مدل های مکانی برای واگذاری سهم بازار و کوچک کردن خدمات

New location models are presented here for exploring the reduction of facilities in a region. The first of these models considers firms ceding market share to competitors under situations of financial exigency. The goal of this model is to cede the least market share, i.e., retain as much of the customer base as possible while shedding costly outlets. The second model considers a firm essentially without competition that must shrink it services for economic reasons. This firm is assumed to close outlets so that the degradation of service is limited. An example is offered within a competitive environment to demonstrate the usefulness of this modeling approach.

Location science, with its components of theory and modeling, continues to grow dramatically in the disciplinary areas of geography, management, mathematics, economics and operations research. In general, the purpose of this research field is to formulate quantitative models to cite a given set of facilities in a region. The region can be represented by a network, continuous space, or can be a set of discrete points. There are models for locating public facilities such as schools or post-offices, models for locating retail facilities in the presence of competition, models for locating emergency services such as fire stations or ambulances, and models for locating plants and warehouses, among others. These quantitative models can be formulated and solved using linear programming, integer programming, dynamic programming or by heuristic or metaheuristic approaches. Facilities may have capacity restrictions, experience congestion, have minimum thresholds for level of service and other defining characteristics. The demand to be served may be deterministic or stochastic to address uncertainty issues. Thus, a myriad of formulations are available within the field of location science to address very different issues related to the formulation, solution and implementation of location problems. An overview of the state of the art in this area is presented in [1]. But most location models (if not all) have one thing in common: they are proactive, in that they all seek the location of new facilities, or they are reactive, in that they seek to relocate and open new locations at the same time. The literature has paid little attention to the fact that sometimes it is necessary to close facilities [2], even though the same mathematical modeling framework in choosing new locations would also be applicable in choosing which existing locations to close. In the private sector, the marketplace for contemporary industrial and service goods is often highly competitive. Firms map out their activities in light of market forces and the action of rival firms in the industry. Changes in the competitive structure of the industry call for new strategies. Strategies do not always succeed as planned, however; plant or store closure may occur as an integral part of strategy or in spite of it. Corporate planners often fail to predict future market trends or are unable to maintain their market share when competitive conditions in the industry change. They may not perceive the gravity of market changes, or they may believe that their established market position leaves them immune to market dynamics. In other cases, production systems do not operate as planned and products fail to meet consumer expectations. As well, new products may be introduced. All these conditions may lead to rivals succeeding in stealing market share. Thus changes in the competitive structure of industries and services may lead to plant or store closures in two distinct ways: as an integral part of the process of strategic adaptation or as a consequence of failure to adapt to new industry conditions. As an example, Plant Closing News, a biweekly, industry-focused newsletter (see www.plantclosings.com), found that in only the first week of 2003 there were more than 500 industrial plant closures in the U.S. and Canada, in very diverse industrial sectors (Table 1). Plant closings are the most visible manifestation of market dynamics and corporate restructuring on the economic landscape.Another reason for plant closure is related to business cycles. When the economy is in a growing period, demand for products and services is high, leading to new investments and the building of new facilities. However, when the business cycle is in recession, some investments are no longer profitable and it becomes necessary to close some of the currently operating facilities in order to survive. In Fig. 1, the growth rate for the U.S. from 1972 to 2003 clearly shows the roller-coaster ups and downs of the economy. The shaded areas represent periods of economic crises, with plant closures, massive layoffs and demand downfall. In these periods, firms need to downsize their capacity and infrastructure to an appropriate size in order to cope with the economic situation.Another argument for plant closures is based on the fact that some economic sectors and industries are in decline. A declining industry is defined as an industry group's employment level decreasing for two quarters by 5% or more over the year. In fact, a significant fraction of U.S. manufacturing output is accounted for by declining industries. In these industries, the important competitive moves pertain to disinvestments rather than investment. Capacity must be reduced in order to restore profitability. Capacity reduction is, however, like a public good; each firm would prefer that its competitors shoulder the reduction. Some plant location models have been developed to address the issue of plant closure in a multiperiod setting. Klincewicz et al. [3] formulated a large-scale multilocation capacity-planning model. The model chooses a multiperiod schedule of openings, expansions, and closings of facilities and assigns demand locations to these facilities. Although generic in nature, this model was developed to plan the evolution of material logistics systems over time. In order to have a truly practical tool, numerous features are considered including existing configuration, arbitrary demand patterns, concave operating costs, single-source assignments, demand location reassignment costs, and others. A real-world application involving the relocation and phase-out of a combined manufacturing plant and warehousing facility was presented by Melachrinoudis and Min [4]. The relocation and phase-out decision was called for to adapt to dynamic changes in business environments surrounding the firm's supply chain operations. Such changes included changes in supplier and customer bases, distribution networks, corporate re-engineering, business climate, and government legislation. To aid management in formulating a more effective relocation strategy, Melachrinoudis and Min [4] assess the viability of a proposed site from multi-echelon supply chain perspectives and determine the optimal timing of relocation and phase-out in the planning horizon using a dynamic, multiple objective, mixed-integer programming model. Wang et al. [2] studied a budget constrained location problem in which they simultaneously consider opening some new facilities and closing some existing facilities. The objective is to minimize the total weighted travel distance for customers subject to a constraint on the budget for opening and/or closing facilities and a constraint on the total number of open facilities desired. Their application focused on locating/relocating bank branches in Amherst, New York. They also discuss the situation where operating costs are part of the objective function. The retailing sector is also affected by business downturns that can cause the closure of many (even hundreds of) retail stores. For example, a serious economic crisis at K-Mart Corporation forced the company to close many of their stores across U.S. after years of struggling against more powerful and successful rivals Wal-Mart Stores Inc. and Target Corp. One chain, Ames, closed all of its stores. In order to ensure a more competitive position and to exit from bankruptcy, K-Mart closed more than 30% of its stores across U.S. [5]. Facility closing is also a common feature in the public sector. For example, on April 14, 1993 the Minister of Health of the Province of Saskatchewan announced the closure of 52 of the 112 small hospitals in the Province based on: size, utilization for two consecutive years and distance to the nearest-neighboring hospital [6]. Weston [7] formulated a model to find the optimal location of telephone answering sites for a non-competitive service organization within the public sector. The methodological approach taken to addressing the telephone site location problem was integer programming. The modeling effort resulted in several organization changes including opening and closing of individual offices, domain realignments of new or existing offices, and significant cost savings primarily due to telecommunication cost reductions and increased utilization of telephone answering manpower. Perhaps the most significant modeling work in the public sector has been for school system consolidation as a result of declining enrolments. Noteworthy initial efforts in this area were of Bruno and Anderson [8] and Diamond and Wright [9]. The work of Diamond and Wright [9] was unique in that balancing utilization was also a goal. Church and Murray [10] also examine consolidation combined with balancing utilization. Other instances where it may be necessary to close facilities are related to public transport. For example, in urban bus transportation it may be necessary to eliminate some stops and relocate others due to changes in population density and network changes. There is, on the one hand, a tradeoff between number of stops and geographical coverage, with more stops providing greater coverage. On the other hand, more stops along a route translate to greater service interruption and longer travel times. Murray and Wu [11] study some modeling approaches for addressing accessibility concerns in an integrated fashion. They illustrate the models using bus-based transit in Columbus, Ohio. Most, if not all, the models developed so far address the closure of specific services to close. In this paper, we formulate the Planned Shrinkage Problem, a new general model to close facilities. We present the general model in the next section. In the third section, computational experience is recounted in the context of a specific example. Finally, some conclusions are offered.

Models of facility closing are not well developed in the literature. We have proposed in this paper two newmodels that address facility closing. One of these in- vestigates facility closing in a competitive environment, and the other examines closing in the situation of finan- cial exigency without competitors. Application resultsfor closing facilities in a competitive environment were presented to demonstrate the power of these models in such situations. The models are based on the Maximal Covering Location Model that, since its first publica- tion in 1974, has been modified and enriched with con- straints such as capacities on the facilities, stochastic demand, or backup coverage, among others. A good re- view of some of these extensions used in the public sec- tor can be found in [15] and can also be implemented when the models focus on plant or service closing.