Inventory management problem for two substitutable products : a bayesian approach

Accurate estimation of demand and the inventory levels are must for customer satisfaction and the protability of a business. In this thesis, we consider two main topics: First, the joint estimation of the demand arrival rate, primary and substitute demand rates in a lost sales environment with two products is provided using a Bayesian methodology. It is assumed that demand arrivals for the products follow a Poisson process where the unknown arrival rate is a random variable. An arriving customer requests one of the two products with a certain probability and may substitute the other product if the primary demand is not available. We consider a general mixture gamma density for prior of the Poisson arrival rate and a general prior for the joint distribution of the primary and substitute demand probabilities. It is observed that the resulting marginal posterior and the conditional posterior density of demand arrival rate given the other parameters, after observation of n-period data, are again in the structure of gamma mixtures. Then, we calculated the inventory levels of the products dynamically with the help of rst part. Using the updated posterior demand rates on the observed data from the previous period, we revised the inventory levels for the following period to maximize the prot. Finally, some numerical results for both parts are presented to illustrate the performance of the estimations.