Weighted tardiness minimization for unrelated machines with sequence-dependent and resource-constrained setups

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimization. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component - vital to guarantee the non-violation of the problem's constraints - which optimally allocates resources with respect to tardiness minimization. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure is revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight deadlines, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights

Exact and heuristic approaches for lot splitting and scheduling on identical parallel machines

In this paper, we address a lot splitting and scheduling problem existent in a textile factory. The factory we study produces a set of products that are made of, or assembled from, a list of components. During production, each component can be split into one or several lots of different sizes and each lot will be produced independently on one of a group of identical parallel machines. We formulate the problem into a mixed integer programming model and develop a heuristic method to solve the model. The heuristic method is based on a network flow model with the objective to minimise the weighted sum of the total tardiness of products and the deviations occurred during production of each product. The deviation of a product is measured by the deviation of product completion time (the last component lot completion time) and completion time of the rest of components lots for the same product. We present computational results and performance measures of the network flow heuristic for a set of randomly generated instances based on real world data.(undefined

New efficient constructive heuristics for the hybrid flowshop to minimise makespan: A computational evaluation of heuristics

This paper addresses the hybrid flow shop scheduling problem to minimise makespan, a well-known scheduling problem for which many constructive heuristics have been proposed in the literature. Nevertheless, the state of the art is not clear due to partial or non homogeneous comparisons. In this paper, we review these heuristics and perform a comprehensive computational evaluation to determine which are the most efficient ones. A total of 20 heuristics are implemented and compared in this study. In addition, we propose four new heuristics for the problem. Firstly, two memory-based constructive heuristics are proposed, where a sequence is constructed by inserting jobs one by one in a partial sequence. The most promising insertions tested are kept in a list. However, in contrast to the Tabu search, these insertions are repeated in future iterations instead of forbidding them. Secondly, we propose two constructive heuristics based on Johnson’s algorithm for the permutation flowshop scheduling problem. The computational results carried out on an extensive testbed show that the new proposals outperform the existing heuristics.Ministerio de Ciencia e Innovación DPI2016-80750-

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for the TWT and TWET problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm for solving the preemptive relaxation formulated as a mixed integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines, and then we exploit recent advances in solving the non-preemptive single machine TWT and TWET problems for constructing non-preemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances up to 5 machines and 200 jobs

A beam-search-based constructive heuristic for the PFSP to minimise total flowtime

In this paper we present a beam-search-based constructive heuristic to solve the permutation flowshop scheduling problem with total flowtime minimisation as objective. This well-known problem is NP-hard, and several heuristics have been developed in the literature. The proposed algorithm is inspired in the logic of the beam search, although it remains a fast constructive heuristic. The results obtained by the proposed algorithm outperform those obtained by other constructive heuristics in the literature for the problem, thus modifying substantially the state-of-the-art of efficient approximate procedures for the problem. In addition, the proposed algorithm even outperforms two of the best metaheuristics for many instances of the problem, using much lesser computation effort. The excellent performance of the proposal is also proved by the fact that the new heuristic found new best upper bounds for 35 of the 120 instances in Taillard’s benchmark.Ministerio de Ciencia e Innovación DPI2013-44461-PMinisterio de Ciencia e Innovación DPI2016-80750-

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date-oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time-related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve the preemptive relaxation formulated as a mixed-integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines. We then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs

Deterministic Assembly Scheduling Problems: A Review and Classification of Concurrent-Type Scheduling Models and Solution Procedures

Many activities in industry and services require the scheduling of tasks that can be concurrently executed, the most clear example being perhaps the assembly of products carried out in manufacturing. Although numerous scientific contributions have been produced on this area over the last decades, the wide extension of the problems covered and the lack of a unified approach have lead to a situation where the state of the art in the field is unclear, which in turn hinders new research and makes translating the scientific knowledge into practice difficult. In this paper we propose a unified notation for assembly scheduling models that encompass all concurrent-type scheduling problems. Using this notation, the existing contributions are reviewed and classified into a single framework, so a comprehensive, unified picture of the field is obtained. In addition, a number of conclusions regarding the state of the art in the topic are presented, as well as some opportunities for future research.Ministerio de Ciencia e Innovación español DPI2016-80750-