Solving assembly scheduling problems with tree-structure precedence constraints: A Lagrangian relaxation approach

Abstract

In this paper, we consider an assembly scheduling problem (ASP) with tree-structured precedence constraints. In our problem, there are a number of work centers. Each work center contains a number of machines of the same functionality. The job to be processed via this system is a job with tree-structure precedence constraints. Each operation in the job has a designated work center. We propose a mixed integer linear programming formulation and solve the problem with a Lagrangian relaxation (LR) approach. We solve the subproblems of the LR problem via a heuristic method and generate feasible solutions via a randomized list scheduling algorithm. Near-optimal results are obtained and the computational time is within a few seconds for problems with size up to 20 machines and 300 operations.Note to Practitioners-Most industrial products are complex assemblies made up of multiple manufactured products-organized as Bills-Of-Materials (BOMs)-that are produced in a shared manufacturing facility with possibly multiple functionally identical machines. There are a few rigorous approaches to deal with these kinds of problems in the literature. The job-shop scheduling problem has been extensively addressed, but these problems do not provide for any relationship between the multiple manufactured parts. In an assembly scheduling problem, the completion time of a child component becomes the release time of the parent part; hence, the multiple jobs become connected in a tree structure defined by the BOM. The second aspect that has been less considered in the scheduling literature is multiple, functionally identical machines-a common occurrence in industry. This paper takes on these two challenges and solves this problem using a LR approach and associated heuristics. Industrial strength problems of about 300 operations and 10 work centers are solved in a few seconds using this approach to near-optimality, while commercial strength mixed integer programming solvers are unable to find useful solutions in an hour.Index Terms-Assembly scheduling, Lagrangian relaxation (LR), makespan, parallel machine scheduling, randomized algorithm, subgradient search.

A Hybrid Algorithm Based on Particle Swarm Optimization and Artificial Immune for an Assembly Job Shop Scheduling Problem

“…At another literature, they put up a hybrid Tabu Search (TS) heuristic to solve the AJSSP [15]. Xu and Nagi consider an assembly scheduling problem with tree-structured precedence constraints [16]. They propose a mixed integer linear programming formulation and solve the problem with a Lagrangian relaxation approach.…”