A Bayesian approach to a dynamic inventory model under an unknown demand distribution |
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Affiliation: | 1. Department of Mechanical Engineering, MLR Institute of Technology, Hyderabad, 500043, India;2. Department of Mechanical Engineering, St. Peter’s University, Chennai, 60054, India;3. Department of Mechanical Engineering, QIS College of Engg & Tech, Ongole, 523272, India;1. Production Engineering Department, Fluminense Federal University, Rua Passo da Pátria 156, 24210-240 Niteroí, RJ, Brazil;2. UMR CNRS 5506 LIRMM, Université de Montpellier, 161 rue Ada, 34392 Montpellier Cedex 5, France |
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Abstract: | In this paper, the Bayesian approach to demand estimation is outlined for the cases of stationary as well as non-stationary demand. The optimal policy is derived for an inventory model that allows stock disposal, and is shown to be the solution of a dynamic programming backward recursion. Then, a method is given to search for the optimal order level around the myopic order level. Finally, a numerical study is performed to make a profit comparison between the Bayesian and non-Bayesian approaches, when the demand follows a stationary lognormal distribution. A profit comparison is also made between the stationary and non-stationary Bayesian approaches to observe whether the Bayesian approach incorporates non-stationarity in the demand. And, it is observed whether stock disposal reduces the losses due to ignoring non-stationarity in the demand.Scope and purposeIn the context of inventory models, one of the crucial factors to determine an optimal inventory policy, is the accurate forecasting or estimation of the demand for items in the inventory. The assumption of a constant demand is seriously questioned in recent times, since in reality the demand is generally uncertain and may even vary with time. For instance, the demand for new products, spare parts, or style goods, is likely to fluctuate widely, the average demand is quite likely to be low, and may exhibit a trend. In such situations, the Bayesian approach is a very useful tool for demand estimation, which is applicable even when past observations are scarce. In this paper, we use this approach to estimate the demand for an item, and obtain the expressions for finding the optimal inventory policies. We give a simpler method to find the optimal inventory policy, since the procedure to obtain the optimal inventory policy in the Bayesian framework, is quite tedious especially for long planning horizons, and in cases where the future demand becomes unpredictable. To widen the application of the method, we have given a general procedure which is not restricted to any particular probability distribution for the demand. We compare the Bayesian approach with the corresponding non-Bayesian approach, in terms of the optimum expected profits, when the demand follows a lognormal distribution. We also investigate how well the Bayesian approach incorporates non-stationarity in the demand. |
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