Chain Stores Location Problem with Bounded Linear Consumption Expansion Function on Paths

Many customers purchased service as part of routine pre-planned trips nowadays, instead of making a special-purpose trip to obtain service. With the assumption that the customer flows at most be serviced for one time, the decision objective for service providers is to find the optimal locations for such service facilities to maximize the number of customers "captured". This sort of problem is called flow interception problem (FIP). This paper proposes utility of each facility and concerns the FIP with bounded linear consumption on the path which is proportional to total utility of same path. Two FIP models with linear bounded expenditures under competitive and monopolistic cases are formulated. Two heuristic algorithms for two cases are developed and computational experiment is described.