Martingale inequalities and NP-complete problems
Mathematics of Operations Research
One warehouse multiple retailer systems with vehicle routing costs
Management Science
A class of Euclidean routing problems with general rout cost functions
Mathematics of Operations Research
Probabilistic Analyses and Practical Algorithms for Inventory-Routing Models
Operations Research
Invited Review: Industrial aspects and literature survey: Combined inventory management and routing
Computers and Operations Research
Cost sharing in distribution problems for franchise operations
Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions
Coordination of split deliveries in one-warehouse multi-retailer distribution systems
Computers and Industrial Engineering
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We consider the Inventory-Routing Problem where n geographically dispersed retailers must be supplied by a central facility. The retailers experience demand for a product at a deterministic rate and incur holding costs for keeping inventory. Distribution is performed by a fleet of capacitated vehicles. The objective is to minimize the average transportation and inventory costs per unit time over the infinite horizon. In this paper, we focus on the set of fixed partition policies. In a fixed partition policy, the retailers are partitioned into disjoint and collectively exhaustive sets. Each set of retailers is served independently of the others and at its optimal replenishment rate. We derive a deterministic (O(n)) lower bound on the cost of the optimal fixed partition policy. A probabilistic analysis of the performance of this bound demonstrates that it is asymptotically 98.5%-effective. That is, as the number of retailers increases, the lower bound is very close to the cost of the optimal fixed partition policy.