Business Applications of Operations Research

CHAPTER 3

Facility Location

1. Supermarkets Serving the Maximum Number of People

Let us consider six neighbouring towns A, B, C, D, E, and F. The distance k_ij between towns i and j (in miles) is indicated in Table 3.1 for towns that have roads connecting them. The population of the towns P_i is also given in the first row of Table 3.1.

Table 3.1

Population (in thousands)	3	8	2	12	7	10
	A	B	C	D	E	F
A	–	50	26	–	15	32
B	50	–	–	34	28	–
C	26	–	–	29	40	17
D	–	34	29	–	18	24
E	15	28	40	18	–	43
F	32	–	17	24	43	–

A supermarket chain wishes to set up supermarkets at two towns such that the two supermarkets are accessible to the maximum number of people of the six neighbouring towns.¹ Supermarkets are considered accessible if the distance ...