Mathematical Problems in Engineering

Research Article

An Integrated Production-Distribution Planning Problem under Demand and Production Capacity Uncertainties: New Formulation and Case Study

Table 1

Summary on the related literature review.
Paper/studyNumber of chain levelsObjective functionsMathematical modellingCommercial solverHeuristic/metaheuristicDeterministicUncertaintyIndustrial application
MultisiteMultiproductMultiperiodIntermodal transportationMono-objectiveMultiobjectiveUncertain parametersUncertainty modelling approach
Safra and Jebali [20]xxxSea/airTC MILPCPLEX X  Textile and apparel industry
He et al. [21]xx Road/sea/airTC   MAX  Apparel and footwear industry
Weskamp et al. [22]xxx P MILPCPLEX  D2STSPApparel industry
Ait-alla et al. [12]xxx P MILP   DROApparel industry
Gupta and Maranas [17]xx  TC MILPCPLEX  D2STSPChemical industry
Niknamfar et al. [6]xxx TC ILPCPLEX  D, Pr, C, CAPROGeneral appliance company
Badri et al. [9]xxx P MILPCPLEX  D, Pr2STSP 
Feng et al. [8]xxx P MILPCPLEX  D, Pr2STSPWood industry
Mohammadi and Mohd [23]xx  TC MILPLINGO  D, C, CAP2STSP 
Mirzapour Al-e-hashem et al. [24]xxx  TC, VTC, PRODMINLPLINGO  D, C2STSP 
Torabi and Hassini [10]xxx  TC, P, Q, CSLMIPOSL  D, CAPFPAutomobile company
Guillén et al. [25]xxx  TC, CSL, FRMILPCPLEX  D2STSP, ROChemical industry
Azaron et al. [26]xx   TC, VTC, FRMINLPLINGO  D, CROWine company
Goodarzian and Hosseini-nasab [14]xxx  TC, QMILPBARONNSGAII D, CFPMould for plastic
Rahimi et al. [27]xxx  P, EIMINLPGAMS  D, C2STSP 
Pasandideh et al. [28]xxx  TC, VTCMINLP NSGAII D, C, STT, PTSP 
Govindan and Fattahi [7]xxxRoad/railTC MILPCPLEX  D2STSP, ROGlass industry
Jabbarzadeh et al. [13]xxxRail/truck/air TC, EI    DROPharmaceutical industry
Entezaminia et al. [18]xxxHeterogeneous fleet of vehicles TC, EIMIPCPLEX  CROWood and paper industry
Nemati and Alavidoost [29]xxxHeterogeneous fleet of vehicles TC, CSLMILPCPLEX  CFPDairy industry
Badhotiya et al. [11]xxxHeterogeneous fleet of vehicles TC, TDT, CSLMILPCPLEX  D, CAPFPAutomobile industry
This studyxxxSea/air TC, CSLILPLINGO  D, CAP2STSPTextile and apparel industry
TC: total costs; MILP: mixed-integer linear programming; D: demand; 2STSP: two-stage stochastic programming; P: profit; MINLP: mixed-integer nonlinear programming; C: cost; RO: robust optimisation; CSL: customer satisfaction level; LP: linear programming; Pr: price; FP: fuzzy programming; Q: quality; MIP: mixed-integer programming; CAP: capacities; SP: stochastic programming; TDT: total delivery time; ILP: integer linear programming; PT: production time; VTC: variance of total costs; STT: setup time; EI: environmental impacts; MA: memetic algorithm; FR: financial risk; OSL: IBM Optimization Subroutine Library; NSGAII: nondominated sorting genetic algorithm II; PROD: productivity.