Mathematical Programming for a Special Case of 2E-LRP in Cash- In-Transit Sector Having Rich Variants

This article proposes a special case of a two-echelon locationroutingproblem (2e-lrp) in the cash-in-transit (cit) sector. totackle this realistic problem and make the model applicable, a richlrp is presented considering several existing real-life variants andcharacteristics named bo-2e-pclrpsd-tw, including differentobjective functions, multiple echelons, multiple periods, capacitatedvehicles, distribution centers and automated teller machines (atms),different types of vehicles in each echelon, and single-depot withdifferent time windows. since routing plans in the cit sector ought tobe safe and efficient, the minimization of total transportation risk andcost are considered simultaneously as objective functions. then, sucha complex problem is formulated in mathematical mixed integerlinear programming (mmilp). to validate the presented model andthe formulation and to solve the problem, the latest version of ε-constraint method namely augmecon2 is applied. this method isspecially efficient for solving multi-objective integer programing(moip) problems and provides the exact pareto fronts. resultssubstantiate the suitability of the model and the formulation