A Continuous Review Inventory System with Lost Sales and Emergency Orders

We analyze a continuous review lost sales inventory system with two types of orders—regular and emergency. The regular order has a stochastic lead time and is placed with the cheapest acceptable supplier. The emergency order has a deterministic lead time is placed with a local supplier who has a higher price. The emergency order is not always filled since the supplier may not have the ability to provide the order on an emergency basis at all times. This emergency order has a higher cost per item and has a known probability of being filled. The total costs for this system are compared to a system without emergency placement of orders. This paper provides managers with a tool to assess when dual sourcing is cost optimal by comparing the single sourcing and dual sourcing models

Cooperation in stochastic inventory models with continuous review

Consider multiple companies that continuously review their inventories and face Poisson demand. We study cooperation strategies for these companies and analyse if there exist allocations of the joint cost such that any company has lower costs than on its own; such allocations are called stable cost allocations. We start with two companies that jointly place an order for replenishment if their joint inventory position reaches a certain reorder level. This strategy leads to a simple expression of the joint costs. However, these costs exceed the costs for non-cooperating companies. Therefore, we examine another cooperation strategy. Namely, the companies reorder as soon as one of them reaches its reorder level. This latter strategy has lower costs than for non-cooperating companies. Numerical experiments show that the gametheoretical distribution rule — a cost allocation in which the companies share the procurement cost and each pays its own holding cost — is a stable cost allocation. These results also hold for situations with multiple companies

The Multi-Location Transshipment Problem with Positive Replenishment Lead Times

Transshipments, monitored movements of material at the same echelon of a supply chain, represent an effective pooling mechanism. With a single exception, research on transshipments overlooks replenishment lead times. The only approach for two-location inventory systems with non-negligible lead times could not be generalized to a multi-location setting, and the proposed heuristic method cannot guarantee to provide optimal solutions. This paper uses simulation optimization by combining an LP/network flow formulation with infinitesimal perturbation analysis to examine the multi-location transshipment problem with positive replenishment lead times, and demonstrates the computation of the optimal base stock quantities through sample path optimization. From a methodological perspective, this paper deploys an elegant duality-based gradient computation method to improve computational efficiency. In test problems, our algorithm was also able to achieve better objective values than an existing algorithm.Transshipment;Infinitesimal Perturbation Analysis (IPA);Simulation Optimization

The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands

We develop an algorithm to compute an optimal Q(s,S) policy for the joint replenishment problem when demands follow a compound correlated Poisson process. It is a non-trivial generalization of the work by Nielsen and Larsen (2005). We make some numerical analyses on two-item problems where we compare the optimal Q(s,S) policy to the optimal uncoordinated (s,S) policies. The results indicate that the more negative the correlation the less advantageous it is to coordinate. Therefore, in some cases the degree of correlation determines whether to apply the coordinated Q(s,S) policy or the uncoordinated (s,S) policies. Finally, we compare the Q(s,S) policy and the closely connected P(s,S) policy. Here we explain why the Q(s,S) policy is a better choice if item-demands are correlated.joint replenishment problem; compound correlated Poisson process

Computing replenishment cycle policy parameters for a perishable item

In many industrial environments there is a significant class of problems for which the perishable nature of the inventory cannot be ignored in developing replenishment order plans. Food is the most salient example of a perishable inventory item. In this work, we consider the periodic-review, single-location, single-product production/inventory control problem under non-stationary stochastic demand and service level constraints. The product we consider can be held in stock for a limited amount of time after which it expires and it must be disposed of at a cost. In addition to wastage costs, our cost structure comprises fixed and unit variable ordering costs, and inventory holding costs. We propose an easy-to-implement replenishment cycle inventory control policy that yields at most 2N control parameters, where N is the number of periods in our planning horizon. We also show, on a simple numerical example, the improvement brought by this policy over two other simpler inventory control rules of common use