Small-sized Instances Research Articles

Minimizing the sum of earliness and tardiness in the multi-factory two-stage assembly scheduling problem

ABSTRACT The geographical dispersion of collaborative factories can provide cost-saving potential for manufacturers and lead them to easier fit the global markets. On the other hand, in such networks of factories, coordination is especially important for the just-in-time delivery of orders. This study investigates a new configuration of factories in a network of collaborative manufacturing. In the first stage, some independent suppliers produce and deliver the different components of the final products to the assembly factory. Each supplier can produce a particular component of a final product. In the assembly factory, the final products are assembled. The objective is to determine the optimal schedule of the jobs in each factory to minimize the sum of earliness and tardiness. A mixed-integer formulation for this problem is proposed, which can find the optimal solution for the small-size instances. The iterated local search methods are also developed to cope with larger instances. Computational experiments show that the iterated local search methods outperform the well-known iterated greedy method in literature.

Solving the yard crane scheduling problem with dynamic assignment of input/output points

This paper introduces an automatic yard crane scheduling problem with additional assignments of input/output (I/O) points at the block. I/O points are the buffer between the block and the rest of the terminal and containers are relocated from the block to the I/O points or vice-versa. The crane schedule therefore not only considers movements, storage and retrieval of containers, but must also be coordinated with the release and due times of containers at the I/O points, which are also limited and need to be assigned during the scheduling process. This results in a complex, but at the same time, more realistic problem. Two GRASP (Greedy Randomized Adaptive Search Procedure) heuristic approaches are proposed along with improvements to the solution construction and local search phases that are specifically tailored for this problem. The proposed algorithms are statistically calibrated and comprehensive experiments are designed to assess the performance of the method, including validation across small, medium, and large size instances. The experimental results show that the proposed methods are effective and competitive when compared to existing approaches. The GRASP manages to obtain an optimality average rate of 71.25% for small instances and finds 461 new best solutions in the 480 medium and large instances, with up to 200 containers, when compared to existing approaches for this problem.

Robust optimization algorithm for integrated crane assignment and scheduling in slab yard with uncertain arrival time

A slab yard served as a key component of the iron and steel plant. Effective slab yard crane assignment and scheduling directly affect the overall efficiency of the steel production process. This work addresses an uncertain slab yard crane assignment and scheduling problem (SYCAS) with the fluctuating arrival time. A stochastic programming model is established to obtain a robust solution that minimises the completion time of slab groups under uncertainty. Due to its NP-hardness, we developed an improved column and cut generation method (IC&CG), which divides the problem into a relaxed master problem (RMP) and a slave problem (SP). A new initialisation strategy for obtaining high-quality solutions and an acceleration strategy for discarding irrelevant scenarios are proposed. We use small-size instances to compare the performance of IC&CG with CPLEX and a generalised column and cut generation method in both deterministic and uncertain environments to validate the effectiveness of the method. For large-size instances, a lower bound (LB) of the optimal objective function is proposed to show the effectiveness of IC&CG. Furthermore, we prove the robustness of the method by sensitive analysis.

Supermarket-chain grocery delivery optimization through crowdshipping

Acknowledging the rising significance of online sales, the grocery business has embraced the challenge of fulfilling the consequently growing consumer expectations for the last-mile delivery efficiency. This paper investigates the grocery delivery optimisation for the supermarket chain based on the crowdshipping mechanism, which can be one of the viable strategies for establishing prompt and affordable delivery service for customers. Considering the deterministic optimisation setting, this study presents a characteristic routing model with crowdsourced couriers named supermarket-chain grocery delivery crowdshipping problem (SCGDCP), which is a variant of the pickup-and-delivery problem, and develops a corresponding mixed integer linear programming (MILP) model. The SCGDCP involves distinctive problem features including individual depots for couriers, multi-trip open routing, and dual time windows of courier operating and order arrival, which pose the computational challenge in problem solving. A bespoke solution procedure based on adaptive variable neighbourhood search (AVNS) strategy is thus designed for tackling the practical-size SCGDCP. The conducted numerical experiments demonstrate the computational efficiency of the proposed MILP model for the small-size instances with no more than 30 grocery orders and the superiority of the developed AVNS procedure for the Grubhub sampling test instances with up to 200 orders.

A Swarm Intelligence Solution for the Multi-Vehicle Profitable Pickup and Delivery Problem

Delivery apps are experiencing significant growth, requiring efficient algorithms to coordinate transportation and generate profits. One problem that considers the goals of delivery apps is the multi-vehicle profitable pickup and delivery problem (MVPPDP). In this paper, we propose eight new metaheuristics to improve the initial solutions for the MVPPDP based on the well-known swarm intelligence algorithm, Artificial Bee Colony (ABC): K-means-GRASP-ABC(C)S1, K-means-GRASP-ABC(C)S2, Modified K-means-GRASP-ABC(C)S1, Modified K-means-GRASP-ABC(C)S2, ACO-GRASP-ABC(C)S1, ACO-GRASP-ABC(C)S2, ABC(S1), and ABC(S2). All methods achieved superior performance in most instances in terms of processing time. For example, for 250 customers, the average times of the algorithms was 75.9, 72.86, 79.17, 73.85, 76.60, 66.29, 177.07, and 196.09, which were faster than those of the state-of-the-art methods that took 300 s. Moreover, all proposed algorithms performed well on small-size instances in terms of profit by achieving thirteen new best solutions and five equal solutions to the best-known solutions. However, the algorithms slightly lag behind in medium- and large-sized instances due to the greedy randomised strategy and GRASP that have been used in the scout bee phase. Moreover, our algorithms prioritise minimal solutions and iterations for rapid processing time in daily m-commerce apps, while reducing iteration counts and population sizes reduces the likelihood of obtaining good solution quality.

A learning-based granular variable neighborhood search for a multi-period election logistics problem with time-dependent profits

Planning the election campaign for leaders of a political party is a complex problem. The party representatives, running mates, and campaign managers have to design an efficient routing and scheduling plan to visit multiple locations while respecting time and budget constraints. Given the limited time of election campaigns in most countries, every minute should be used effectively, and there is very little room for error. In this paper, we formalize this problem as the multiple Roaming Salesman Problem (mRSP), a new variant of the recently introduced Roaming Salesman Problem (RSP), where a predefined number of political representatives visit a set of cities during a planning horizon to maximize collected rewards, subject to budget and time constraints. Cities can be visited more than once and associated rewards are time-dependent (increasing over time) according to the day of the visit and the recency of previous visits. We develop a compact Mixed Integer Linear Programming (MILP) formulation complemented with effective valid inequalities. Since commercial solvers can obtain optimal solutions only for small-sized instances, we develop a Learning-based Granular Variable Neighborhood Search and demonstrate its capability of providing high-quality solutions in short CPU times on real-world instances. The adaptive nature of our algorithm refers to its ability to dynamically adjust the neighborhood structure based on the progress of the search. Our algorithm generates the best-known results for many instances.

Multi-objective shipment consolidation and dispatching problem

In recent years, with the increase in global production and demand, transportation problems have become a widely studied area, and studies focus on providing high-quality service at the lowest cost. This study considers a bi-objective shipment consolidation and dispatching problem with the objectives of minimizing the total cost and the total distance. To the best of our knowledge, this is the first study to include both objectives in this problem. Additionally, different from the literature, where usually predefined routes are assumed, we incorporate the routing decisions in our model. In order to create a non-dominated solution set, a multi-objective mixed integer linear programming model is developed and augmented ϵ-constraint method is used to generate the non-dominated frontier. However, this approach is not capable of finding the non-dominated solution set in a reasonable time, even for small-sized instances, and therefore, we propose a multi-objective variable neighborhood search heuristic. To measure the performance of the proposed approach, a computational experiment is conducted on randomly generated instances available in the literature. The experimental results indicate that the multi-objective variable neighborhood search heuristic performs efficiently in reasonable time.

Test Center Location Problem: A Bi-Objective Model and Algorithms

The optimal placement of healthcare facilities, including the placement of diagnostic test centers, plays a pivotal role in ensuring efficient and equitable access to healthcare services. However, the emergence of unique complexities in the context of a pandemic, exemplified by the COVID-19 crisis, has necessitated the development of customized solutions. This paper introduces a bi-objective integer linear programming model designed to achieve two key objectives: minimizing average travel time for individuals visiting testing centers and maximizing an equitable workload distribution among testing centers. This problem is NP-hard and we propose a customized local search algorithm based on the Voronoi diagram. Additionally, we employ an ϵ-constraint approach, which leverages the Gurobi solver. We rigorously examine the effectiveness of the model and the algorithms through numerical experiments and demonstrate their capability to identify Pareto-optimal solutions. We show that while the Gurobi performs efficiently in small-size instances, our proposed algorithm outperforms it in large-size instances of the problem.

Bi-objective scheduling of physical therapy treatments with coupled operations for inpatients in rehabilitation departments

In recent years, the field of physical therapy has experienced significant growth, particularly due to the impact of the Covid-19 pandemic. However, the capacity of rehabilitation services remains inadequate. This current study deals with scheduling physical therapies with coupled operations and multiple resources in rehabilitation departments, considering bi-objective optimization by minimizing both makespan and waiting time. Based on detailed analysis of practical operations, a mixed integer linear programming model is formulated. For small-size instances, optimal solutions can be obtained using software such as Gurobi. To handle large instances, a compound NSGA-II algorithm (CNSGA-II) is proposed. CNSGA-II consists of First-NSGA-II and Second-NSGA-II, which are associated with patient sequences and their respective treatments. Furthermore, practical heuristics are used to improve the initial solutions for CNSGA-II. The results of a real-work instance show that makespan is reduced by approximately 8.0%–10.8% and the maximum waiting time is reduced by about 26.4%–30.0%, comparing to the Queue Length Priority Algorithm commonly used in practice. The proposed CNSGA-II is further assessed using randomly generated instances and compared to MOEA/D and NSGA-II based on HV and IGD metrics. The results indicate the superior performance and effectiveness of the proposed CNSGA-II algorithm.

The multi-factory two-stage assembly scheduling problem

The recent notable focus on distributed production management in academic and industrial contexts has underscored the importance of scheduling across multiple factories. Accordingly, this study investigates a new multi-factory configuration in which non-identical factories produce different components of a final product in the first stage. Each factory is considered as a classical flow-shop, which can manufacture a unique component. These components are assembled into final products in the assembly factory, which is located in the second stage. Unlike other distributed scheduling problems, to determine a united production sequence in such a system, there is no need to find a suitable factory to assign a job since each factory is qualified for a particular task. In real-world applications, these systems encounter challenges that span from information architectures and negotiation mechanisms to the development of scheduling algorithms. The objective of this research is to schedule the jobs in each factory to minimize the makespan of the entire process. For this purpose, a mixed-integer programming model is developed to deal with small-size instances. Then, the lower bound is derived and incorporated to develop a branch and bound method. Furthermore, to deal with larger instances, five heuristic methods are developed, and the worst-case analysis is carried out. Computational experiments are conducted for different test classes to compare and to highlight the performance of the proposed solution procedures.

New features for customer classification in the Flying Sidekick Traveling Salesman Problem

The increasing interest in the deployment of truck and drone delivery systems leads to the definition of new and complex vehicle routing problems. In this context, the flying sidekick traveling salesman problem (FS-TSP) is the first truck-and-drone routing problem defined in the literature. Several variants appeared in the last years differing in the operating conditions and the structure of the hybrid truck-and-drone delivery system. Exact and heuristic solution methods have been proposed in the literature to solve these problems effectively. However, the exact solution methods can generally solve only small-size instances due to the complexity of these problems. On the other hand, heuristic solution methods are able to find feasible solutions with an acceptable computational burden but without any guarantee of the quality of the solution. This work aims to investigate the possibility of using data science and machine learning techniques to reduce the complexity of solving an FS-TSP instance. The idea is to determine a good/optimal customer-to-vehicle assignment apriori to reduce the number of decisions involved in the FS-TSP solution. The assignment is determined through the classification of customers based on a subset of features specifically defined for the FS-TSP. This information can be exploited by existing solution approaches for the FS-TSP to improve their performance. An extensive computational campaign on benchmark instances is carried out with a twofold objective. On the one hand, we aim to evaluate the impact of the features on customer classification. On the other hand, we intend to show the relationship between classification and combinatorial optimization results by observing the effect of the customer classification on the FS-TSP solution.

Demand Allocation and Lot-Sizing Solution of Single Product Deterministic Demand

In this study, a two-phase algorithm has been developed to address the single-product supplier selection and order allocation problem (SP-SSOAP). In the first phase, a novel demand allocation algorithm is developed using a recursive demand equation. Subsequently, an adaptive genetic algorithm is employed in the second phase, with additional constraints for capacity and minimum order quantity, to determine the best lot-sizing plan for each supplier. Experimental results demonstrate that, on average, the proposed heuristic achieves an objective value within 1% of the optimal solution for small-sized instances and outperforms the previous heristic solution by an average of 12% in terms of objective value for larger problems. Additionally, the numerical results emphasize that the proposed method performs better when input parameters such as price, ordering cost, and holding cost exhibit lower fluctuations. This suggests that managers should focus on improving supplier relationships and coordination strategies to reduce variability in price, order cost, and holding cost.

Minimizing the maximum tardiness for a permutation flow shop problem under the constraint of sequence independent setup time

In this work, we will study a permutation flow shop scheduling problem under the constraint of sequence independent setup time. In our case, each machine requires a certain setup time to process all the different jobs assigned to it. Hence, this setup time will be independent of sequence of jobs, but will depend only on the nature of machine. The optimization objective is to minimize the maximum tardiness criterion. To solve this optimization problem, an exact method, heuristics and metaheuristics are the three main resolution methods that we have used. The exact method is represented by the mixed integer linear programming (MILP) model. In terms of the second category of resolution methods, we have been focused on two methods, the first is a modified heuristic based on Johnson rule (HBJR) while the second is based on the Nawaz–Enscore–Ham (NEH) algorithm. Finally, three metaheuristics have been used, namely the iterated local search (ILS) method, the iterated greedy (IG) algorithm and the genetic algorithm (GA). Our numerical results indicate that for the problems with small size instances, the NEH heuristic outperforms HBJR approach, while for relatively large size instances, the developed IG algorithm gives best results than both other metaheuristics ILS and GA.

The Flexible Job Shop Scheduling Problem with Setups and Operator Skills: an application in the textile industry

The Flexible Job Shop Scheduling Problem (FJSSP) is one of the most studied problems in the literature thanks to its practical relevance. Many industrial production scheduling problems can be seen as a FJSSP with different constraints and objectives. The studied problem arises in a textile factory, precisely in the sewing process. Multiple real-world constraints are tackled. Individual skills of operators and different types of setup times are considered: machine-change setup time for operators, colour-change setup times and configuration-change setup times. The objective is to minimize the total tardiness. To the best of the authors’ knowledge, this is the first study that tackles this variant of the problem. This paper presents a preliminary study to validate the approach and evaluate the tractability of the industrial problem. A mixed-integer linear programming (MILP) model is proposed and solved using a commercial solver. Real-world data are used to generate more than 1000 problems that are clustered in 4 groups based on the number of jobs to be scheduled, the number of operators and flexibility of their skills. The results show that the proposed MILP model can reach optimality for the small size instances but it is intractable for most large-sized instances. Moreover, the results highlight how diversifying the operators’ skills can help find better solutions.

A hybrid genetic algorithm based on reinforcement learning for the energy-aware production scheduling in the photovoltaic glass industry

Recently, the growing solar energy capacity has played a significant role in developing a clean energy supply system in China. However, the resulting rapid expansion of photovoltaic component (e.g., glass) manufacturing intensifies the energy demand in the locality of the plant. Therefore, this paper considers the energy-aware production scheduling of a deep-processing line in the photovoltaic glass plant, whose layout is a hybrid flow shop with batch and non-batch machines. Firstly, we establish a mixed integer programming model with the minimization of the energy consumption and the penalty for excess of the due date. Then, we propose a hybrid genetic algorithm (GA) based on reinforcement learning to solve the problem. Specifically, the expected Sarsa is used to extract critical knowledge about algorithmic parameters during the population evolution to guide the exploration of the GA. Finally, we conduct extensive numerical experiments to validate the effectiveness of the proposed algorithm by comparing it with a commercial optimization solver and other metaheuristics. The numerical results show that the average gap between the solver and the proposed algorithm is around 4% in small-sized instances. Compared with the heuristic used in the plant, the improvements of this paper are about 16%∼18% and 17%∼21% in practical-sized instances for the delay penalty and energy consumption objectives, respectively. In addition, the computational results provide managerial insights for managers in further pursuing energy efficiency from higher-level decision-making, e.g., planning over multiple periods from a tactical perspective, and changing production line configurations and introducing new processing techniques from a strategic perspective.

Self-adaptive General Variable Neighborhood Search algorithm for parallel machine scheduling with unrelated servers

This paper introduces a machine learning-augmented General Variable Neighborhood Search algorithm, termed Self-adaptive General Variable Neighborhood Search (SGVNS), for solving the two-identical parallel machine scheduling problem with unrelated servers. The studied problem is of high practical relevance in various industries and presents a significant gap in the existing literature. The motivation for this study stems from the healthcare industry, specifically surgery scheduling with limited anesthesiologists’ availability. Two mathematical formulations are presented to solve this scheduling problem. However, these formulations are limited to small-scale problems, prompting the need for an efficient metaheuristic. Therefore, a novel variant of the General Variable Neighborhood Search metaheuristic is developed, incorporating a self-adaption mechanism based on an Extreme Learning Machine (ELM) algorithm. Extensive experiments are conducted to assess the performance of the SGVNS metaheuristic on various classes of instances. The results demonstrate the effectiveness and efficiency of SGVNS in solving previously unsolved small-sized instances, outperforming both formulations while maintaining reasonable computation times.

An artificial bee colony algorithm for medical goods distribution and pharmacological waste collection by hybrid vehicles considering environmental criteria

PurposeThis paper aims to focus on a medical goods distribution problem and pharmacological waste collection by plug-in hybrid vehicles with some real-world restrictions. In this research, considering alternative energy sources and simultaneous pickup and delivery led to a decrease in greenhouse gas emissions and distribution costs, respectively.Design/methodology/approachHere, this problem has been modeled as mixed-integer linear programming with the traveling and energy consumption costs objective function. The GAMS was used for model-solving in small-size instances. Because the problem in this research is an NP-hard problem and solving real-size problems in a reasonable time is impossible, in this study, the artificial bee colony algorithm is used.FindingsThen, the algorithm results are compared with a simulated annealing algorithm that recently was proposed in the literature. Finally, the results obtained from the exact solution and metaheuristic algorithms are compared, analyzed and reported. The results showed that the artificial bee colony algorithm has a good performance.Originality/valueIn this paper, medical goods distribution with pharmacological waste collection is studied. The paper was focused on plug-in hybrid vehicles with simultaneous pickup and delivery. The problem was modeled with environmental criteria. The traveling and energy consumption costs are considered as an objective function.

A bi-objective optimization for finance-based and resource-constrained robust project scheduling

Numerous finance-based projects encounter disturbances from a variety of uncertain factors during their execution, under which both the original baseline schedule and financing alternative become infeasible. However, many previous studies on the finance-based project scheduling problem (FBSP) neglected a potential feature of stochastic activity durations. In this paper, we address the issue of generating a robust project schedule that not only satisfies financing credit and renewable resource limits, but also tackles disruptions due to activity uncertainty. A bi-objective model for finance-based and resource-constrained robust project scheduling problem (FBRCRPSP) is constructed, where the trade-off between profit and robustness is considered. Based on the transformed integer programming model, an exact procedure of ε- constraints is proposed to obtain Pareto-optimal solutions for small-sized instances. For large-scale projects, a non-dominated sorting genetic algorithm with local search (NSGA-II-LS) that deeply explores the neighboring solution space is developed, in which a generic procedure with two new recursion policies is proposed to determine the robustness of schedules. Benchmarking is conducted to evaluate the efficiency of the algorithms via some performance criteria. The results show that all developed approaches have good performance in small-sized instances, and the NSGA-II-LS outperforms the non-dominated sorting genetic algorithm without local search (NSGA-II) in terms of the spread, convergence, and diversity of Pareto-optimal solutions significantly. In addition, some managerial insights are summarized to enlighten project managers.

Global optimization for cardinality-constrained minimum sum-of-squares clustering via semidefinite programming

AbstractThe minimum sum-of-squares clustering (MSSC), or k-means type clustering, has been recently extended to exploit prior knowledge on the cardinality of each cluster. Such knowledge is used to increase performance as well as solution quality. In this paper, we propose a global optimization approach based on the branch-and-cut technique to solve the cardinality-constrained MSSC. For the lower bound routine, we use the semidefinite programming (SDP) relaxation recently proposed by Rujeerapaiboon et al. (SIAM J Optim 29(2):1211–1239, 2019). However, this relaxation can be used in a branch-and-cut method only for small-size instances. Therefore, we derive a new SDP relaxation that scales better with the instance size and the number of clusters. In both cases, we strengthen the bound by adding polyhedral cuts. Benefiting from a tailored branching strategy which enforces pairwise constraints, we reduce the complexity of the problems arising in the children nodes. For the upper bound, instead, we present a local search procedure that exploits the solution of the SDP relaxation solved at each node. Computational results show that the proposed algorithm globally solves, for the first time, real-world instances of size 10 times larger than those solved by state-of-the-art exact methods.

Synchronizing delivery and installation with vehicle sharing: A hybrid adaptive large neighborhood search

This paper presents the real-life synchronized delivery and installation with vehicle sharing problem (SDIVSP). Two fleets of vehicles serve a set of customers within their specified time windows. Delivery vehicles drop products to customers while installation vehicles drop and pick up technicians without necessarily waiting for them. Delivery must precede installation. This paper models SDIVSP as a mixed integer linear program, which solves small-sized instances. For large instances, this paper proposes a heuristic HALNS that hybridizes adaptive large neighborhood search and variable neighborhood search. Extensive experimentation provides computational evidence of the superiority of HALNS when solving well-known benchmark instances of (synchronized) vehicle routing problems with time windows and its effectiveness in tackling newly proposed SDIVSP instances. HALNS outperforms two state-of-the-art algorithms by an average 6.41% and 12.43% on synchronized vehicle routing with time windows benchmark sets. It further provides computational evidence of the benefits of shared installation vehicles: Total cost decreases by 41.72% and 35.35% as the installation vehicle capacity increases for tight and large time windows respectively.