A discrete time Markov chain model for a periodic inventory system with one-way substitution.

This paper studies the optimal design of an inventory system with “one-way substitution”, in which a high-quality (and hence, more expensive) item fulfills its own demand and simultaneously acts as backup safety stock for the (cheaper) low-quality item. Through the use of a discrete time Markov model we analyze the effect of one-way substitution in a periodic inventory system with an (R,s,S) or (R,S) order policy, assuming backorders, zero replenishment leadtime and correlated demand. In more detail, the optimal inventory control parameters (S and s) are determined in view of minimizing the expected total cost per period (i.e. sum of inventory holding costs, purchasing costs, backorder costs and adjustment costs). Numerical results show that the one-way substitution strategy can outperform both the “no pooling” (only product-specific stock is held, and demand can never be rerouted to stock of a different item) and “full pooling” strategies (implying that demand for a particular product type is always rerouted to the stock of the flexible product, and no product-specific stock is held) − provided the mix of dedicated and flexible inputs is chosen adequately − even when the cost premium for flexibility is significant. Furthermore, we can observe that decreasing the demand correlation results in rerouting more demand to the flexible product and because of the risk-pooling effect reduces the optimal expected total cost.Inventory management; One-way substitution;

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Managing inventories with one-way substitution: a newsvendor analysis

This paper presents an insightful approach to analyze two-item periodic inventory systems with one-way substitution. The objective is to minimize the expected total cost per period, which consists of expected purchasing costs, expected inventory holding costs, expected shortage costs, and expected adjustment costs. This approach helps derive the optimality conditions in both single-period and infinite horizon settings and yields useful insights into the impact of substitution on the service level, the optimality of a borderline case in which the order-up-to level of the inflexible item is reduced to zero, and the pivotal role of the purchasing cost.nrpages: 30status: publishe

A discrete time Markov chain model for a periodic inventory system with one-way substitution

This paper studies the optimal design of an inventory system with “one-way substitution”, in which a high-quality (and hence, more expensive) item fulfills its own demand and simultaneously acts as backup safety stock for the (cheaper) low-quality item. Through the use of a discrete time Markov model we analyze the effect of one-way substitution in a periodic inventory system with an (R,s,S) or (R,S) order policy, assuming backorders, zero replenishment leadtime and correlated demand. In more detail, the optimal inventory control parameters (S and s) are determined in view of minimizing the expected total cost per period (i.e. sum of inventory holding costs, purchasing costs, backorder costs and adjustment costs). Numerical results show that the one-way substitution strategy can outperform both the “no pooling” (only product-specific stock is held, and demand can never be rerouted to stock of a different item) and “full pooling” strategies (implying that demand for a particular product type is always rerouted to the stock of the flexible product, and no product-specific stock is held) − provided the mix of dedicated and flexible inputs is chosen adequately − even when the cost premium for flexibility is significant. Furthermore, we can observe that decreasing the demand correlation results in rerouting more demand to the flexible product and because of the risk-pooling effect reduces the optimal expected total cost.status: publishe

Optimal pooling of inventories with substitution: a literature review

In many inventory management systems, some kind of substitution flexibility exists, meaning that a substitute or more flexible item can be used (at an additional cost) when the preferred product stocks out. Through the use of substitution flexibility, we can take advantage of the risk pooling effect on the flexible item. Since risk pooling reduces total inventory holding costs, a trade-off between inventory holding costs and flexibility costs will determine the optimal inventory control parameters for the different items. In this research paper, we focus on different types of inventory management systems with substitution flexibility, and discuss three methods suggested in the literature (i.e., newsvendor models, simulation and continuous-time Markov chains) in order to optimally exploit substitution flexibility.status: publishe