Review Article

Mathematical Models in Humanitarian Supply Chain Management: A Systematic Literature Review

Table 1

Facility location models in HSC.

AuthorsObjective functionConstraints/decisionProblem type

Balcik and Beamon [21]Maximize (demand coverage by distribution centers)Budget constraint, inventory level at distribution centersMaximal covering location model

Bozorgi-Amiri et al. [22]Minimize (costs for predisaster setup, procurement, transportation, holding, shortage)Capacity for relief distribution canter, commodity flow, supply and demandLocation-allocation model

Horner and Downs [23]Minimize (costs of distributing relief goods)Demand fulfilment constraint, number of distribution centersIntermediate distribution facility model

Dekle et al. [15]Minimize (facilities for each area with a given distance)Identify the location of the facility for each areaCovering location model

Hong et al. [25]Minimize (total logistics cost)Distance between warehouse and facility, number of facilities, demandFacility location model

Chang et al. [16]Minimize (transportation cost, facility setup cost, distance of rescue equipment cost)Number of facilities and their capacity, prioritization of facility allocation, storage, shortage, penalties for surplusLocation allocation model

McCall [17]Minimize (victim nautical miles, shortage)Facility capacity, number of kits for prepositioning before disaster, unsatisfied demandsFacility location model

Rawls and Turnquist [91]Minimize (costs of facility opening, unsatisfied demand, transportation)Location and inventory level decision at each facilityLocation-allocation model

Zhang et al. [24]Minimize (cost of the total time of dispatching emergency resources)Equilibrium of supply and demand for primary disaster, equilibrium of supply and demand for potential secondary disaster, resources available for secondary disasterLocation-allocation model

Akgün et al. [18]Minimize (risk for unsatisfied demand)Response time, distance between facility and disaster pointFacility location model

Barzinpour and Esmaeili [27]Maximize (cumulative coverage of population)
Minimize (total cost)
Demand and supply, transportation capacity, facility storage capacityLocation-allocation model

Abounacer et al. [26]Minimize (distance from distribution center to demand point, number of facilities, unsatisfied demand)Daily working hours, supply and demand, vehicle capacityLocation-transportation model

Rawls and Turnquist [19]Minimize (costs of commodity acquisition, stocking decision, transportation, shortage, holding)Demand, number of facilities, inventory levelDynamic allocation model

Murali et al. [28]Maximize (number of people who receive medication)Supply and demand, distance, facility capacityMaximal covering location model

Lin et al. [20]Minimize (shortage penalty cost, delayed delivery penalty cost, shipping cost, unfairness of service cost) Number of depots, vehicles, travel time, delivery items quantityFacility location model