Logic-based Benders Decomposition for Alternative Resource Scheduling with Sequence Dependent Setups

Unrelated parallel machine scheduling problem with special controllable processing times and setups

This article concerns the resolution of a hybrid flow shop with dedicated machines, sequence dependent setup and time lags. Such a configuration is encountered in the pasta production industry. The objective is to minimize the maximum completion time of all the jobs (makespan). We first propose a mathematical model for the problem. Given the complexity of the problem, we also developed an upper bound using genetic algorithm and a lower bound in order to evaluate the GA. Computational experiments are applied to a number of randomly generated test problems. The results show that the proposed algorithm can produce results that are very close to optimal schedules if they are known or very close to the lower bounds.

A lot sizing and scheduling problem from a foundry is considered in which key materials are produced and then transformed into many products on a single machine. A mixed integer programming (MIP) model is developed, taking into account sequence-dependent setup costs and times, and then adapted for rolling horizon use. A relax-and-fix (RF) solution heuristic is proposed and computationally tested against a high-performance MIP solver. Three variants of local search are also developed to improve the RF method and tested. Finally the solutions are compared with those currently practiced at the foundry.

This paper investigates the NP-hard problem of scheduling $n$ jobs on a single machine, where the machine must be stopped periodically for maintenance after a certain continuous working time. The objective is to minimize the total weighted completion time. Two-phase heuristic algorithms are proposed: in the first phase, initial solutions are obtained by WSPT or look-ahead (LA) algorithms; then, in the second phase, the solutions are improved through improvement procedures. Additionally, a mixed integer programming (MIP) model and a branch and bound (BAB) algorithm are developed. The results of computational experiments demonstrate that when the number of jobs is less than or equal to 20, the BAB is competitive compared with an MIP model implemented in a commercial solver because in most instances the former can obtain optimal solutions faster. The results also indicate that the LA algorithm significantly outperforms the WSPT algorithm in terms of the solution quality, and the proposed improvement procedure is evidently useful in refining the solution quality for both the WSPT and LA algorithms.

Lotsizing in capacitated pure flow shop with sequence-dependent setups has been considered in this paper. An exact formulation of the problem is provided as a mixed-integer program. It is well known that the capacitated lotsizing and scheduling problem (CLSP) is NP-hard. The introduction of serially arranged machines and sequence-dependent setups makes the problem even more complicated. Five MIP-based heuristics based on iterative procedures are provided. The first three heuristics are based on the original model but to solve non-small instances of problem, the last two heuristics are based on permutation flow shop problem which ignores the majority of combinations. To test the accuracy of heuristics, two lower bounds are developed and compared against the optimal solution. The trade-offs between solution quality and computational times of heuristics are also provided.

We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we compare the constraint programming (CP) model with the mixed-integer programming (MIP) model for F-JSSPs. Second, we exploit the decomposable structure within the models and develop an efficient CP–logic-based Benders decomposition (CP-LBBD) technique that combines the complementary strengths of MIP and CP models. Using 193 instances from the literature, we demonstrate that MIP, CP, and CP-LBBD achieve average optimality gaps of 25.50%, 13.46%, and 0.37% and find optima in 49, 112, and 156 instances of the problem, respectively. We also compare the performance of the CP-LBBD with an efficient Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, which has been appraised for finding 125 optima on 178 instances. CP-LBBD finds 143 optima on the same set of instances. We further examine the performance of the algorithms on 96 newly (and much larger) generated instances and demonstrate that the average optimality gap of the CP increases to 47.26%, whereas the average optimality of CP-LBBD remains around 1.44%. Finally, we conduct analytics on the performance of our models and algorithms and counterintuitively find out that as flexibility increases in data sets the performance CP-LBBD ameliorates, whereas that of the CP and MIP significantly deteriorates.

A cutting plane algorithm for the site layout planning problem with travel barriers

<p style='text-indent:20px;'>In today's competitive world, scheduling problems are one of the most important and vital issues. In this study, a bi-objective unrelated parallel machine scheduling problem with worker allocation, sequence dependent setup times, precedence constraints, and machine eligibility is presented. The objective functions are to minimize the costs of tardiness and hiring workers. In order to formulate the proposed problem, a mixed-integer quadratic programming model is presented. A strategy called repair is also proposed to implement the precedence constraints. Because the problem is NP-hard, two metaheuristic algorithms, a multi-objective tabu search (MOTS) and a multi-objective simulated annealing (MOSA), are presented to tackle the problem. Furthermore, a hybrid metaheuristic algorithm is also developed. Finally, computational experiments are carried out to evaluate different test problems, and analysis of variance is done to compare the performance of the proposed algorithms. The results show that MOTS is doing better in terms of objective values and mean ideal distance (MID) metric, while the proposed hybrid algorithm outperforms in most cases, considering other employed comparison metrics.</p>

This paper introduces the problem of scheduling a set of jobs with sequence dependent setup times on a machine with a pair of coupled processing lines, i.e., both lines must be operated simultaneously. A heuristic procedure is developed to find a good schedule which then is used as a starting point for a tabu search. A mixed integer programming formulation of the problem is also given. Computational results on real-world problems are presented.

• Evacuation network design with road capacity improvement and uncertainty is stated. • A non-convex mixed-integer nonlinear program model is established. • Second-order cone programming reformulations are developed. • Benders decomposition with various acceleration strategies is devised. • Efficiency of proposed methods and comparison of existing method are explored. This work first presents a stochastic shelter location and evacuation planning problem with considering road capacity improvement strategies, in which the fixed setup cost of shelters and the improvement cost of road capacity are subject to a budget limit. To explicitly capture the impact of traffic volumes and road capacity improvement decisions on evacuation time, the Bureau of Public Roads function is employed. The problem is formulated as a non-convex mixed-integer nonlinear program (MINLP) model that is difficult to solve directly since the objective function is a multivariable non-convex nonlinear function. To tackle the non-convex MINLP, second-order cone programming (SOCP) reformulations that can be directly solved by using the state-of-the-art solvers are developed. Furthermore, a Benders decomposition (BD) approach that utilizes duality results of SOCP and employs acceleration strategies associated with valid inequalities, multi-cut, strengthened Benders cuts, knapsack inequalities, and callback routine, is proposed to solve large-scale problems. Moreover, extensive numerical experiments and a real-world case study (a potential hurricane risk zone in Texas, U.S.) are conducted to verify the applicability and effectiveness of the proposed model and solution approaches. Computational results show that the derived reformulations are competitive in dealing with small- and medium-scale problems, whereas BD approach demonstrates the best computational performance in solving large-scale problems. The devised acceleration strategies are effective in improving the computational efficiency of the BD approach. In addition, exerting investment for those shelters and arcs that are close to evacuation regions is useful to reduce the expected total evacuation time.

We consider here the lot sizing and scheduling problem in single-level manufacturing systems. The shop floor is composed of unrelated parallel machines with sequence dependent setup times. We propose an integer programming model embedding precise capacity information due to scheduling constraints in a classical lot-sizing model. We also propose an iterative approach to generate a production plan taking into account scheduling constraints due to changeover setup times. The procedure executes two decision modules per iteration: a lot-sizing module and a scheduling module. The capacitated lot-sizing problem is solved to optimality considering estimated data and aggregate information, and the scheduling problem is solved by a GRASP heuristic. In the proposed scheme the information flow connecting the two levels is managed in each iteration. We report a set of computational experiments and discuss future work.

Rolling horizon-based heuristics for solving a production-routing problem with price-dependent demand

Manufacturing as a Service (MaaS) systems facilitate collaboration, leading to more efficient resource utilisation, improved supply chain resilience, and increased competitiveness. Sectors such as machinery manufacturing, additive manufacturing, and automotive supply chains benefit from shared resources, allowing for greater flexibility and quicker adaptation to market and technological shifts. MaaS systems are multi-agent by nature, as each service provider and customer pursues their own objectives and therefore requires coordination of activities. This paper addresses this multi-agent scheduling challenge through scalable combinatorial optimisation formulations and solution methods. Novel exact Mixed-Integer Programming (MIP) and Constraint Programming (CP) models, together with a Logic-Based Benders Decomposition (LBBD) algorithm that exploits both models, are developed. State-of-the-art exact solvers are used for implementing and tuning the exact models and the LBBD algorithm, while a metaheuristic solver is employed for benchmarking. An extensive set of novel instances, including practical extensions arising from manufacturing and distribution processes, is generated. Computational experiments for benchmarking the developed models and methods, along with sensitivity analysis, demonstrate the applicability of the proposed solution methods to large-scale instances of the problem.

Multi-product production systems with sequence-dependent setup times are typical in manufacturing of semiconductor chips and other electronic products. In such systems, the scheduling policies to coordinate the production of multiple product types play an important role. In this paper, we study a multi-product manufacturing system with finite buffers, sequence-dependent setup times and various scheduling policies. Using continuous time Markov chain models, we evaluate the performance of such systems under seven scheduling policies, i.e., cyclic, shortest queue, shortest processing time, shortest overall time (including setup time and processing time), longest queue, longest processing time, and longest overall time. The impact of these policies on systemthroughput are compared, and the conditions characterizing the superiority of each policy are investigated. The results of this work can provide production engineers and supervisors practical guidance to operate multi-product manufacturing systems with sequence-dependent setups.

In apparel manufacturing, cut pieces produced by the cutting process are a key input work-in-process (WIP) to the bottleneck sewing process. However, an excessive inventory of cut pieces not only requires extra storage space but also creates difficulties with shop floor control. This study determines the ideal cutting times of fabric lays by minimising the cut piece inventory under the constraint that sufficient cut pieces are produced in time to satisfy the bottleneck usage. This study proposes a mixed integer programming (MIP) model and a heuristic method to solve the problem. The solutions for most test instances of the problem that are calculated by the heuristic method are not as good as those by the MIP solver; however, the heuristic method computation times are negligible. The experiments show that the MIP model’s efficiency significantly improves by starting from an initial solution provided by the proposed heuristic method.