We deal with a multi-echelon inventory system in which one warehouse supplies an item to multiple retailers. Customer demand arrives at each retailer at a constant rate. The retailers replenish their inventories from the warehouse which in turn orders from an outside supplier. It is assumed that shortages are not allowed and lead times are negligible. These distribution/inventory systems are en...

The joint replenishment problem has been extensively studied and the strategy adopted by a large variety of retailers in recent years. However, under minimum order quantity other constraints does not receive sufficient attention. This paper analyzes retailing supply chain involving supplier that provides discount schedules limits quantity. include requirements for each item as to total quantity...

In this paper we analyze the optimal joint decisions of when, how and howmuch to replenish customers with products of varying ages. We discuss the main features of the problem arising in the joint replenishment and delivery of perishable products, and we model them under general assumptions. We then solve the problem by means of an exact branch-and-cut algorithm, and we test its performance on ...

We consider the following two deterministic inventory optimization problems over a finite planning horizon T with non-stationary demands. • Submodular Joint Replenishment Problem. This involves multiple item types and a single retailer who faces demands. In each time step, any subset of item-types can be ordered incurring a joint ordering cost which is submodular. Moreover, items can be held in...

In the Joint Replenishment Problem (JRP), the goal is to coordinate the replenishments of a collection of goods over time so that continuous demands are satisfied with minimum overall ordering and holding costs. We consider the case when demand rates are constant. Our main contribution is the first hardness result for any variant of JRP with constant demands. When replenishments per commodity a...

The integration with different decisions in the supply chain is a trend, since it can avoid the suboptimal decisions. In this paper, we provide an effective intelligent algorithm for a modified joint replenishment and location-inventory problem (JR-LIP). The problem of the JR-LIP is to determine the reasonable number and location of distribution centers (DCs), the assignment policy of customers...