A joint replenishment competitive location problem

Competitive Location Models seek the positions which maximize the market captured by an entrant firm from previously positioned competitors. Nevertheless, strategic location decisions may have a significant impact on inventory and shipment costs in the future affecting the firm’s competitive advantages. In this work we describe a model for the joint replenishment competitive location problem which considers both market capture and replenishment costs in order to choose the firm’s locations. We also present an metaherusitic method to solve it based on the Viswanathan’s (1996) algorithm to solve the Replenishment Problem and an Iterative Local Search Procedure to solve the Location Problem.N/

On the efficiency of optimal algorithms for the joint replenishment problem: a comparative study

In this paper we proposed an efficient algorithm to solve the joint replenishment problem to optimality. We perform a computational study to compare the performance of the proposed algorithm with the best one reported in Viswanathan [6]. The study reveals that for large minor set-up costs and moderate major set-up cost, our algorithm outperforms the latter.inventory;joint replenishment;deterministic demand

The submodular joint replenishment problem

The joint replenishment problem is a fundamental model in supply chain management theory that has applications in inventory management, logistics, and maintenance scheduling. In this problem, there are multiple item types, each having a given time-dependent sequence of demands that need to be satisfied. In order to satisfy demand, orders of the item types must be placed in advance of the due dates for each demand. Every time an order of item types is placed, there is an associated joint setup cost depending on the subset of item types ordered. This ordering cost can be due to machine, transportation, or labor costs, for example. In addition, there is a cost to holding inventory for demand that has yet to be served. The overall goal is to minimize the total ordering costs plus inventory holding costs. In this paper, the cost of an order, also known as a joint setup cost, is a monotonically increasing, submodular function over the item types. For this general problem, we show that a greedy approach provides an approximation guarantee that is logarithmic in the number of demands. Then we consider three special cases of submodular functions which we call the laminar, tree, and cardinality cases, each of which can model real world scenarios that previously have not been captured. For each of these cases, we provide a constant factor approximation algorithm. Specifically, we show that the laminar case can be solved optimally in polynomial time via a dynamic programming approach. For the tree and cardinality cases, we provide two different linear programming based approximation algorithms that provide guarantees of three and five, respectively.National Science Foundation (U.S.) (CAREER Grant CMMI-0846554)United States. Air Force Office of Scientific Research (Award FA9550-11-1-0150)SMA GrantSolomon Buchsbaum AT&T Research Fun

Approximation Algorithms for the Joint Replenishment Problem with Deadlines

The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supply-chain 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 costs. We study the approximability of JRP-D, the version of JRP with deadlines, where instead of waiting costs the retailers impose strict deadlines. We study the integrality gap of the standard linear-program (LP) relaxation, giving a lower bound of 1.207, a stronger, computer-assisted lower bound of 1.245, as well as an upper bound and approximation ratio of 1.574. The best previous upper bound and approximation ratio was 1.667; no lower bound was previously published. For the special case when all demand periods are of equal length we give an upper bound of 1.5, a lower bound of 1.2, and show APX-hardness

Controlling inventories in a supply chain: a case study

This article studies specific aspects of the joint replenishment problem in a real supply chain setting. Particularly we analyze the effect on inventory performance of having minimum order quantities for the different products in the joint order, given a complex transportation cost structure. The policies suggested have been tested in a simulation model with real data.Inventory;Supply chain management;Minimum order quantities;Joint replienishment

Better Approximation Bounds for the Joint Replenishment Problem

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 $\rho$ has a fixed cost $c_\rho$. In addition, retailers incur waiting costs for each order. The objective is to minimize the overall cost of satisfying all orders, namely the sum of all shipping and waiting costs. JRP has been well studied in Operations Research and, more recently, in the area of approximation algorithms. For arbitrary waiting cost functions, the best known approximation ratio is 1.8. This ratio can be reduced to 1.574 for the JRP-D model, where there is no cost for waiting but orders have deadlines. As for hardness results, it is known that the problem is APX-hard and that the natural linear program for JRP has integrality gap at least 1.245. Both results hold even for JRP-D. In the online scenario, the best lower and upper bounds on the competitive ratio are 2.64 and 3, respectively. The lower bound of 2.64 applies even to the restricted version of JRP, denoted JRP-L, where the waiting cost function is linear. We provide several new approximation results for JRP. In the offline case, we give an algorithm with ratio 1.791, breaking the barrier of 1.8. In the online case, we show a lower bound of 2.754 on the competitive ratio for JRP-L (and thus JRP as well), improving the previous bound of 2.64. We also study the online version of JRP-D, for which we prove that the optimal competitive ratio is 2

Two notes on the joint replenishment problem under constant demand

Inventory Control;Inventory Models;management science

New Bounds for the Joint Replenishment Problem: Tighter, but not always better

In this paper we present new bounds on the basic cycle time for optimal methods to solve the JRP. They are tighter than the ones reported in Viswanathan [7]. We carry out extensive numerical experiments to compare them and to investigate the computational complexity.computational complexity;joint replenishment problem;bounds

Generalized Solutions for the joint replenishment problem with correction factor

In this paper we give a complete analysis of the joint replenishment problem (JRP) under constant demands and continuous time. We present a solution method for the JRP when a correction is made for empty replenishments, and we test the solution procedures with real data. We show that the solutions obtained differ from the standard JRP when no correction is made in the cost function. We further show that the JRP with correction outperforms independent ordering. Additional numerical experiments are presented.inventory;joint replenishment;correction factor