Mathematical modeling and two efficient branch and bound algorithms for job shop scheduling problem followed by an assembly stage

Abstract

Purpose Two-stage production systems including a processing shop and an assembly stage are widely used in various manufacturing industries. These two stages are usually studied independently which may not lead to ideal results. This paper aims to deal with a two-stage production system including a job shop and an assembly stage. Design/methodology/approach Some exact methods are proposed based on branch and bound (B&B) approach to minimize the total completion time of products. As B&B approaches are usually time-consuming, three efficient lower bounds are developed for the problem and variable neighborhood search is used to provide proper upper bound of the solution in each branch. In addition, to create branches and search new nodes, two strategies are applied including the best-first search and the depth-first search (DFS). Another feature of the proposed algorithms is that the search space is reduced by releasing the precedence constraint. In this case, the problem becomes equivalent to a parallel machine scheduling problem, and the redundant branches that do not consider the precedence constraint are removed. Therefore, the number of nodes and computational time are significantly reduced without eliminating the optimal solution. Findings Some numerical examples are used to evaluate the performance of the proposed methods. Comparison result to mathematical model (mixed-integer linear programming) validates the performance accuracy and efficiency of the proposed methods. In addition, computational results indicate the superiority of the DFS strategy with regard to CPU time. Originality/value Studies about the scheduling problems for two-stage production systems including job shop followed by an assembly stage traditionally present approximate method and metaheuristic algorithms to solve the problem. This is the first study that introduces exact methods based on (B&B) approach.

Occupational hazards and economic indicators in the scheduling of a make-to-order system

“…Concerning the perspective of exact techniques, two articles oriented to examine multi-objective sequencing in "Job Shop" were detected. Thus, the first of these articles incorporates the following methods in its analysis: Monte Carlo simulation, Markov chains, and waiting lines [14], while the second article uses the Branch and Bound technique [37].…”

A New Method for Solving the Flow Shop Scheduling Problem on Symmetric Networks Using a Hybrid Nature-Inspired Algorithm

“…This architecture is often referred to in the literature as an FSSP and a multi-processor flow shop [12,13]. Each phase has at least one device in parallel in the hybrid flow shop layout, and there is exclusively more than one machine at least in one of the phases [14]. Since it takes into account both the allocation and scheduling of work at each point, the hybrid FSSP is trickier to answer than the regular FSSP [15].…”

Problem Decomposition and Multi-shot ASP Solving for Job-shop Scheduling

“…In real-world production scheduling, the number of operations to process can easily go into tens of thousands (Da Col and Teppan 2019; Kopp et al 2020;Kovács et al 2021), which exceeds exact optimization capacities even of state-of-the-art solvers for Answer Set Programming (ASP), Mixed Integer Programming (MIP), or Constraint Programming (CP) (Daneshamooz et al 2021;Francescutto et al 2021;Shi et al 2021). Hence, more efficient approaches to approximate good-quality schedules instead of striving for optimal solutions have attracted broad research interest.…”