A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory Problem

Abstract

A one-warehouse N-retailer deterministic inventory system is examined. The objective is to determine the stocking policy which minimizes average system cost per unit time over the infinite time horizon. Necessary properties of an optimal policy are derived, and optimal solutions for the one-retailer and N identical retailer problems are given. Heuristic solutions for the general problem are suggested, tested against analytical lower bounds and, on the basis of these tests, found to be near optimal.

Cost Allocation for Joint Replenishment Models

“…Therefore, from (21), in order to find a core allocation (β i : i ∈ N ), we only need to find a vector (θ i : i ∈ N ) that satisfies conditions (19) and (20).…”

“…It is clear that (19) holds for (θ * π i : i ∈ N ). In order to verify condition (20), we first make a simple observation.…”

“…This assumption is common in the literature; see, e.g., Schwarz [20], Roundy [18], and Federgruen et al [6].…”

A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design

“…It has been shown for the one-warehouse multi-retailer inventory problem that if an optimal solution exists, then an optimal solution can be found that satisfies the following three properties (Roundy 1985;Schwarz 1973):…”

“…-Zero-Inventory Ordering: Each warehouse or retailer orders only when its inventory level reaches zero (Schwarz 1973). -Last-Minute Ordering: The warehouse orders only when at least one of the retailers orders.…”