Modeling of periodic location routing problem with time window and satisfaction dependent demands

In most of real cases such as distribution of perishable food with short life time or medicine products, delivery in shortest time or in specific time window is important, so ignoring these requirements may affect customer's satisfaction. In some cases, customers have different specific time windows in different periods and are eager to receive their demands in mentioned time windows. Therefore the predefined demand of customers in each period may be decreased due to the violation of time windows in previous periods. Since classical LRPs are unable to handle these kinds of assumptions simultaneously, so a new model of periodic location problem is proposed which minimizes the lost demand costs over the multiperiods. To show the verification of model and comparison with classic PLRP, a numerical example is used. The results show the efficiency of the proposed model.