Stochastic facility and transfer point covering problem with a soft capacity constraint

Existing models for transfer point location problems (TPLPs) do not guarantee the desired service time to customers. In this paper, a facility and TPLP is formulated based on a given service time that is targeted by a decision maker. Similar to real‐world situations, transportation times and costs are assumed to be random. In general, facilities are capacitated. However, in emergency services, they are not allowed to reject the customers for out of capacity reasons. Therefore, a soft capacity constraint for the facilities and a second objective to minimize the overtime in the facility with highest assigned demand are proposed. To solve the biobjective model with random variables, a variance minimization technique and chance‐constraint programming are applied. Thereafter, using fuzzy multiple objective linear programming, the proposed biobjective model is converted to a single objective. Computational results on 30 randomly designed experimental problems confirm satisfactory performance of the proposed model in reducing the variance of solutions as well as the overtime in the busiest facility.