Dynamic lot sizing problem with continuous-time Markovian production cost |
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| Authors: | Amir Azaron Ou Tang Reza Tavakkoli-Moghaddam |
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| Institution: | aMichael Smurfit Graduate School of Business, University College Dublin, Carysfort Avenue, Blackrock, Co. Dublin, Ireland;bDepartment of Management and Engineering, Linköping University, Linköping, Sweden;cDepartment of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran;dSchool of Economics and Management, Tongji University, Shanghai, China |
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| Abstract: | This paper develops a polynomial algorithm for obtaining dynamic economic lot sizes in a single product multiperiod production system with the objective of minimizing total production and inventory costs over T periods. It is assumed that production costs are linear, inventory costs are concave, setup costs are zero and backlogging is not permitted in all periods. Moreover, the unit production cost is a stochastic variable, which is evolved according to a continuous-time Markov process over the planning horizon. The model is formulated as a stochastic dynamic programming (DP) optimization with the state variable being unit production cost. Then, it is solved using the backward dynamic programming approach. To justify the application of the proposed model, two practical cases are presented. |
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| Keywords: | Dynamic lot sizing Dynamic programming Stochastic processes |
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