Essays in inventory control

This thesis studies four important problems faced in the theory of inventory control. The first chapter addresses the issue of calculating optimal inventory policies in stochastic inventory problems, when unknown demand parameters are estimated from a sample of demand observations. A general framework for combining estimation and optimization problems is developed for a class of inventory problems when the demand distribution belongs to the scale-location family. The results show that biasing the scale parameter estimates gives better inventory policies for both cost minimization and service achievement objectives. The second chapter studies a periodic review, single-product, single facility inventory problem with multiple customer classes, each requiring a different service level. Customer demands are random and independent with a stationary probability distribution. The objective is to find a stock allocation policy among the customers and an inventory replenishment policy so as to achieve target customer service levels with minimum possible inventory holding cost. An easy-to-calculate myopic heuristic allocation-order policy is developed and its performance is tested through simulation. The third chapter finds an optimal inventory policy for a classical single-stage, singleproduct, unit demand, continuous review inventory problem where the interdemand times are independent identically distributed random variables with increasing failure rate. Unmet demand is fully backlogged and orders arrive after a lead time. The costs of backlogging and inventory carrying are linear. The objective is to minimize the long run average cost. If there is no fixed cost for placing an order, it is proven that a Delayed- (s-l,s) policy is optimal. In case of a fixed order cost, a Delayed-(s,S) policy is proven to be optimal. In chapter four, the same problem as in chapter three is studied for a Poisson demand in the case of lost sales. No fixed cost for placing an order is assumed. For this problem, an optimal policy is unknown and it is commonly believed that an (s-l,s) policy is sufficiently good. A new heuristic policy is suggested as an alternative, which uses more information, but is myopic in nature and its performance is compared with that of (s-l,s).Business, Sauder School ofOperations and Logistics (OPLOG), Division ofGraduat