An EOQ lot sizing model with random supplier capacity |
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| Institution: | 1. College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia;2. Ecole Polytechnique de Tunesie, B.P. 748, 2078 La Marsa, Tunisia;1. Joseph L. Rotman School of Management, University of Toronto, Toronto, M5S 3E6, Canada;2. Department of Industrial Engineering and Management, Ben Gurion University of the Negev, P.O. 653 Beer Sheva 84105, Israel;1. Departamento de Ingeniería Industrial y de Sistemas, Pontificia Universidad Católica de Chile, Chile;2. Center for Operations Research and Econometrics, Université catholique de Louvain, Belgium;1. School of Industrial Engineering, College of Engineering, University of Tehran, Iran;2. Department of Industrial Engineering, Kish International Campus, University of Tehran, Iran;3. Institute of Production and Supply Chain Management, Department of Law and Economics, Technische Universität Darmstadt, Darmstadt, Germany;1. Ruprecht Karls Universitat Heidelberg, INF 205, 69120, Heidelberg, Germany. |
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| Abstract: | This paper presents a general formulation of the inventory lot sizing model with random supplier capacity under the EOQ framework. For a general capacity distribution, we show that the expected cost per unit of time is a unimodal function and pseudo-convex in the ordering quantity. Moreover, we derive some simple data-dependent bounds for both optimal lot size and expected cost per unit of time. In order to illustrate the general model, three types of distributions for the random capacity are analyzed as special cases. These are the uniform, exponential, and truncated normal distributions. For each of these distributions, we find that the maximum cost penalty of using the EOQ lot size instead of the optimal one is almost negligible (not greater than 0.52%, 1.81%, and 0.91% for the uniform, exponential, and truncated normal distributions, respectively). In addition, we extend the general model to allow for the presence of defective units in the quantity received from the supplier. It is shown that this extra randomness does not affect the optimal ordering policy for the original model. |
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