The single-period (news-vendor) problem: literature review and suggestions for future research
Introduction
The classical single-period problem (SPP) is to find a product's order quantity that maximizes the expected profit under probabilistic demand. The SPP model assumes that if any inventory remains at the end of the period, a discount is used to sell it or it is disposed of [1]. If the order quantity is smaller than the realized demand, the news-vendor, hereafter NV, forgoes some profit. The SPP is reflective of many real life situations and is often used to aid decision making in the fashion and sporting industries, both at the manufacturing and retail levels [2]. The SPP can also be used in managing capacity and evaluating advanced booking of orders in service industries such as airlines and hotels [3].
Interest in the SPP has increased in the last decade with over 40 papers published since 1988. In this paper we review the literature on the SPP. The SPP literature is very large and complete coverage is beyond the scope of a single paper. A partial review of the SPP literature has been recently conducted in a textbook by Silver et al. [4]. Because of the depth of the SPP literature, many of the papers we review here were omitted in that review. To avoid redundancy we concentrate our efforts on papers that received little or no treatment in Silver et al.'s book. In Section 2 we introduce the SPP. In Section 3 we develop a taxonomy of SPP extensions and place the reviewed models into the classes of the taxonomy. In Section 4 we provide a discussion of the models. We close with some concluding remarks and suggestions for future research in Section 5.
Section snippets
The classical single-period problem
Researchers have followed two approaches to solving the SPP. In the first approach, the expected costs of overestimating and underestimating demand are minimized. In the second approach, the expected profit is maximized. Both approaches yield the same results. We use the second approach in stating the SPP. Define the following notation:x quantity demanded, a random variable. f(x) the probability density function of x. F(x) the cumulative distribution function of x. P selling price per unit. C cost per
Extensions of the classical single-period model
The SPP has wide applicability especially in service industries which dominates the US economy. As product life cycles continue their downward trend, the importance of the SPP will grow. It is not surprising that many SPP extensions have been suggested with many of them appearing in the last five years. Extensions to the SPP can be classified into 11 categories:
- 1.
Extensions to different objectives and utility functions.
- 2.
Extensions to different supplier pricing policies.
- 3.
Extensions to different
Discussion
While many extensions of the SPP have been proposed, very little comparative work has been done. As described in Section 3.1, the SPP has been solved under many objectives. However, little work has been performed on comparing the results obtained under these differing objectives. For example, under what conditions in terms of demand distribution and problem parameters do the objectives of maximizing E(π) and PB lead to similar or different Q*. Additionally, while many objectives have been
Conclusion and suggestions for future research
Interest in the SPP has increased over the past 40 years. This interest can be attributed in part to the increased dominance of service industries for which the SPP is very applicable in both retailing and pure service organizations such as air transportation. Also, the reduction in product life cycles brought about by technological advances makes the SPP more relevant.
Further areas of SPP research include a joint determination of the optimal order quantity and the discounting policy which
Acknowledgements
The author would like to thank the referees for their helpful suggestions.
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