A combined facility location and network design model with multi-type of capacitated links and backup facility and non-deterministic demand by fuzzy logic

Recently so many researches are concerned with the combined facility location and network design models for facility location and coverage problems. In this models we want to find the optimum location of facility by constructing an underlying network. We can use this for distribution network, transportation networks, health centers and emergency allocations, etc. At this study a mathematical programming model is introduced that facilities are opened on the nodes and it is assumed for connecting demand nodes and facilities there are different links with different quality that just one of them should be selected. Also if a facility in a node can't satisfy demand the demand is sent to a facility in other node and satisfied by this facility called backup facility. Also decision process is affected by uncertainty and concept of information inherently is mixed with uncertainty. Fuzzy logic can introduce mathematical models for hazy concepts and variables and systems and also showing a way for argument, control and making decision in uncertainty condition. In complex systems with high uncertainty fuzzy logic is best way for the modeling. At this study demands are considered in uncertain form and are introduced in the form of fuzzy numbers. The problem is modeled for different size and the computational results are compared.