Single‐warehouse multi‐retailer inventory systems with full truckload shipments

Abstract

Abstract:We consider a multi-stage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Fixed costs are incurred for each truck dispatched and all trucks have the same capacity limit. Costs are stationary, or more generally monotone as in Lippman (Management Sci 16, 1969, 118-138). Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system-wide inventory and transportation costs without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T 2 ) algorithm for the single-stage dynamic lot sizing problem; (2) an O(T 3 ) algorithm for the case of a single-warehouse single-retailer system; and (3) a nested shortest-path algorithm for the single-warehouse multi-retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single-stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems. Finally, we show that the decentralized solution is asymptotically optimal.

A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

“…Here we are using ideas and techniques that were introduced by Jain and Vazirani in their seminal paper on the facility location problem (Jain and Vazirani 2001). Jin and Muriel (2005) also consider this model and propose several heuristics based on centralized and decentralized approaches.…”

Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs

“…The maximal set of affinely independent feasible integer points in X e which make constraint (10) tight are as follows: Set 1 = {(9, 9, 8, 1, 1, 1, 3, 3, 3), (9,8,9,1,1,1,3,3,3), (8, 9, 9, 1, 1, 1, 3, 3, 3)}. One can observe that for these 3 points, the valid inequality y i ≤ 1 is also tight.…”

“…• The idea of the flow cover inequalities is to add the slack variables (1 − y i ) with a certain coefficient φ i in the left hand side of constraint (10). Let us first add φ 1 (1 − y 1 ).…”

“…• The idea of the integer flow cover inequalities is to add the slack variables ( P V − z i ) with a certain coefficient ϕ i in the left hand side of constraint (10). Constraint (10) is not tight for the three following points: Set 3 = {(9, 9, 6, 1, 1, 1, 3, 3, 2), (9, 6, 9, 1, 1, 1, 3, 2, 3), (6, 9, 9, 1, 1, 1, 2, 3, 3)}.…”

A multi-objective ant colony optimization method applied to switch engine scheduling in railroad yards

“…This feature is known in the literature as full truckload and it is the most common mode of transportation in industrial applications (Jin & Muriel, 2006). The yard block must be transported directly from its pickup to its delivery location, i.e., it is not permitted to interrupt a request in course, attend another request, and continue to attend the interrupted request (maybe with a different switch engine), even if this strategy could eventually lead to an overall cost reduction.…”