The multi-item newsboy problem is used to determine the value of two types of incomplete information, global information and product-mix information. It is shown that this value depends on the number of products, the existence of a budget restriction and the degree of substitutability.
In the last decade, the newsboy problem in general and the multi-item newsboy problem or newsstand problem in particular have been studied in a large number of papers [1]. In contrast to the classical newsboy, who sells a single product, the multi-item newsboy sells several products to a single group of customers. When demand for different products is unrelated, the multi-item newsboy can attain maximal expected profits by maximising the expected profits from individual products [2] and [3]. To create non-trivial multi-item newsboy problems, three complications have been introduced: performance criteria other than expected profits [2] and [3], budget or capacity constraints [4], [5], [6], [7] and [8], and substitutability, which implies that customers may switch to a different product if the demand for their preferred product cannot be satisfied [9] and [10].
A recent survey shows that, within the context of the multi-item newsboy problem, scarcely any attention has been given to the value of information [1], though this subject has attracted interest in discussions of the single-item newsboy problem [11] and [12]. In this paper, we try to determine the value of information in the multi-item newsboy problem, and specifically, we are interested in the value of two types of incomplete information, global information and product-mix information [13]. Global information implies that the combined demand for all products can be accurately predicted, but the distribution over the products is unknown. Product-mix information implies that total demand is unknown, but the distribution over products is known exactly. According to the Bayesian approach, we compute the value of information by comparing expected profits when the information in question is available with expected profits when only the distribution of expected demand is known. Consequently, we do not consider the alternative success criteria discussed in [2] and [3].
The remainder of this paper is structured as follows. In Section 2, the basic multi-item newsboy problem is outlined and the value of global and product-mix information is computed. In 3 and 4, respectively, the multi-item newsboy problem with a budget constraint and the multi-item newsboy problem with substitutability are discussed. In both instances, we only compute results for the two-item case. Section 5 contains conclusions and suggestions for further research.
In two respects, this research differs from the mainstream of the research on the news-vendor problem [1]. First, it focuses on the value of information in simple models and not on methods to attain an optimal solution in increasingly complex situations, and second, no analytical results are given, but results are computed numerically.
It has been shown that the multi-item newsboy problem is a satisfactory model to assess the value of incomplete information in the form of product-mix information and global information. In the basic model, the value of product-mix information increases, and the value of global information decreases with the number of products. A budget constraint diminishes the value of information, and this effect is more prominent for global information than for product-mix information. Moreover, a budget constraint also diminishes the value of perfect information and with a fairly tight budget, the value of product-mix information approaches the value of perfect information. On the other hand, substitutability increases the value of global information and decreases the value of product-mix information.
This research can be extended in a number of directions,. First, a number of simplifications can be removed, such as the assumption that price, cost and demand distribution of all products are the same, and that substitutability is symmetric. Second, complicating factors can be introduced, such as fixed order costs, salvage values or penalties for lost demand. Third, budget constraints and substitutability can be combined. As substitution is an alternative for product-mix information, it may be especially profitable with a tight budget. Finally, the value of information can be studied in relation to its cost. For example, the cost of acquiring product-mix information probably increases with the number of products, and this increase may surpass the concomitant increase in value.
However, it is important that such studies are in line with the original purpose of the newsboy problem, to supply a framework for research into the value of information, rather than the computation of optimal order quantities.
