This paper presents a study of solving the joint replenishment problem (JRP) by using the RAND method, a heuristic approach that has been proven to find almost as good as optimal solutions, under uncertain customer demands and inaccurate unit holding cost estimation. The classical JRP deals with the issue of determining a replenishment policy that minimizes the total cost of replenishing multip...

This paper deals with the problem of coordinated ordering of items having deterministic but time varying demands where there is a common ordering cost if one or more of these items are ordered in addition to individual items ordering costs. To solve this NP-hard problem we propose a number of heuristics. Also we report on a comparative study that we undertaken to evaluate the relative performan...

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 ...

We establish a duality theory for a broad class of deterministic inventory control problems on continuous spaces that includes the classical joint replenishment problem and inventory routing. Using this theory, we establish the existence of an optimal policy, which has been an open question. We show how a primal-dual pair of infinite dimensional linear programs encode both cyclic and non-cyclic...

We address the Joint Replenishment Problem (JRP) where, in the presence of joint setup costs, dynamic lot sizing schedules need to be determined for m items over a planning horizon of N periods, with general time-varying cost and demand parameters. We develop a new, so-called, partitioning heuristic for this problem, which partitions the complete horizon of N periods into several relatively sma...

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 ...

We provide a practical methodology for solving the generalized joint replenishment (GJR) problem, based on a mathematical programming approach to approximate dynamic programming. We show how to automatically generate a value function approximation basis built upon piecewise-linear ridge functions, by developing and exploiting a theoretical connection with the problem of finding optimal cyclic s...

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...