teams) play a significant role in achieving parallel execution for solving such problems. Research objectives. This work investigates the application of portfolios constructed from modifications of the repeated iterated tabu search algorithm to the quadratic assignment problem. The effectiveness of these portfolios was evaluated through experimental computations. Results. The portfolios, derived from modifications of the repeated iterated tabu search algorithm, were applied to the quadratic assignment problem. For the most demanding test instances, the proposed algorithms were evaluated on the SCIT-4 supercomputer, alongside previously published results from the authors, confirming their competitive performance. Additionally, we assessed the parallel efficiency of these portfolios in solving instances of the quadratic assignment problem. The results demonstrate their ability to accelerate the optimization process (with speedup dependent on problem size and utilized processors), enabling the solution of large-scale problems. Conclusions. The conducted studies demonstrate that employing algorithm portfolios significantly accelerates the solution process for the quadratic assignment problem. Analysis of the results reveals a near-linear speedup factor achieved by the portfolio. For the challenging test instance tai100a, a new best solution value of 21040996 was obtained using a portfolio of 16 algorithms. Keywords: quadratic assignment problem, algorithm portfolios, experimental research, algorithm portfolios efficiency.

An Elite Wolf Pack Algorithm Based on the Probability Threshold for a Multi-UAV Cooperative Reconnaissance Mission

In the task assignment problem of multi-UAV collaborative reconnaissance, existing algorithms have issues with inadequate solution accuracy, specifically manifested as large spatial spans and knots of routes in the task execution of UAVs. To address the above challenges, this paper presents a multi-UAV task assignment model under complex conditions (MTAMCC). To efficiently solve this model, this paper proposes an elite wolf pack algorithm based on probability threshold (EWPA-PT). The EWPA-PT algorithm combines the wandering behavior in the traditional wolf pack algorithm with the genetic algorithm. It introduces an ordered permutation problem to calculate the adaptive wandering times of the detective wolves in a specific direction. During the calling phase of the algorithm, the fierce wolves in the wolf pack randomly learn the task assignment results of the head wolf. The sieging behavior introduces the Metropolis criterion from the simulated annealing algorithm to replace the distance threshold in traditional wolf pack algorithms with a probability threshold, which dynamically changes during the iteration process. The wolf pack updating mechanism leverages the task assignment experience of the elite group to reconstruct individual wolves, thereby improving the individual reconstruction’s efficiency. Experiments demonstrate that the EWPA-PT algorithm significantly improves solution accuracy compared to typical methods in recent years.

A cooperative task assignment framework with minimum cooperation cost in crowdsourcing systems

Crowdsourcing provides a new problem-solving paradigm that utilizes the intelligence of crowds to solve computer-hard problems. Task assignment is a foundation problem in crowdsourcing systems and applications. However, existing task assignment approaches often assume that workers operate independently. In reality, worker cooperation is necessary. In this paper, we address the cooperative task assignment (CTA) problem where a worker needs to pay a monetary cost to another worker in exchange for cooperation. Cooperative working also requires one task to be assigned to more than one worker to ensure the reliability of crowdsourcing services. We formalize the CTA problem with the goal of minimizing the total cooperation cost of all workers under the workload limitation of each worker. The challenge is that the individual cooperation cost that a worker pays for a specific task highly depends on the task distribution. This increases the difficulty of obtaining the assignment instance with a small cooperation cost. We prove that the CTA problem is NP-hard. We propose a two-stage cooperative task assignment framework that first assigns each task to one worker and then makes duplicate assignments. We also present solutions to address the dynamic scenarios. Extensive experimental results show that the proposed framework can effectively reduce the cooperation cost.

An assignment-based decomposition approach for the vehicle routing problem with backhauls

In the context of the Vehicle Routing Problem with Backhauls, which involves delivering to linehaul and picking up from backhaul customers, we propose a novel mathematical model that can decompose the main problem into three sub-problems: two Open Vehicle Routing Problems and one Assignment Problem. In our proposed model, Open Vehicle Routing Problems optimize routes for homogeneous vehicles serving linehaul/backhaul customers, while the Assignment Problem matches linehaul and backhaul routes. We utilize Lagrangian decomposition approach and solve subproblems in parallel and sequential layouts. We measure the performance of the foregoing arrangements (in terms of solution quality and computational efficiency) by testing our model on two benchmark datasets, proposed by Goetschalckx and Jacobs-Blecha (1989) and Toth and Vigo (1997) and are known as GJ and TV datasets in the extant literature, respectively. Our model matches best known solutions in 35 % and 33 %, with most within 2 % deviation, for GJ and TV instances, respectively. We also showcase our model on a real-world transportation network containing 100, 250, and 500 customers and geographically located in Lansing, Michigan. To reduce the computational burden of solving the Vehicle Routing Problem with Backhauls on the Lansing dataset, we present a cluster first-route second algorithm and then analyze the impact of vehicle capacity on the solution quality of our proposed algorithm.

A neural mechanism for learning from delayed postingestive feedback.

Animals learn the value of foods based on their postingestive effects and thereby develop aversions to foods that are toxic1-6 and preferences to those that are nutritious7-14. However, it remains unclear how the brain is able to assign credit to flavors experienced during a meal with postingestive feedback signals that can arise after a substantial delay. Here, we reveal an unexpected role for postingestive reactivation of neural flavor representations in this temporal credit assignment process. To begin, we leverage the fact that mice learn to associate novel15-18, but not familiar, flavors with delayed gastric malaise signals to investigate how the brain represents flavors that support aversive postingestive learning. Surveying cellular resolution brainwide activation patterns reveals that a network of amygdala regions is unique in being preferentially activated by novel flavors across every stage of the learning process: the initial meal, delayed malaise, and memory retrieval. By combining high-density recordings in the amygdala with optogenetic stimulation of genetically defined hindbrain malaise cells, we find that postingestive malaise signals potently and specifically reactivate amygdalar novel flavor representations from a recent meal. The degree of malaise-driven reactivation of individual neurons predicts strengthening of flavor responses upon memory retrieval, leading to stabilization of the population-level representation of the recently consumed flavor. In contrast, meals without postingestive consequences degrade neural flavor representations as flavors become familiar and safe. Thus, our findings demonstrate that interoceptive reactivation of amygdalar flavor representations provides a neural mechanism to resolve the temporal credit assignment problem inherent to postingestive learning.

A Novel Score Function for Spherical Fuzzy Sets and Its Application to Assignment Problem

A Novel Score Function for Spherical Fuzzy Sets and Its Application to Assignment Problem

Runway assignment optimisation model for Istanbul Airport considering multiple parallel runway operations

Abstract The aviation industry has rapidly developed in recent years. Due to the increased number of flight operations, managing air traffic has become essential. The air traffic management system aims to reduce the air traffic control workload and use existing resources more efficiently. This study proposed a new mixed integer linear programming model to minimise the total fuel consumption during taxi operations for the runway assignment problem, comparing the actual Istanbul Airport runway assignment data. The average taxi times are calculated using the 30,000-flight operations data for each arrival and departure taxi route. Also, 47 different aircraft types are obtained using the data for the fuel consumption calculation. The International Civil. Aviation Organisation (IACO) aircraft engine emissions databank provides the fuel consumption values for each aircraft according to engine type. This approach allows our model to calculate more realistic fuel consumption for taxi operations, as each aircraft engine type has a different fuel consumption value. The proposed model is implemented at Istanbul Airport, the busiest airport in Turkey, where multiple parallel runway operations are applied. The results showed that the proposed model reduced total fuel consumption for taxi operations between 6.6% and 14.4% compared to the actual Istanbul Airport runway assignment data.

Study on Single-Machine Common/Slack Due-Window Assignment Scheduling with Delivery Times, Variable Processing Times and Outsourcing

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.

An agent-based simulation modeling framework for Mobility-as-a-Service (MaaS)

This study develops an agent-based intelligent Mobility-as-a-Service (MaaS) simulation model consisting of three types of agents (i.e., MaaS fleet unit, travelers, and central intelligent mobility assignment module) to assess mobility service assignment processes balancing conflicting entities (e.g., demand and supply) within the MaaS ecosystem. The study follows a two-level optimization method (i.e., lower, and upper levels). It employs artificial intelligence and multicriteria decision making to solve two-dimensional mobility assignment problems (demand vs. supply). The novelty of this assignment process is that it implements an intelligence module accounting for the past system performance to make a future assignment decision in favor of both sides of the operation. This study processes 24-hour trip requests extracted from Nova Scotia Travel Activity (NovaTRAC) survey data in real-time. Two scenarios (1-D and 2-D assignments) are compared using the cost criteria, such as total waiting time, empty time, and idle time. The 1-D scenario refers to mobility assignment that emphasizes the demand side only, and the 2-D scenario formulates mobility assignment by balancing the demand and supply sides of the MaaS ecosystem. Experimental results indicate that a MaaS fleet of 350 units is the most balanced fleet in both scenarios. However, the 2-D optimization method reduces the overall supply cost by 25%. Moreover, 2-D operation demonstrates a higher fleet utilization over a considerable period, whereas the 1-D design guarantees a higher fleet utilization only during the peak period. Results of this study provide us with a benchmark for assessing more complex MaaS operation scenarios which will further aid in advancing the operational MaaS ecosystem. Our findings can help policymakers implement cost-effective MaaS solutions supporting sustainable urban mobility and SDG 13: Climate Action.

Integrating storage allocation with manual order picking and replenishment operations in a distribution centre

ABSTRACT This paper introduces a mathematical programming formulation and a simulation-based heuristic for the allocation of storage positions to products picked by human operators on man-aboard vehicles traveling through the warehouse of a wholesale company. In this problem, the tactical level of the assignment decisions affects the operational level of the picking process. We propose a simulation-optimisation framework that integrates the two. Our formulation of the storage location assignment problem also handles the constraint according to which a picking position should be paired with a (vertical) replenishment position for a given item. To solve realistic instances, we design an iterated local search (ILS) metaheuristic with an embedded discrete-event simulator (DES) that evaluates the most promising moves at each iteration. The DES allows reproducing the handling operations performed by multiple order pickers under uncertainty, mutual interferences and congestion-related phenomena. Overall, the flexible simulation-optimisation (SO) framework evaluates the operational times and daily productivity of the order picking organisation. Numerical results are presented for real data, under an S-shape picking policy with a skip-and-go rule to deal with lacking items. Under a proper tuning of the ILS parameters, the SO framework allows to achieve a nearly 17% improvement in warehouse productivity.

The ascending auction with flexible reporting

In the assignment problem where multiple heterogeneous indivisible items are assigned to unit-demand bidders, we introduce a novel ascending auction called the Flexible Reporting Ascending Auction to balance the privacy preservation and the speed of the ascending auction. Assuming bidders behave truthfully, it always results in a Walrasian equilibrium, along with the minimum Walrasian equilibrium price vector. If each bidder reports without a contradiction, bidders’ truthful behavior forms a Nash equilibrium. Our auction generalizes some well-known ascending auctions in literature, and we also provide simulation results to compare these auctions.

Integrated train timetable with supply–demand interactions at the Chinese high-speed railway

In traditional Chinese railway operations, train timetable and unit assignment are usually separated from pricing and seat allocation, resulting in a decrease in revenue and an increase in operating costs. In this paper, we study the integrated problem of train timetable, unit assignment, pricing, and seat allocation, where passenger choice behavior is modeled by the multinomial logit (MNL) model. This integration enables us to explicitly capture supply–demand interactions. The problem is formulated as a mixed integer nonlinear programming model with the objective of maximizing total profit. By converting the MNL model into its equivalent convex form, we recast the model as a tractable reformulation, allowing the use of a general-purpose solver to solve practical-sized instances. Based on real data from high-speed railway lines in China, three sets of case studies are conducted to validate the effectiveness and efficiency of the proposed approach.

Solving the storage location assignment of large-scale automated warehouse based on dynamic vortex search algorithm

This paper establishes the mathematical model for Storage Location Assignment (SLA) problem in large-scale automated warehouses by combining three objectives: efficiency, shelf stability, and stacker load balancing. Along with a novel repair strategy to handle the complex constraints of large-scale problems. Additionally, a coding method and solution approach suitable for practical application scenarios are developed. In order to solve large-scale SLA problem, an improved vortex search algorithm is proposed based on attraction operation in flow field, dimension-by-dimension dynamic radius and leadership decision-making mechanism (FDVSA). In the experimental part, the algorithm effectiveness experiment of FDVSA was first conducted using the large-scale global optimization test sets IEEE congress on evolutionary computation 2010 and 2013 (CEC2010, CEC2013). The results show that: (1) Compared with other comparison algorithms, the comprehensive average optimization rate of FDVSA in CEC2010 and CEC2013 is 88 % and 78 %, respectively. (2) The experimental results of FDVSA showed that each improvement strategy has advantages in dealing with large-scale problems. (3) The post-hoc analysis showed that there are significant differences between FDVSA and other comparison algorithms, and FDVSA is significantly better. Finally, FDVSA and other comparison algorithms are solved on three different scale and complexity of SLA cases. The results show that: (1) FDVSA has significant advantages in solving large-scale SLA problem, and the comprehensive average optimization rate is 19 %. (2) The convergence curve and boxplot showed that FDVSA has good convergence speed and solving stability. (3) The effectiveness of the repair strategy was verified by experiments in the large-scale SLA problems.

A New Integer Model for Selecting Students at Higher Education Institutions: Preparatory Classes of Engineers as Case Study

This study addresses the challenge of selecting outstanding students at higher education institutions under multiple constraints. We propose a novel integer programming solution to manage this process, formulating it as a constrained assignment problem with a maximization objective function. This function prioritizes the fair selection of students while respecting criteria such as academic qualifications, required skills, and student preferences. The goal is to develop a decision support system that efficiently selects qualified students at higher education institutions within a reasonable time. The model was tested using real data from Moroccan preparatory classes, achieving important assignment rates across all student categories. Results demonstrate significance in execution time, fulfillment of student choices, and prioritization of outstanding students. This approach offers a flexible, efficient solution for managing academic merit-based selections, optimizing resource utilization, and enhancing fairness in the selection process.

A novel framework for production planning and class-based storage location assignment: Multi-criteria classification approach

Efficient warehouse management is essential for optimizing inventory, minimizing transportation costs, and enhancing overall performance. This research introduces a novel Mixed-Integer Nonlinear Programming (MINLP) model to address the Storage Location Assignment Problem (SLAP) in warehouse management. Integrating multi-criteria decision-making with strategic production planning, our model advances warehouse operations by allocating storage locations to products strategically, focusing on reducing transportation distances and maximizing storage efficiency. The distinctive innovation of this study is the nuanced application of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) results to strategic storage location assignments, enhancing the model's capability to consider a comprehensive evaluation of inventory attributes, including physical characteristics and perishability. This approach evolves TOPSIS's application in warehouse management, enabling it to consider both physical characteristics and perishability of products. The outcomes of TOPSIS, including product classifications and preferences, serve as vital inputs to the mathematical model, facilitating a comprehensive evaluation of storage locations that encompasses spatial, demand-related, and physical aspects of inventory. Additionally, our research introduces a versatile decision support system, adaptable to various operational requirements. This system enhances practical decision-making in warehouse management, accommodating scenarios based on single or multiple criteria, including the cube-per-order index (COI). The research results highlight the significant impact of this innovative approach in enhancing warehouse management. By addressing the complexities of storage location assignment and integrating multiple criteria, we achieve more efficient and cost-effective warehouse operations. The approach has been shown to be adaptable and practical, making it a valuable contribution to the field of logistics and warehouse management.