Designing multi-objective supply chain design relief services with considering to equipment, screening and fuzzy demand in earthquake using the LP-metric method

In these days many people lost their lives and properties to natural events like floods, earthquakes, and storms.  planning before the occurrence of a crisis in order to come up against it is very important and decreases the number of injured and response time.in addition, choosing the number of emergency stations, production centers, and their location is effective for response teams and maximum the use of equipment and space. In this article a two objective mathematical model that minimum costs of transporting relief items and Relief times is proposed, the model also helps us to choose the number of server centers and production centers according to the severity of the earthquake.

Besides in this research we assume that injured people are in three categories green, red and yellow depends on the severity of their injury. Since the problem assumes for programming before the crisis, the proposed model is solved in two-stage. In the first stage, we assume that all injured and relief items transport on time. Then in the second stage, we solve the model with the assumption that we may make some mistakes in the predictions of capacity and demand especially when we confront a drastic earthquake and for this reason, some of the injured people can't transport on time. The proposed model is solved in GAMS with the LP-metric method.

Solving the model shows that patient classification helps us decide which service centers to send relief items to and which centers do not in cases where we have a shortage of resources and cannot send enough relief items. The same is true when ambulances and helicopters do not have enough space to evacuate the injured, in this case, the model helps us decide whether or not to send patients, in such a way that the time of sending items and patients and non-service costs are minimized.

Performance of the model evaluates with solving different examples, Model sensitivity analysis results show that predictions about the number of injuries and the also the costs that we assume for Penalty of not sending equipment and injuries are some of the most effective parameters in the model result. Also, our predictions about the percentage of injured who turn to green, yellow and red patients and the percentage of injured yellow who turn to the red patient has an important effect on the number of patients referred to service centers and the allocation of medical items to service centers.