With the recent trend toward just-in-time deliveries and reduction of inventories, many firms are reexamining their inventory and logistics policies. Some firms have dramatically altered their inventory, production, and shipping policies with the goal of reducing costs and improving service. Part of this restructuring may involve a specific contract with a trucking company, or it may entail establishing in-house shipping capabilities. This restructuring, however, raises new questions regarding the choice of optimal trucking capacity, shipping frequency, and inventory levels. In this study, we examine a two-level distribution system composed of a warehouse and a retailer. We assume that demand at the retailer is random. Since the warehouse has no advance notice of the size of the retailer order, inventory must be held there as well as at the retailer. We examine inventory policies at both the warehouse and the retailer, and we explicitly consider the trucking capacity, and the frequency of deliveries from the warehouse to the retailer. Both linear and concave fixed transportation costs are examined. We find the optimal base stock policies at both locations, the optimal in-house or contracted regular truck capacity, and the optimal review period (or, equivalently, delivery frequency). For the case of normally distributed demand we provide analytical results and numerical examples that yield insight into systems of this type. Some of our results are counterintuitive. For instance, we find some cases in which the optimal truck capacity decreases as the variability of demand increases. In other cases the truck capacity increases with variability of demand. © 1993 John Wiley & Sons, Inc.
[1]
Randolph W. Hall,et al.
Distribution Strategies that Minimize Transportation and Inventory Costs
,
1985,
Oper. Res..
[2]
Bruce L. Golden,et al.
A Framework For Probabilistic Vehicle Routing
,
1979
.
[3]
D. Blumenfeld,et al.
Analyzing trade-offs between transportation, inventory and production costs on freight networks
,
1985
.
[4]
Marshall L. Fisher,et al.
Coordination of production and distribution planning
,
1994
.
[5]
Carlos F. Daganzo,et al.
Logistics Systems Analysis
,
1991
.
[6]
F. Tillman.
The Multiple Terminal Delivery Problem with Probabilistic Demands
,
1969
.
[7]
Lawrence Bodin,et al.
PLANNING FOR TRUCK FLEET SIZE IN THE PRESENCE OF A COMMON‐CARRIER OPTION
,
1983
.
[8]
Julian Benjamin,et al.
An Analysis of Inventory and Transportation Costs in a Constrained Network
,
1989,
Transp. Sci..
[9]
Robert L. Bregman,et al.
A Heuristic for the Control of Inventory in a Multi-echelon Environment with Transportation Costs and Capacity Limitations
,
1990
.
[10]
L. Zurich,et al.
Operations Research in Production Planning, Scheduling, and Inventory Control
,
1974
.
[11]
Thomas M. Cook,et al.
A SIMULATION AND STATISTICAL ANALYSIS OF STOCHASTIC VEHICLE ROUTING WITH TIMING CONSTRAINTS
,
1978
.
[12]
Awi Federgruen,et al.
A Combined Vehicle Routing and Inventory Allocation Problem
,
1984,
Oper. Res..