On multi-criteria chance-constrained capacitated single-source discrete facility location problems

Abstract

This work aims at investigating multi-criteria modeling frameworks for discrete stochastic facility location problems with single sourcing. We assume that demand is stochastic and also that a service level is imposed. This situation is modeled using a set of probabilistic constraints. We also consider a minimum throughput at the facilities to justify opening them. We investigate two paradigms in terms of multicriteria optimization: vectorial optimization and goal programming. Additionally, we discuss the joint use of objective functions that are relevant in the context of some humanitarian logistics problems. We apply the general modeling frameworks proposed to the so-called stochastic shelter site location problem. This is a problem emerging in the context of preventive disaster management. We test the models proposed using two real benchmark data sets. The results show that considering uncertainty and multiple objectives in the type of facility location problems investigated leads to solutions that may better support decision making.

Multi-Criteria Location Model of Emergency Shelters in Humanitarian Logistics

“…Certain studies have built multi-level optimization models to support shelter location selection and post-disaster evacuation decision making. Most of them jointly optimize the objective functions [20][21][22] or rank the objectives [23]. A few scholars have focused on facility optimization at different levels.…”

“…Shelters are better protected from secondary disasters, such as floods and landslides on the plain than on the hills. Candidate sites should avoid fault lines, and slopes should not exceed 7%, preferably between 2% and 4% [22]. Concurrently, in rainy areas, the existence of vegetation helps consolidate the soil and prevent debris flow [19,21,26].…”

“…Therefore, shelters should have basic power facilities [5,19,24,26]. Shelters must also provide clean drinking water to maintain normal daily living, and sewage treatment facilities are highly important for refugees [19,21,22]. On the basis of Chinese national standards, Turkish Red Crescent standards, and related studies, the six qualitative factors affecting the location of emergency shelters are identified, namely, topography, There are two different kinds of needs that will emerge for the victims after the disaster, namely basic needs for living materials and medical or psychological assistance.…”

“…Trivedi and Singh [7], GB/T 33744-2017 [19], Kılcı et al [30] Vegetation GB/T 33744-2017 [19], Li et al [21], Yahyaei and Bozorgi-Amiri [26] Power facilities Zhu et al [5], GB/T 33744-2017 [19], Yuan et al [24], Yahyaei and Bozorgi-Amiri [26] Sanitation system GB/T 33744-2017 [19], Li et al [21], Kınay et al [22] A committee composed of experts with experience in evaluating the selection criteria and recorded personal preferences through questionnaires is employed. Table 2 presents the representation method of transforming language variables into numerical variables.…”

“…Objective function (21) optimizes the number of open shelters. Constraints (22) and (23) stipulate that the number of households allocated to each refuge center cannot exceed the capacity of the facility. Among them, in natural disasters with high destructiveness and casualties, victims who need psychological or medical assistance must receive considerable concern.…”