دانلود رایگان ترجمه مقاله یکی کردن زمان انتظار با مدل های محل رقابتی (نشریه اسپرینگر 2007)

یکی کردن زمان انتظار با مدل های محل رقابتی

Incorporating Waiting Time in Competitive Location Models

Abstract

In this paper we propose a metaheuristic to solve a new version of the Maximum Capture Problem. In the original MCP, market capture is obtained by lower traveling distances or lower traveling time, in this new version not only the traveling time but also the waiting time will affect the market share. This problem is hard to solve using standard optimization techniques. Metaheuristics are shown to offer accurate results within acceptable computing times.

1 Introduction

ReVelle’s (1986) Maximum Capture Problem initiated a series of studies on the location of retail facilities in discrete space (see Serra and ReVelle 1995). The MAXCAP model makes the following assumptions: (1) the product sold is homogeneous, (2) the consumer’s decision on patronizing the store is based on distance and (3) unit costs are the same in all stores regardless of ownership. Examples of services that best fit these three assumptions can be found mainly in the fast food sector, in convenience stores and in the banking sector. However, in all these examples, not only the distance but also waiting time seems to determine the consumer’s decision. The number of persons the consumer finds in queue, when he or she arrives at the store, can be a measure for the consumer’s perception of waiting time. Furthermore, the waiting time for one visit may affect future decisions as to which store to patronize the next visit. This seems to be quite relevant for some retail stores, fast food restaurants or ATM machines. Kohlberg (1983), in pioneer work in the same line of research, considers a variant of the classical Hotelling model for store locations. The author assumes that when choosing a store, consumers take into account not only travel time but also waiting time for the service at each store, which in turn depends on the number of consumers patronizing that store. Assuming that each consumer makes the decision that minimizes travel time plus waiting time, stores’ market shares are shown to be continuous functions of their locations. There is also a general consensus that the distances may be interpreted in a functional, proximity, or similarity context rather than in a geometrical one. Our claim is that in some types of services, waiting time has a strong impact on the consumer’s perception of proximity. In Section 2 we will revise some literature on competitive spatial modeling. In Section 3 we describe a model, which incorporates explicitly waiting time, and in Section 4 we propose a metaheuristic to solve the model. Some results of our computational experiments are described in Sections 5 and 6.