This thesis studies the optimal operation policies with heterogeneous demand. There are two main approaches to deal with the heterogeneous demand: the capacity based control approach and the price based control approach. In the first two problems of this thesis, the capacity based control approach is used to deal with multiple demand classes in production and inventory systems. The third problem studies a two location transportation system where the price based control approach is adopted to handle the heterogeneous demand....[ Read more ]

This thesis studies the optimal operation policies with heterogeneous demand. There are two main approaches to deal with the heterogeneous demand: the capacity based control approach and the price based control approach. In the first two problems of this thesis, the capacity based control approach is used to deal with multiple demand classes in production and inventory systems. The third problem studies a two location transportation system where the price based control approach is adopted to handle the heterogeneous demand.

In the first problem, we study a periodic review, capacitated, make-to-stock production and inventory system with two demand classes. The production capacity in each period is limited. The demand from each class is random. The unsatisfied demand is lost and incurs lost sales cost. The demand classes are distinguished by the lost sales cost. In each period, the manufacturer makes the production decision and inventory allocation decision. Since the production capacity is limited in each period, the allocation decision must take the future demand into consideration. If the inventory in the current period is low, it could be better to reject the demand from the less profitable class in anticipation of the future demand from the more profitable class. We prove that a base stock rationing policy, which is characterized by a base stock level and a rationing level, is optimal for both finite and infinite horizon problems. For production, we show that the optimal policy is a base stock policy. If the inventory level is below the base stock level, it is increased to the base stock level or as close as possible given the limited production capacity; otherwise the manufacturer should not produce. For inventory allocation, we show that the optimal policy is a rationing policy. The manufacturer should satisfy the demand from the more profitable class as much as possible but satisfy the demand from the less profitable class only if the inventory level is above the rationing level. Through an extensive numerical study, we investigate the cost saving of the optimal policy compared against a common used heuristic policy, which adopt the based stock policy as production policy but the first-come-first-served (FCFS) policy as the allocation policy. The numerical study shows that the cost saving by the optimal policy can be significant.

In the second problem, we consider a more general production system, which is a multi stage assembly system with multiple demand classes. The system consists of multiple production facilities, each producing a different item. To produce one unit of an item, one unit from each of its predecessor items is needed. Upon production completion, items are placed in inventory. At each decision epoch, we must determine whether or not to produce an item and when demand from a particular class arise for the end item whether or not to satisfy it from existing inventory, if any is available. Hence, at each epoch, we must make decisions about both production and inventory allocation. In doing so, we must balance inventory holding costs against shortage costs (lost sales or backorders). We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. For production, we show that the optimal policy for each item is a state-dependent base-stock policy with the base-stock level non-increasing in the inventory level of items that are downstream and non-decreasing in the inventory level of all other items. For inventory allocation, we show that the optimal policy is a multi-level state-dependent rationing policy with the rationing level for each demand class non-increasing in the inventory level of all non-end items. We describe several additional properties for both the production and inventory allocation policies. Using numerical results, we compare the performance of the optimal policy against a heuristic policy that controls production and inventory allocation using fixed base-stock and rationing levels. We find that such a policy is effective in systems with lost sales but can perform poorly in systems with backorders.

In the third problem, we study a stable transportation market with two firms, who provide transportation services between two locations and compete for customers in price. The demands for transportation service in different directions are heterogeneous in market size, price sensitivity and competition intensity etc. The difference of market sizes between two directions is indicated by market imbalance. Equipment is required to transport demand from one location to the other. To sustain the business, firms have to reposition the empty equipment from a surplus location to a shortage location. Firms make decisions on transportation prices. We build a mathematical model to study the pricing policy of firms. The optimal pricing policy is either to achieve the balance of realized demands or to treat demands in two directions separately. We also examine the impact of market imbalance on profit and market performance. We show that market imbalance may not be seen as a curse but an opportunity, since large market imbalance can bring great profit although it results in extensive repositioning cost. Furthermore, we corroborate how the profit is affected by price sensitivity, competition intensity and unit repositioning cost. It is surprising to find that profit may increase with price sensitivity and unit repositioning cost in a competitive market. Our work fills the absence of existing literature and provides managerial insights to understand the transportation industry.