Optimal production lot-sizing model considering the bounded learning case and shortages backordered
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Optimal production lot-sizing model considering the bounded learning case and shortages backordered Y-W Zhou1 and H-S Lau2 1
Hefei University of Technology, Anhui, P.R.C. and 2Oklahoma State University, USA
In this paper, we develop an optimal manufactured lot-sizing model under the consideration of learning and shortages. Here the learning phenomenon conforms to the De Jong bounded learning curve. A one-dimensional search method is presented for determining the unique optimal production schedule, which minimises the sum of labour and material costs, ®xed set-up costs, the holding cost and the shortage cost per unit time. A numerical example is used to illustrate the solution procedure; sensitivity analyses are also shown. Keywords: backorder; bounded learning curve; production lot-size
Introduction In a manufacturing system and in real life, it is often the case that the performance of a person engaged in a repetitive task improves with time. This phenomenon is called the learning curve,1 which is a decrease in the effort required for producing each unit in a repetitive manufacturing operation. Factors leading to this phenomenon may include increased familiarity with operation tasks and the work environment, enhanced management ef®ciency, or more effective use of tools and machines. Peterson and Silver2 believed that the learning phenomenon must have economic and decision-making implications in an inventory management system. Therefore, in the last two decads, some researchers3±10 have made much effort in considering the effects of the learning phenomenon on an optimal production lot size. However, their models all employed the unbounded power function formulation introduced by Wright.11 A common theoretical drawback of this curve is that the results obtained are not meaningful as the cumulative production approaches in®nity. Fisk and Ballou12 previously studied the manufactured lot-sizing problem with the consideration of the bounded learning situation, but they did not provide the total holding cost with a closed algebraic form. Recently, Jaber and Bonney,13 employing the De Jong14 bounded learning curve, attempted to present an ef®cient mathematical approximation for the total holding cost expression with a closed algebraic form; unfortunately, their analysis contained mathematical errors which rendered the developed model invalid. More recently, Zhou15 pointed out the errors in Jaber and Bouney's mathematical formulation and proposed the correct model for this problem.
All of the above-mentioned models assumed that shortages are not permitted to occur. Nevertheless, in many practical situation, stockout is unavoidable due to various uncertainties. Moreover, there are many situations in which the inventory holding cost of items is high compared to their backorder cost, in this case, consideration of shortages is economically desirable. Therefore, the occurrence of shortages in inventory is a
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