The design of capacitated facility networks for long term care service

• Current research results are extended by allowing more than one type of facilities.
• Also, the capacity of facilities is considered with closest assignment requirement.
• A branch and bound algorithm is developed for exact solution with pruning rules, lower bound and upper bound.
• A genetic algorithm is presented for solving large sized problem.

Life expectancy is going up and the demand of long term care facilities is increasing in most countries. This study deals with designing problem of facility networks for long-term care services in a city consisting of a number of regions. Assuming that in each region a candidate site for long-term care facility exists, we seek to identify regions where opening of a long-term care facility is desirable and also determine the type of new facility. For the problem, an integer programming model is formulated with the objective of minimizing the total construction cost. The closest assignment rule is adopted to reflect the preference of patient in choosing long term care facility by assigning patient to an open facility closest from his home. To solve the model, we develop a branch and bound algorithm for exact solution and a genetic algorithm to solve large sized problem. The validity of the mathematical model and the proposed algorithms are illustrated through a number of problem instances.