Abstract
In this paper, we investigate the resource-constrained order acceptance and scheduling on unrelated parallel machines that arise in make-to-order systems. The objective of this problem is to simultaneously select a subset of orders to be processed and schedule the accepted orders on unrelated machines in such a way that the resources are not overutilized at any time. We first propose two formulations for the problem: mixed integer linear programming formulation and set partitioning. In view of the complexity of the problem, we then develop a column generation approach based on the set partitioning formulation. In the proposed column generation approach, a differential evolution algorithm is designed to solve subproblems efficiently. Extensive numerical experiments on different-sized instances are conducted, and the results demonstrate that the proposed column generation algorithm reports optimal or near-optimal solutions that are evidently better than the solutions obtained by solving the mixed integer linear programming formulation.
Highlights
In many industries, the increasing demand for product variety and customization has intensified competitions among manufacturers to such an extent that attracting and retaining customers is more important than before. e fierce competition has stimulated manufacturers to switch from make-to-stock production to make-to-order production
We further report computational results obtained for large-sized instances in Tables 8 and 9. ese instances become more challenging for the mixed integer linear programming (MILP) formulation, which can be indicated by computation time
We can observe that column generation performs significantly better than the MILP formulation in terms of number of instances solved to optimality and computation times
Summary
The increasing demand for product variety and customization has intensified competitions among manufacturers to such an extent that attracting and retaining customers is more important than before. e fierce competition has stimulated manufacturers to switch from make-to-stock production to make-to-order production. 2. Literature Review e scheduling problem addressed in this work is related to two fields of research: (i) order acceptance and scheduling and (ii) resource-constrained unrelated parallel machine scheduling. Literature Review e scheduling problem addressed in this work is related to two fields of research: (i) order acceptance and scheduling and (ii) resource-constrained unrelated parallel machine scheduling Existing studies on both topics is reviewed . Emami et al [5] consider the simultaneous order acceptance and scheduling problem in an unrelated parallel machines environment with the assumption of uncertain revenue and job-processing times. E proposed branch-andbound algorithm which follows the paradigm of “divide and conquer” branches on the number of accepted orders and recursively solves the reduced unrelated parallel machine scheduling problem at each child node. There are a number of studies on order acceptance and scheduling as well as resource-constrained parallel machine scheduling, but this field of research still requires further development due to its widespread applications. e key extension of our paper which differentiates ours from existing studies is the consideration of order acceptance and resource-constrained parallel machine scheduling in an integrated manner
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