The single-period (news-vendor) problem: literature review and suggestions for future research

doi:10.1016/S0305-0483(99)00017-1

Omega

Volume 27, Issue 5, October 1999, Pages 537-553

https://doi.org/10.1016/S0305-0483(99)00017-1 Get rights and content

Abstract

The single-period problem (SPP), also known as the newsboy or news-vendor problem, is to find the order quantity which maximizes the expected profit in a single period probabilistic demand framework. Interest in the SPP remains unabated and many extensions to it have been proposed in the last decade. These extensions include dealing with different objectives and utility functions, different supplier pricing policies, different news-vendor pricing policies and discounting structures, different states of information about demand, constrained multi-products, multiple-products with substitution, random yields, and multi-location models. This paper builds a taxonomy of the SPP literature and delineates the contribution of the different SPP extensions. This paper also suggests some future directions for 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 P_B 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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The single-period (news-vendor) problem: literature review and suggestions for future research

Abstract

Introduction

Section snippets

The classical single-period problem

Extensions of the classical single-period model

Discussion

Conclusion and suggestions for future research

Acknowledgements

Omega

Eur J Opl Res

Eur J Opl Res

Int J Prod Econ

Eur J Opl Res

Eur J Opl Res

Int J Prod Econ

Comput Ind Eng

Eur J Opl Res

J Oper Manage

Int J Prod Econ

Oper Res Lett

Eur J Opl Res

Int J Prod Econ

Int J Prod Econ

Int J Prod Econ

Comput Ind Eng

Omega

Production and operations management

The distribution free newsboy problem: review and extensions

J Opl Res Soc

Inventory management and production planning and scheduling

Pricing objectives in large companies

Am Econ Rev

Optimizing and satisfying in stochastic cost–volume–profit Analysis

Decis Sci

Inventory models and management objectives

Sloan Manage Rev

Some extensions of Ismail–Louderback's stochastic CVP model under optimizing and satisfying criteria

Decis Sci

The newsboy problem under alternative optimization objectives

J Opl Res Soc

Maximizing the probability of achieving a target profit level in a two-product newsboy problem

Decis Sci

A two-product newsboy problem with satisfying objective and independent exponential demands

IIE Trans

Refinements in the Ismail–Louderback's stochastic CVP model

Decis Sci

Optimal order quantity for pre-determined level of profit

Manage Sci

A general decision model for cost–volume–profit analysis under uncertainty

Account Rev

Optimality criteria and risk in inventory models: the case of the newsboy problem

J Opl Res Soc

Incentives, uncertainty, and risk in the newsboy problem

Decis Sci

Risk in inventory models: the case of the newsboy problem, optimality conditions

J Opl Res Soc

The risk averse (and prudent) newsboy

Manage Sci

Cost–volume–profit analysis, uncertainty and capital market equilibrium

J Account Res

A stochastic demand CVP model with return on investment criterion

Contemp Account Res

A comment on “Optimality criteria and risk in inventory models: the case of the newsboy problem”

J Opl Res Soc

A general decision model for cost–volume–profit analysis under uncertainty: a comment

Account Rev

A comment on Shih's general decision model for CVP analysis

Account Rev

Single-period inventory models with demand uncertainty and quantity discounts: behavioral implications and a new solution procedure

Naval Res Logist Q

The generalized newsboy problem, contract negotiations and secondary vendors

IIE Trans

A Note on the newsboy problem with an emergency supply option

J Opl Res Soc

Standard container size discounts and the single-period Inventory problem

Decis Sci

The newsboy problem with progressive retailer discounts and supplier quantity discounts

Decis Sci

The newsboy problem with price-dependent demand distribution