A branch and price solution approach for order acceptance and capacity planning in make-to-order operations

Make-to-order (MTO) operations have to effectively manage their capacity to make long-term sustainable profits. This objective can be met by selectively accepting available customer orders and simultaneously planning for capacity. We model a MTO operation of a job-shop with multiple resources having regular and non-regular capacity. The MTO firm has a set of customer orders at time zero with fixed due-dates. The process route, processing times, and sales price for each order are all given. Since orders compete for limited resources, the firm can only accept some orders. In this paper we formulate a Mixed-Integer Linear Program (MILP) to aid an operational manager to decide which orders to accept and how to allocate resources such that the overall profit is maximized. A branch-and-price algorithm is devised to solve the MILP effectively. The MILP is first decomposed into a master problem and several sub-problems using Dantzig-Wolfe decomposition. Each sub-problem is represented as a network flow problem and an exact procedure is proposed to solve the sub-problems efficiently. We also propose an approximate branch-and-price scheme, Lagrangian bounds, and approximations to fathom nodes in the branch-and-bound tree. Computational analysis shows that the proposed branchand-price algorithm can solve large problem instances with relatively short time. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 (815) 753‐6748 [email protected] November 2, 2009 Dear Editor, We are submitting our manuscript entitled "A Branch and Price Solution Approach for Order Acceptance and Capacity Planning in Make‐to‐Order Operations" for review and publication in European Journal of Operational Research. The problem under study can be observed at several manufacturing facilities. The co‐authors have personally interacted with several make‐to‐order firms. The model and the solution proposed in this paper can benefit industry and stimulate academic research to consider several extensions of this problem. We hope you will find this paper and its contribution worthy to publish in your journal. If you need additional information with regards to the manuscript, please write to me. I look forward to hearing your comments and the reviewers’ comments/suggestions on our manuscript. Sincerely, Purushothaman Damodaran Department of Industrial and Systems Engineering Northern Illinois University De Kalb, IL 60115 Cover Letter Click here to view linked References