Single-Period Multiproduct Inventory Models with Substitution

Bassok, Yehuda; Anupindi, Ravi; Akella, Ram

doi:10.1287/opre.47.4.632

Cited by 306 publications

(173 citation statements)

References 10 publications

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“…Some researchers have focused on singleperiod multidimensional newsvendor models. For example, Bassok et al (1999) propose a general multiproduct inventory model to study the benefits of substitution. Pasternack and Drezner (1991) find the optimal stocking policy for goods with stochastic demand and substitution in both the 'up' and 'down' directions.…”

Section: Related Literaturementioning

confidence: 99%

“…If we let T = 1, model DYN collapses into the single-period (or static) model studied by Bassok et al (1999), , and others (we will use the acronym STC to refer to this model).…”

Section: Related Modelsmentioning

confidence: 99%

“…However, for many applications this 'single-period' assumption overestimates profits and, as we shall see, may also overestimate the value of inventory flexibility. Therefore, this model can be seen as an extension of the single-period multi-product newsvendor models of Bassok et al (1999), , and others, to an environment with multi-period demand. Another model with this flavor is the 'newsvendor network' of Van Mieghem and Rudi (2002), but their model allows the firm to replenish inventories between each period.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Capacity Management with Substitution

Shumsky

Zhang

2009

Operations Research

120

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We examine a multiperiod capacity allocation model with upgrading. There are multiple product types, corresponding to multiple classes of demand, and the firm purchases inventory of each product before the first period and thereafter replenishment is not possible. Within each period, after demand arrives, products are allocated to customers. Customers who arrive to find that their product has been depleted can be upgraded by at most one level. We show that the optimal solution is a simple two-step algorithm: first use any available inventory to satisfy same-class demand and then upgrade customers until inventory reaches a protection limit. We describe how to find optimal protection limits by backward induction and show that the protection limits are monotonic in current inventory and in time. The monotonicity results lead to simple bounds for the optimal protection limits, and we demonstrate that heuristic protection limits based on the bounds are effective in solving large problems.For a model with two time-periods and two products (dedicated and flexible), we compare the optimal initial capacity under our dynamic model with the optimal capacity under a singleperiod 'static' model. For a given capacity level, the marginal value of the dedicated capacity is always greater under the dynamic model than under the static model. Numerical experiments show that the optimal level of dedicated capacity is greater under the dynamic model than under that static model, although the optimal flexible capacity can be smaller, or greater, under the dynamic model.

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Section: Related Literaturementioning

confidence: 99%

“…If we let T = 1, model DYN collapses into the single-period (or static) model studied by Bassok et al (1999), , and others (we will use the acronym STC to refer to this model).…”

Section: Related Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic Capacity Management with Substitution

Shumsky

Zhang

2009

Operations Research

120

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“…Substitution has started to be explored in an inventory context, and its effects are likely to be similar in capacity problems. An important issue is whether the substitution is executed by the firm or by customers, as discussed in Bassok et al (1999) and Netessine and Rudi (2003).…”

Section: Unsatisfied Demand and Capacity Shortagesmentioning

confidence: 99%

Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments

Mieghem

2003

M&SOM

510

240

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T his paper reviews the literature on strategic capacity management concerned with determining the sizes, types, and timing of capacity investments and adjustments under uncertainty. Specific attention is given to recent developments to incorporate multiple decision makers, multiple capacity types, hedging, and risk aversion. Capacity is a measure of processing abilities and limitations and is represented as a vector of stocks of various processing resources, while investment is the change of capacity and includes expansion and contraction. After discussing general issues in capacity investment problems, the paper reviews models of capacity investment under uncertainty in three settings:The first reviews optimal capacity investment by single and multiple risk-neutral decision makers in a stationary environment where capacity remains constant. Allowing for multiple capacity types, the associated optimal capacity portfolio specifies the amounts and locations of safety capacity in a processing network. Its key feature is that it is unbalanced; i.e., regardless of how uncertainties are realized, one typically will never fully utilize all capacities. The second setting reviews the adjustment of capacity over time and the structure of optimal investment dynamics. The paper ends by reviewing how to incorporate risk aversion in capacity investment and contrasts hedging strategies involving financial versus operational means.

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“…As for the model considered in this paper, the management becomes much more intricate due to the one-sided interplay between the two types of items. Such an interplay between different types of items is commonly known as substitution or lateral transshipment in multi-product inventory systems (see, e.g., [5,2,27]). …”

Section: Introductionmentioning

confidence: 99%

Two perishable inventory systems with one-way substitution

2016

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Motivated by the ABO issue of the blood banks system, in which the portions stored have constant shelf life, we consider two subsystems of perishable inventory. The two Perishable Inventory Subsystems -PIS A and PIS B, are correlated to each other through a so-called one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsystem are four Poisson processes which are independent of one another. However, if the shelf of PIS A (blood of type O) is empty of items an arriving demand of type A is unsatisfied, since demand of type A cannot be satisfied by an item of type B (blood portions of type AB), but if the shelf of PIS B is empty of items an arriving demand of type B is applied to PIS A, since demands of type B can be satisfied by both types. Such a one-way substitution of the issuing policy generates for PIS A a modulated Poisson demand process operating in a two-state non-Markovian environment. The performance analysis of PIS B is known from previous work. Hence, in this study we focus on the marginal performance analysis of PIS A. Based on a fluid formulation and a Markovian approximation for the one-way substitution demands process, we develop a unified approach to efficiently and accurately approximate the performance of PIS A. The effectiveness of the approach is investigated by extensive numerical experiments.

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Single-Period Multiproduct Inventory Models with Substitution

Cited by 306 publications

References 10 publications

Dynamic Capacity Management with Substitution

Dynamic Capacity Management with Substitution

Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments

Two perishable inventory systems with one-way substitution

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