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In this paper, a double-type double-standard model (DtDsM) for maximal covering location problem is proposed which has several applications in determining the location of public emergency facilities. DtDsM includes two types of facilities: normal and backup facilities. Although backup facilities have a greater coverage distance, they offer not a full service but only a primary service. In DtDsM, each demand point must lie within the coverage distance of a backup facility if it does not lie in the coverage distance of a normal facility ensuring it to receive minimal primary services within a predetermined time. Furthermore, an accelerated Benders decomposition algorithm is proposed to solve the model. The speed and accuracy of the algorithm are compared with the commercial solver CPLEX.

This paper deals with preemptive priority based multi-objective network design problems in which construction times together with travel costs are taken into account. These cost and time objective functions are ordered lexicographically with respect to manager’s strategies in order to decrease total cost and total construction time of the network. To solve this preemptive problem, instead of the standard sequential approach, a modified Benders decomposition algorithm is developed. It is proved that this algorithm decreases the (expected) number of computations and so this algorithm is efficient for large-scale network design problems.