Economic lot scheduling problem with imperfect production processes and setup times
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Economic lot scheduling problem with imperfect production processes and setup times I Moon*, BC Giri and K Choi Pusan National University, Pusan, South Korea Deteriorating production processes are common in reality. Although every production process starts in an ‘in-control’ state to produce items of acceptable quality, it may shift to an ‘out-of-control’ state, owing to ageing, at any random time and produce defective items. In the present article, we study the Economic Lot Scheduling Problem (ELSP) with imperfect production processes having significant changeovers between the products. The mathematical models are developed for the ELSP using both the common cycle approach and the time-varying lot sizes approach, taking into account the effects of imperfect quality and process restoration. Numerical examples are cited to illustrate the solution procedures and to compare the performances of the solution methodologies adopted to solve the ELSP. Journal of the Operational Research Society (2002) 53, 620–629. doi:10.1057/palgrave.jors.2601350 Keywords: economic lot scheduling problem; capacity constraint; imperfect production processes; common cycle approach; time-varying lot sizes approach
Introduction The Economic Lot Scheduling Problem (ELSP) is the problem of finding the production sequence, production times and idle times of several products in a single facility (machine) on a repetitive basis so that the demands are made without stockouts or backorders and average inventory holding and setup costs are minimized. The problem is NP hard1,2 as it requires to satisfy simultaneously the production capacity constraint and synchronization constraint (only one product can be produced at a time). Since the products must be made on the same facility, production of each product would be in lots or batches. The issue of batching arises because the system usually incurs a setup cost and/or a setup time when the machine switches from one product to another. Setup cost is the cost of changing over production equipment among families and within families, the cost due to cleaning or to scrap losses when machine settings are adjusted for the next product. Setup time is downtime during which the machine can not produce, which in turn implies a need to carry more inventory. The setup cost and setup time depend only on the item going into production. The ELSP has been studied by researchers extensively over the past 40 years by assuming typically that the production and demand rates of each item are known to be product-dependent constants and setup cost and setup times are known to be product-dependent but sequence-
independent constants. To solve the ELSP, researchers have followed so far one of the following two approaches:3 (i) Analytic approaches that achieve the optimum of a restricted version of the original problem. For example, Common Cycle (CC) approach4 which restricts all the products’ cycle times to equal leng
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