Stochastic Models For Inventory Control And Management

This thesis consists of two research topics related to stochastic inventory con-trol and management.The first research topic is on dynamic capacity management with upgrades.Inspired by a retailer's consulting project,this research topic ex-plores the issue of the retailer selling multiple products to meet multiple demands.In this problem,each type of customer's demand is a specific type of product,and the retailer can provide customers with free upgrades to higher-end(expensive)products(regardless of whether such products are out of stock or not).However,due to customer's preference,he may not accept the upgrade.When customers ar-rive successively over time,the retailer needs to decide whether to provide upgrade service to each arriving customer.In order to solve the problem of how the retailer can meet the multiple demands by providing multiple upgrades,this paper formu-lates the problem with Markov decision process modeling to demonstrate that the optimal profit function of the model preserves anti-multimodularity.Then based on the properties of anti-multimodularity,it is demonstrated that the optimal procurement policy is a base-stock policy.The optimal upgrade policy can be described as a rationing policy with dynamic thresholds determined by the inven-tory levels of all products,and the optimal upgrade policy has some monotonicity.Specifically,there is an upgrade threshold for each product,and if the inventory level for such products is above the upgrade threshold,it is best to provide this product as a free upgrade;otherwise,it is best not to do so.In addition,the upgrade threshold will not increase as the inventory levels of other higher-end products increase,nor will it decrease as the inventory levels of other lower-end products increase.Under the model settings of this article,with the possibility that customers would reject upgrades,it is optimal to offer upgrades before the stock out of the desired models,and offering upgrades only after stockout could lead to significant profit loss.The second research topic is based on the research of coordinating procure-ment/production and pricing in retailing and manufacturing industries.The lit-erature has confined itself mainly to models with single-product,no setup cost or single setup cost,since researchers have been crippled by the technical intractabil-ity of models with multiple products and multiple setup costs.This paper focuses on models with periodic review,finite horizon,multiple products,and multiple setup costs.Specifically,the ordering cost we consider consists of a variable cost for each product,a joint setup cost,and an individual setup cost for each prod-uct.The joint setup cost is incurred if a positive order is placed for any product,and an individual setup cost is incurred if any positive order is placed for the corresponding product.The goal is to find the optimal joint ordering and pric-ing policy that maximizes the expected discounted profit over the finite horizon.This paper demonstrates the optimality of the(?,?,S,p)policy by proposing a new concept of(K,?)quasiconcave function.The policy possesses the(?,?,S)ordering policy associated with an optimal pricing strategy.In such an ordering policy,it is optimal:to order nothing when the inventory state vector is in ?,to order up to S when the inventory state vector is in ?,and finally,to order certain quantities when the inventory state vector is neither in ? nor in a.Fur-thermore,given an inventory state vector in ?,then any inventory state vector which is component-wise less than that state vector must be in ? as well.Similarly given an inventory state vector in ?,then,any inventory state vector which is component-wise greater than that state vector must be in ?.We also obtain some monotonicity properties of the optimal replenishment policy for the state vectors belongs to ?.And,in such a price strategy,the best price for each product is de-termined by a response function of the expected demand based on the inventory position at the beginning of each period.The results can hold for any subadditive setup costs,e.g.,the setup costs consist of a joint setup cost,an individual setup cost for each product,and a setup cost for ordering a subset of products.This paper also obtains lower bounds and upper bounds for the parameters of the op-timal policy.Finally,this paper numerically depicts the optimal ordering policy and investigate the performances of two simple heuristic policies for our problems.