Roy D. Shapiro

Optimal adaptive price search

Consider the problem of a consumer desiring to buy a good which is sold at a variety of prices. Such a buyer will be able to obtain a sequence of price quotations from various sellers. When should the buyer stop searching for a lower price? If he continues, he may obtain a lower price, but he incurs additional time, effort and expense in searching. The optimal price search decision is one of balancing the expectation of a possibly lower price obtained by continued search against cumulative costs from search. When the prices arise from a known probability distribution, the optimal search strategy has certain well-defined and desirable properties. In the more realistic case that the buyer has only partial information about the price distribution and must update his beliefs after observing prices in the marketplace, the problem becomes more complex, and search strategies become less well behaved. The major purpose of this article is to determine new conditions under which optimal policies have these desirable characteristics in the case where the consumer possesses only incomplete information about the distribution of prices. Price quotations he receives, in addition to providing him with price possibilities, provide him with information about that distribution. Rothschild [ 151, in citing an unpublished paper of Gastwirth, has noted that small specification errors for an assumed distribution can lead to substantial changes in expected number of searches and expected cost. Consequently, the assumption of a known distribution of prices can have a profound effect on total cost. 1 0022-053 l/8 l/040001-20

Managing the Service Mix: After Sale Service for Competitive Advantage

02.00/O

Variable block search with prior information

More and more, customer service is proving to be a source of competitive advantage for manufacturing firms, enabling leaders to remain ahead of the pack and providing the added thrust to allow a challenger to attack and overtake the leader. The articulation of the role of service must take place during the formulation of business unit strategy. Defining the mix of services to be provided requires the understanding of customer needs throughout the entire life cycle of the customer/supplier relationship. To be successful in providing those services, management must recognize that service is a corporate‐wide activity, requiring careful cross‐functional coordination.

From supply chain to demand chain: the role of lead time reduction in improving demand chain performance

Abstract Consider the problem of optimizing an unknown, unimodal, univariate function by direct function evaluation. This article replaces the classic criterion for evaluating search strategies, minimax, by one we feel to be more practical, minimum expected final interval of uncertainty. This latter measure of effectiveness is useful when the experimenter has some prior knowledge of the underlying function and can specify a probability distribution on the location of the optimum. We show here that for a large class of search strategies under the uniform distribution, minimax is equivalent to minimum expected final interval length, i.e., the uniform distribution represents a ‘worst-case’ prior. In addition, computational procedures are develooed for determining the optimal search strategy for arbitrary a priori distributions. Several examples are included.