THE OPTIMAL LOCATIONS OF BRANCH FACILITIES AND MAIN FACILITIES WITH CONSUMER SEARCH*

ABSTRACT. This paper examines the socially optimal locations of branch facilities (or small stores) and main facilities (or large stores) on a finite linear market that is uniformly populated from position 0 to position 1. Each consumer has a probability w of finding the desired service (or product) at a branch facility, and a probability 1 of finding the desired service (or product) at a main facility. Two types of consumer search are considered: phone search and visit search. Different assumptions are made about the numbers of branch facilities and main facilities (each involving one or two facilities of each type). Under visit search, the socially optimal locations of branch facilities tend to be closer to main facilities than under phone search, and this tendency is more pronounced for smaller values of w.     

Markov Models of Inertia and Dynamism on Two Contiguous Ohio Landscapes

This study examined landcover change during 1940–1988 in two contiguous landscapes of approximately 12,400 hectares in central Ohio, USA: an inertial till plain area and a more dynamic moraine area. Agriculture dominated both landscapes throughout, however, the cover of natural vegetation and urban-suburban development increased over time on the moraine while natural vegetation decreased and agriculture increased on the till plain. Markov process models for landcover change were constructed for three 14–17-year time intervals and for the entire forty-eight-year study period. Probabilities of self-replacement for agricultural lands (0.91–0.97) were higher and those for forests (0.54–0.65) lower than those reported for other landscapes. Predictions of landcover percentages for fifty years in the future were made using Markov process models derived from actual cover changes in 1940–1957, 1971–1988, and 1940–1988. All three models produced similar predictions for the inertial till plain area. In contrast, the three models' predictions differed considerably for the moraine area. Only the 1971–1988 transition matrix was sensitive to increases in urbanization and reforestation which began on the moraine in the 1970s. These results indicate that reliance on lengthy study intervals and net rates of change can obscure spatial and temporal patterns of landcover change that are caused by natural and socioeconomic factors operating on shorter time scales.