Type-2 Integrated Process-Planning and Scheduling Problem: Reformulation and Solution Algorithms

Abstract

We study the type-2 integrated process-planning and scheduling (IPPS) problem where each job is represented by a directed network graph. To the best of our knowledge, there is only one mathematical model in the literature implementing the type-2 IPPS partially, and the solution methods available for this problem are all based on heuristics and metaheuristics. We introduce three properties that enable us to fully formulate all aspects of the type-2 IPPS problem with a mathematical programming model for the first time. To solve our model, we propose a logic-based Benders decomposition hybridized with constraint programming. We decompose the problem into two smaller problems in such a way that we can use the best solution technique for each part. To enhance our solution approach, we develop a relaxation. We evaluate our proposed method using a well-known benchmark including 24 instances and compare its performance with eight existing solution methods solving the same benchmark. We solve all the 24 instances of this benchmark to optimality where seven of these 24 instances are solved to optimality for the first time. We also generate a set of new 144 larger instances to further evaluate our solution methods and provide insights on when each method performs better.

Keywords: Type-2 integrated process planning and scheduling problem, Benders decomposition, constraint programming, optimality cut.