Optimal control policies for an inventory system with commitment lead time (original) (raw)

We consider a firm which faces a Poisson customer demand and uses a base-stock policy to replenish its inventories from an outside supplier with a fixed lead time. The firm can use a preorder strategy which allows the customers to place their orders before their actual need. The time from a customer's order until the date a product is actually needed is called commitment lead time. The firm pays a commitment cost which is strictly increasing and convex in the length of the commitment lead time. For such a system, we prove the optimality of bang-bang and all-or-nothing policies for the commitment lead time and the base-stock policy, respectively. We study the case where the commitment cost is linear in the length of the commitment lead time in detail. We show that there exists a unit commitment cost threshold which dictates the optimality of either a buy-to-order (BTO) or a buy-to-stock strategy. The unit commitment cost threshold is increasing in the unit holding and backordering costs and decreasing in the mean lead time demand. We determine the conditions on the unit commitment cost for profitability of the BTO strategy and study the case with a compound Poisson customer demand. KEYWORDS advance demand information, commitment cost, inventory management, preorder strategy 1 INTRODUCTION The consequences of demand and supply uncertainties and eventual mismatch between demand and supply are well known to many companies. The need for designing company operations such that this mismatch is minimized or avoided has motivated many researchers and resulted in a rich literature on demand and supply management. Among the various methods, information sharing has received a lot of attention. The benefits of acquiring and providing information about future demand are undeniable. Having information on future customer demand helps companies in reducing their inventory levels without sacrificing high service levels. Customers, who provide information on the timing and quantity of their future demand get a high quality service. One form of advance demand information (ADI) is a pre-order strategy in which customers place orders ahead of their actual need. The preorder strategy is characterized by a commitment lead time which is defined as the time that elapses between the moment an order is communicated by the customer and the moment the order must be delivered to the customer. Although in today's competitive market firms cannot force their customers to place orders before their actual need, they can tempt them to follow the preorder strategy by giving a bonus. In order to make long commitment lead times acceptable and attractive, companies should propose bonuses which increase with the length of commitment lead times. The commitment lead time contracts reduce the companies' demand uncertainty risk and the customers' inventory unavailability risk (