A two-phase method for the capacitated facility problem of compact customer sub-sets

The cost optimal design of the majority of distribution and servicing systems consists of decisions on a number and on the locations of facilities from which customers’ demands are satisfied; however, there are severe difficulties in solving exact procedures because the underlying mathematical model is NP-hard. These decisions should respect some additional conditions as a limited capacity of located facilities. The objective is to minimize the overall costs of the system and to satisfy all customers’ demands. In this paper, we enrich the set of constraints by a new requirement called sub-pool compactness. This property of customer subset influences the quality of vehicle routes subsequently formed in a sub-set of customers served by the same facility. This paper formulates the problem of the enriched capacitated facility location considering compactness condition, formalizes and studies the property of compactness and suggests the compound method solving this problem.