The Joint Replenishment Problem (JRP) deals with optimizing shipments of goods from a supplier to retailers through a shared warehouse. Each shipment involves transporting goods from the supplier to the warehouse, at a fixed cost C, followed by a redistribution of these goods from the warehouse to the retailers that ordered them, where transporting goods to a retailer ρ has a fixed cost cρ. In ...

In most multi-item inventory systems, the ordering costs consist of a major cost and a minor cost for each item included. Applying for every individual item a cyclic inventory policy, where the cycle length is a multiple of some basic cycle time, reduces the major ordering costs. An e cient algorithm to determine the optimal policy of this type is discussed in this paper. It is shown that this ...

The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supplychain management, concerned with optimizing the flow of goods from a supplier to retailers. Over time, in response to demands at the retailers, the supplier ships orders, via a warehouse, to the retailers. The objective is to schedule these orders to minimize the sum of ordering costs and retailers’ waiting cos...

An uncertain economic order quantity (UEOQ) model with payment in advance is developed to purchase high-price raw materials. A joint policy of replenishments and pre-payments is employed to supply the materials. The rate of demand is considered LR-fuzzy variables, lead-time is taken to be constant, and it is assumed that shortage does not occur in the cycles. The cycle is divided into three par...

We give an efficient polynomial-time approximation scheme (EPTAS) for the Joint Replenishment Problem (JRP) with stationary demand. Moreover, using a similar technique, we give a PTAS for the capacitated JRP with non-stationary demand but constant size capaci-

This paper introduces a collaborative strategy in the supply chain that demonstrates potential to reduce management inventory costs, through the coordinated replenishment of multiple items from noncompetitors vendors. The proposed approach is an extension of the classical joint replenishment problem (JRP) denominated as stochastic collaborative joint replenishment problem (S-CJRP) since conside...

A “phantom stockout” is a retail stockout phenomenon caused either by inventory shrinkage or by shelf execution failure. Unlike the conventional stockout which can be corrected by inventory replenishment, a phantom stockout persists and requires human interventions. In this paper, we propose two partially-observable Markov decision models: one for the shrinkage problem and the other for the she...