Cyclical schedules for the joint replenishment problem with dynamic demands

Abstract

The Joint Replenishment Problem (JRP) involves production planning for a family of items. The items have a coordinated cost structure whereby a major setup cost is incurred whenever any item in the family is produced, and an item‐specific minor setup cost is incurred whenever that item is produced. This paper investigates the performance of two types of cyclical production schedules for the JRP with dynamic demands over a finite planning horizon. The cyclical schedules considered are: (1) general cyclical schedules—schedules where the number of periods between successive production runs for any item is constant over the planning horizon—and (2) power‐of‐two schedules—a subset of cyclical schedules for which the number of periods between successive setups must be a power of 2. The paper evaluates the additional cost incurred by requiring schedules to be cyclical, and identifies problem characteristics that have a significant effect on this additional cost. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 577–589, 1997.

Discounted costs and obsolescence with the Joint replenishment problem

“…The JRP considers the coordinated replenishments of different types of items in the same order (Khouja & Goyal, 2008), and so it has potential applications whenever a family of items can be defined on the basis of a common supplier, common mode of transportation or common production facility (Webb et al, 1997). Typically, the objective is to minimize the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand.…”

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

“…The solution for this type of problem is not necessarily a cyclic replenishment policy as for the traditional JRP. For the DJRP different formulations and heuristic solution methods have been proposed and studied ( Boctor, Laporte, & Renaud, 2004;Narayanan & Robinson, 2006;Robinson, Narayanan, & Gao, 2007;Webb, Buzby, & Campbell, 1997 ) and Robinson, Narayanan, and Sahin (2009) have provided an overview of available solution methods. Webb et al (1997) studied fixed replenishment cycle models for the problem and compared these to optimal solutions that do no constrain the replenishment cycle.…”

“…For the DJRP different formulations and heuristic solution methods have been proposed and studied ( Boctor, Laporte, & Renaud, 2004;Narayanan & Robinson, 2006;Robinson, Narayanan, & Gao, 2007;Webb, Buzby, & Campbell, 1997 ) and Robinson, Narayanan, and Sahin (2009) have provided an overview of available solution methods. Webb et al (1997) studied fixed replenishment cycle models for the problem and compared these to optimal solutions that do no constrain the replenishment cycle. Boctor et al (2004) proposed several linear programming formulations, tested several heuristic solution methods and proposed an improvement procedure that can be used in combination with a heuristic method.…”

A review of the joint replenishment problem literature: 1989–2005

“…Also, several heuristics, which are a focus of this paper, have been suggested for solving the DJRP. Webb et al (1997) investigated the performance of two types of cyclical schedules for the DJRP: (1) general cyclical schedules in which the number of periods between successive orders for any product is constant over the planning horizon. In this case the length of the basic cycle must belong to the set f1; 2; .…”