Complexity

Research Article

A Mixed Integer Linear Formulation and a Grouping League Championship Algorithm for a Multiperiod-Multitrip Order Picking System with Product Replenishment to Minimize Total Tardiness

Table 1

Summary of the related literature.
ReferenceAbbreviationCase studyMathematical modelHeterogeneous/homogenous pickersLayoutSolution methodRoutingBatchingJob assignmentMulti- periodLimited access to pickerMulti-trip routingCongestion
Petersen [25]OPRP———Rectangular, low-levelStatistic (ANOVA)✓——————
Ii [46]OPPP✓——Rectangular, low-levelSimulation—✓—————
Jan and De Kosher [28]OPRMA———Rectangular, two blocks, low-levelDynamic programming algorithm✓——————
Petersen and Aase [27]PRSPOP———Rectangular, low-levelSimulation✓✓—————
Wäscher [30]OP———Rectangular, low-levelReview a few solutions✓✓—————
Won and Olafsson [31]JOBOP—IP——Sequential batching and picking (SBP) algorithm✓✓—————
Ho and Tseng [32]OB———Rectangular, low-levelStatistic (ANOVA)✓✓—————
Tsai et al. [23]MG-OB—IPHomRectangular, low-levelMultiple-GA✓✓✓————
Dallari et al. [24]DOPS✓———Analytical method———————
Henn et al. [33]MOBP—IP—Rectangular, low-levelIterated local search, ant colony—✓—————
Theys et al. [47]TSPHORP———Rectangular, two blocks, low-levelTSP-heuristic✓——————
Henn and Schmid [48]OBSP—MIP—Rectangular, two blocks, low-levelIterated local search, attribute-based hill climber—✓✓————
Kulak et al. [35]JOBPR—IP—Rectangular, two blocks, low-levelTabu search integrated with a novel clustering algorithm✓✓—————
Pan et al. [36]SAP-TDABC——HomRectangular, low-levelHeuristic algorithm——————✓
Hong et al. [49]OPB_PC—MIPHomRectangular, low-levelSimulated annealing algorithm✓✓————✓
Henn [8]OBSPMP—MILPHomRectangular, low-levelVariable neighborhood descent and search algorithms✓✓✓————
Oncan [37]OPB—MILPHomRectangular, low-levelIterated local search algorithm with tabu search✓✓—————
Chen et al. [38]IOBSRP—MINLPHetRectangular, low-levelAnt colony, genetic algorithm✓✓✓————
Chabot et al. [29]CAN-OPP✓MILP—3D narrow aisle. High-levelLarge neighborhood search, branch &bound—✓—————
Chen et al. [50]ORP_MC—IPHomRectangular, two blocks, low-levelOnline ant colony optimization✓—————✓
Su & Hwang [51]OPRP_FS———Rectangular, multi block, low-levelFuzzy clustering✓——————
Valle et al. [39]OS-_JOBRP✓IPHomRectangular, two blocks, low-levelExact, heuristic✓✓—————
Scholz and Wäscher [20]OBI RP—ILP—Rectangular, two blocks, low-levelIterated local search✓✓—————
Scholz et al. [42]JOBA SRP—MILPHomRectangular, two blocks, low-levelVariable neighborhood descent algorithm✓✓✓————
Menéndez et al. [41]OBP—ILP—Rectangular, low-levelVariable neighborhood search✓ —————
Van Gils et al. [44]ISBZPRPD✓———Statistic (ANOVA)✓✓✓————
Žulj et al. [43]OBP—IP——Adaptive large neighborhood search and tabu search—✓—————
Chen et al. [40]OOBA—ILPHomRectangular, two blocks, low-levelNonparametric heuristic method, green area———————
Moons et al. [45]I-OP-VRP—MILPHet—Record-to-record travel algorithm✓✓—————
Kuhn et al. [52]IOBVRPGR✓——Rectangular, three block, low-levelGeneral adaptive large neighborhood search (GALNS)✓✓—————
Briant et al. [19]JOBPR✓——Rectangular, two blocks, low-levelColumn generation✓——————
The current studyMPMTR✓MILPHetRectangular, two blocks, low-levelGrouping algorithms✓✓—✓✓✓—
OPRP: order picking routing policies OPPP: order picking policies problem Oprma: order picker routing with middle aisle PRSPOP: picking routing storage policies order picking OP: order picking Jobop: joint order batching and order picking OB: order batching MG-OB: a multiple-GA method to solve order batching DOPS: design of order picking system MOBP: metaheuristic for order batching problem TSPHORP: travel salesman problem heuristic for order routing problem OBSP: order batching sequencing problem JOBPR: joint order batching and picker routing SAP-TDABC: storage assignment problem with travel distance and blocking congestion OPB_PC: order picking batching _ picker congestion OBSPMP: order batching sequencing problem with multiple pickers Iobsrp: integrated order batching, sequencing, and routing problem CAN-OPP: capacity narrow aisle order picking problem ORP_MC: order routing problem_ multi picker congestion OPRP_FS: order picking routing problem-fuzzy set OS-_JOBRP: optimally solve_ joint order batching and routing problem OBI RP: order batching and integrated routing problem JOBA SRP: the joint order batching, assignment, sequencing and routing problem ISBZPRPD: integrating storage batching, zone picking, and routing policy decisions OOBA: online order batching and assigning I-OP-VRP: integrated order picking-vehicle routing problem MPMTR: multi-period, multi-trip assumptions with the possibility of product replenishment IP: integer programming MIP: mixed integer programming NMLIP: nonlinear mixed integer programming.