Relatively optimal policies for stock management in a supply chain with option for inventory space limitation

Abstract

Coordination between a single manufacturer (vendor) and a buyer (retailer), via the delivery schedule in joint economic lot–sizing problem for a two stage supply chain, is investigated. To satisfy the buyer’s demands, the product is delivered in discrete equal size sub-batches from the vendor’s stock to the buyer’s stock. Under stock management (SM) policy, the vendor delivers each sub-batch as soon as the buyer’s inventory reduces to zero. For consignment stock (CS) policy, in the case of buyer’s warehouse space limitation, the maximum level of the buyer’s, consequently of the vendor’s, inventory position can be controlled by the vendor’s just in time or delayed deliveries (CS-k policies). If a space limitation is attached to vendor’s warehouse, then the maximum level of the vendor’s, consequently of the buyer’s, inventory position can be controlled by just in time, or advanced for the buyer deliveries (in our notation SM-v-policies). Relatively optimal SM-v-policies can be obtained as solutions of adequate constrained problems. A comparative study, done in this paper, shows that the SM-v-policies can perform better than policies obtained as solutions of the sharply constrained problem where the maximal vendor’s inventory level is equal to the maximum attainable space limit. Numerical examples are presented with appropriate comments to the solutions obtained by the proposed algorithm