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Mathematical and Computer Modelling 46 (2007) 1373–1387 www.elsevier.com/locate/mcm

Integer programming approach to reactive scheduling in make-to-order manufacturing$
Tadeusz Sawik ∗
AGH University of Science & Technology, Department of Operations Research and Information Technology, Faculty of Management, Al.Mickiewicza 30, 30-059 Krak´ w, Poland o Received 2 June 2006; received in revisedform 15 December 2006; accepted 10 January 2007

Abstract New algorithms based on mixed integer programming formulations are proposed for reactive scheduling in a dynamic, maketo-order manufacturing environment. The problem objective is to update a long-term production schedule subject to service level and inventory constraints, whenever the customer orders are modified or new orders arrive.Different rescheduling policies are proposed, from a total reschedule of all remaining and unmodified customer orders to a non-reschedule of all such orders. In addition, a medium restrictive policy is considered for rescheduling only a subset of remaining customer orders awaiting material supplies. Numerical examples modeled after a real-world scheduling/rescheduling of customer orders in theelectronics industry are presented and some results of computational experiments are reported. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Production scheduling; Dynamic rescheduling; Make-to-order environment; Integer programming

1. Introduction In make-to-order manufacturing the performance of production planning and scheduling is evaluated by customer satisfaction and production costs. Atypical measure of the customer satisfaction is customer service level, i.e., the fraction of customer orders filled on or before their due dates; see e.g. [1,2]. On the other hand, to achieve low unit production cost, both the input inventory of purchased materials waiting for processing in the system and the output inventory of finished products waiting for delivery to the customers should beminimized. To reduce the required input inventory of purchased materials, the materials should be delivered as late as possible, i.e., the order earliness should be as small as possible. On the other hand the smaller the earliness of customer orders, the smaller is the output inventory of finished products completed before customer required shipping dates and waiting for delivery to the customers.However, if for some customer orders the earliness is smaller than the minimum earliness, i.e., ready periods and due dates are closer to each other, then reallocation of orders to the earlier
$ The author is grateful to two reviewers for providing comments which helped to improve this paper. This work has been partially supported by KBN research grant # 3 T11F 010 28 and AGH grant # 10.10.200.164(Poland) and by Motorola (USA). ∗ Tel.: +48 12 617 39 92; fax: +48 12 617 39 84. E-mail address: ghsawik@cyf-kr.edu.pl.

0895-7177/$ - see front matter c 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2007.01.010

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T. Sawik / Mathematical and Computer Modelling 46 (2007) 1373–1387

periods with surplus of capacity is restricted due to later material availability. As a result,the number of tardy orders may increase, or some orders may even remain unscheduled during the planning horizon. A make-to-order manufacturing environment is dynamic in nature and the customers may modify, cancel or add orders during the planning horizon. As a result, a predetermined production schedule may become inefficient and may need to be revised in reaction to unexpected changes of customerorders. In practice, reactive scheduling algorithms are applied for a dynamic rescheduling. A review of the literature (e.g. [3]) indicates that research on reactive scheduling is mostly focused on heuristic approaches such as genetic algorithms [4] or various AI techniques [5,6]. In the literature on production planning and scheduling, integer programming models have been widely used; see e.g....