在带货盘替代通道的自动化仓库中安排整车运作【中文8400字】
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Applied Soft Computing 52 (2017) 566574Contents lists available at ScienceDirectApplied Soft Computingj ourna l ho me page: /locate /asocScheduling the truckload operations in automatedalternative aisles for palletsDidema,b, cabof Florida,caArticleReceivedReceivedAcceptedAvailableKeywords:AutomatedTruckloadFlexibleGeneticis anareas timeis presentedleading1. IntroductionAutomated storage and retrieval system (AS/RS) is a warehous-ing system that uses mechanic devices for the storage and retrievalofAutomaticitemslectorbecausepalletsretrieveslectorendaimprovedThedesignmizationinagement,(J.A.Because of the high complexity of the problem, simulation andmetaheuristics have been widely used in warehouse schedulingoptimization 4. A detailed literature review about the method-ologies developed for AS/RS design and scheduling is given in/10.1016/j.asoc.2016.10.0131568-4946/products in both distribution and production environments 1,2.cranes move through aisles between racks to put theon the racks and retrieve those items from storage to the col-for fulfilling the customer orders. AS/RS is fully automated,no intervention of an operator is needed for handling the2. When an order is received for an item, a stacker cranethe pallet from its storage location and carries it to the col-at the top of the aisle that is a gravity roller conveyor. At theof the roller conveyor, the conveyed pallet is picked up usingforklift truck. High space utilization, improved material flow, andinventory control are some of the advantages of AS/RS 3.best utilization from such a system can be succeed by optimaland optimal scheduling of the system.Warehouse scheduling optimization is a combinatorial opti-problem which cannot be solved with exact algorithmsreasonable computational time for high dimensional instances.Corresponding author at: Department of Industrial Engineering, Faculty of Man-Istanbul Technical University, Istanbul, Turkey.E-mail addresses: cinard.tr (D. Cinar), zandps.uminho.ptOliveira), topcuil.tr (Y. Ilker Topcu), pardalos (P.M. Pardalos).Section 3.In this study, the scheduling of truck load operations arisingin AS/RS is investigated. The problem is modelled as a flexible jobshop scheduling problem (FJSP) by considering the loads as jobs andpallets of a load as its operations. The forklifts which are used fortransportation of pallets from collectors to trucks are consideredas machines. The main contributions of this paper are twofold: (1)scheduling of truck load operations is modelled as a flexible jobshop scheduling problem, (2) a real problem arising in an AS/RSwarehouse installed by a leading supplier of automated materialshandling and storage systems is solved by using a priority basedgenetic algorithm and the effect of aisle selection flexibility is inves-tigated. To the best of the authors knowledge, this work is thefirst time that the FSJP is used to model the retrieving operationof pallets in an AS/RS warehouse.The paper is organized as follows. Section 2 provides a briefexplanation on investigated automated storage system. In Sec-tion 3, a literature review on scheduling of truck load operationsis given. Section 4 represents a mixed integer programming (MIP)formulation for a truckload operations scheduling problem in AS/RSand discusses the modelling of the problem as a flexible job shopscheduling problem. Section 5 presents the devoted methodology.2016 Elsevier B.V. All rights reserved.Cinar , Jos Antnio Oliveira , Y. Ilker TopcuDepartment of Industrial Engineering, Faculty of Management, Istanbul Technical University,Department of Industrial and Systems Engineering, Faculty of Engineering, UniversityALGORITMI Research Centre, University of Minho, Braga, Portugalr t i c l e i n f ohistory:5 June 2015in revised form 27 June 201613 October 2016online 19 October 2016storage and retrieval systemsoperations schedulingjob shop schedulingalgorithmsa b s t r a c tIn this study, the schedulinginvestigated. The problemalternative aisles. It is modelledas jobs, the pallets of a loaditems to the trucks are seento minimize the throughputbased genetic algorithmfor encoding and a constructiveproblem is applied for decoding.warehouse installed by awarehouses witha, Panos M. PardalosbIstanbul, TurkeyGainesville, United Statesof truck load operations in automated storage and retrieval systems isextension of previous ones such that a pallet can be retrieved from a set ofas a flexible job shop scheduling problem where the loads are consideredregarded as the operations, and the forklifts used to remove the retrievingmachines. Minimization of maximum loading time is used as the objectiveof orders and maximize the efficiency of the warehouse. A priorityto sequence the retrieving pallets. Permutation coding is usedalgorithm generating active schedules for flexible job shop schedulingThe proposed methodology is applied to a real problem arising in asupplier of automated materials handling and storage systems. 2016 Elsevier B.V. All rights reserved.D. Cinar et al. / Applied Soft Computing 52 (2017) 566574 567of theSectionhouse2.warehousearetheadvance,tomerbystackerfromaisle.hasprocessmentplanningsequenceanddreddeliverybeloadsprocessedbeforeisof613areisloadThewithloadexisttheFig. 1. Schema6 gives the computational results for a real life AS/RS ware-problem. Finally, Section 7 presents the conclusion.Storage systemThe methodology proposed in this study is applied to an AS/RSin Italy which works as a distribution center. Productsstored by the warehouse and loaded to the trucks to fulfillorders of customers. Routes of the trucks, which are known inare determined considering the delivery deadline of cus-orders. The warehouse consists of eleven aisles constitutedpallet racks with the capacity of 40,000 pallets. An automaticcrane or S/R machine works in each aisle to move the palletstheir respective rack to the collector at the beginning of theForklifts transport the pallets to the trucks. The warehouse13 docking bays to load the trucks. A scheme of the loadingin this warehouse is shown in Fig. 1.Warehouse Planning System (WPS) and Warehouse Manage-System (WMS) are used to operate the warehouse. Dailyof loadings for each truck is executed by WPS. Theof retrieving pallets and the movement of S/R machinesforklifts are determined by WMS. Approximately one hun-loads are retrieved per day by a truck. Each truck has its owntime which is considered by WPS and loading must notdelayed. In the strategy defined for the WPS, the whole set ofare divided into subsets called batches. Loads in a batch aresimultaneously. Loading of a batch cannot be startedthe loads of previous batch are finished. The size of a batchdetermined with respect to delivery deadlines and the numberdocking bays. A standard daily plan includes 1520 batches withloads for each one.An order of a customer consists a product or a set of products thatdelivered on one or more pallets. The set of products for an orderknown in advance, and it is available in the warehouse. A truckconsists of a set of pallets transported for one or more clients.sequence of loading pallets on the truck is determined by WMSLIFO (Last In First Out) rule. Since the sequence of pallets in ais predetermined and cannot be changed, precedence relationsbetween pallets of a load.The pallets of a load can be retrieved from any aisle. To facilitateassignment of the trucks to the docking bays, several palletswarehouse.are placed in different aisles to reduce the time of load prepara-tion, allowing a pallet to be selected in an aisle that is close tothe truck and respecting the FEFO (First-Expired-First-Out) rule.The S/R machine is programmed to retrieve the pallets from thecorresponding aisle.We assume that each forklift can work for only one aisle. Aftera forklift receives a pallet from its own aisle, it can carry the palletto any truck. For safety reasons, more than one forklift cannot beallowed to place pallets in a truck at the same time. So, one loadshould receive one pallet at a certain time. After a pallet is loadedto the truck, the forklift returns to its aisle and communicates toWMS that it is available for a new transportation. Then the nextpallet for the same load is programmed. A forklift can receive onlyone pallet at each transportation. Detailed information about theanalysed AS/RS warehouse can be obtained from 5.Different sequences of pallets in a batch retrieved by S/Rmachines result in different processing times. An illustrative exam-ple is the following. Assume that there are 5 aisles in the warehouserepresented by A1, A2, . . ., A5. The problem is planning the retriev-ing sequence of a batch including 3 loads. Each load consists of 4pallets, which have precedence relations in advance, representinga total of 12 pallets to be retrieved in the batch. There is one forkliftfor each aisle to carry the pallets from the aisle to the correspond-ing truck. Although a pallet can be retrieved from several aisles, inprevious studies 5,6 it was assumed that it is the WMS that previ-ously selects the pallets considering the distance to the aisle wherethe load is prepared. The aisle for each pallet and the processingtimes are given in Table 1.The aisle storing pallet j and the transportation time betweenrelated aisle and truck are shown as (Ak, t) where Akrefers thekth aisle and t is the transportation time from aisle Akto truck.For example, the first pallet of the second load must be retrievedTable 1An illustrative example for real problem.jth palletLoad i 1 2 3 41 (A1,1) (A2,2) (A3,3) (A4,4)2 (A3,1) (A1,3) (A3,1) (A4,2)3 (A4,2) (A4,2) (A3,3) (A5,1)568 D. Cinar et al. / Applied Soft Computing 52 (2017) 566574fromconsecutivelyThesequence,side)representsforcollectedandsignificantlyFig.3.cessesproperconstitutedopingheuristicsretrievalWhitewithnearestdualuation.tostoragementandferetcombiningthealgorithms.Fig. 2. Two different schedulesthe third aisle with time 1. For convenience, the pallets werenumbered from 1 to 12.Fig. 2 shows two different sequences of retrieving pallets.numbers inside the rectangles identify the pallets. For eachFig. 2 presents the Gantt chart for the set of aisles (leftand the Gantt chart for the set of loads (right side), whichbetter the processing time of the batch. The sequencesretrieving pallets only differ at Aisle 3, where the pallet 11 iseither after pallets 3 and 7 (Fig. 2(a), or before pallets 37 (Fig. 2(b). The decision when to retrieve pallet 11 producesdifferent processing times for the entire batch of loads.2(a) presents the optimal solution for this small example.Literature reviewIn an AS/RS, planning and performing of accurate loading pro-are very important to meet the customer orders at thetime 5. Among previous studies, analysis oriented onesthe majority of the literature rather than those devel-models and techniques for warehouse design 7. Simpleand simulation techniques were used for storage andproblems in automated warehousing systems. Bozer and8 proposed travel time models for automated S/R machinessingle and dual command mode. Han et al. 9 proposed aneighbour heuristic for retrieval sequencing in AS/RS withcommand cycles and used Monte Carlo simulation for eval-Eben-Chaime 10 also used a nearest neighbour heuristicsequence the retrievals. Hausman et al. 3 compared severalassignment rules to determine the optimal storage assign-policy. Schwarz et al. 11 analysed both storage assignmentinterleaving rules with a simulation model. Lee and Schae-12 formulated the problem, which is also handled by Hanal. 9, as an assignment problem. They proposed a methodologythe Hungarian method and the ranking algorithm forassignment problem with the tour-checking and tour-breakingfor retrieving the pallets.In the last few years, besides the mathematical modeling andsimulation approaches, metaheuristics have been used in theseareas. Comprehensive reviews of warehouse design and control canbe found in de Koster et al. 13, Gu et al. 14 and Baker and Canessa15. Moreover, detailed explanations of the current state of theart in AS/RS design are provided by Roodbergen and Vis 2 andVasili et al. 16. Manzini et al. 17 developed a multi-parametricdynamic model for a product-to-picker storage system with class-based storage allocation of products. They investigated the factorsaffecting the warehousing system performance. Yin and Rau 18combined simulation and genetic algorithms for the dynamic selec-tion of sequencing rules for a class-based unit-load AS/RS. Changet al. 19 proposed a multi-objective mathematical programmingmodel and a genetic algorithm for the order picking of stackercranes. Kung et al. 20 developed a dynamic programming basedorder scheduling methodology for the AS/RS with multiple stackercranes on a common rail. The problem includes both assignmentof orders to each crane and scheduling of cranes without collision.Brezovnik et al. 21 used a multi-objective ant colony optimizationmethod for the storage allocation problem in an AS/RS. Based onthe computational results obtained from a home appliance deviceswarehouse, it was shown that optimal space utilization can beachieved when the products with lower weight and height arestored at higher levels. Yang et al. 22 inferred that the speed profileof an S/R machine has an important effect on the optimal stor-age rack for a multi-deep AS/RS. Atmaca and Ozturk 4 proposeda mathematical programming model and a simulated annealingapproach for the storage allocation and storage assignment prob-lems to minimize storage costs. Optimal solution was obtained bythe proposed mathematical model for problems having up to 103materials. Dooly and Lee 23 modelled a shift-based sequencingproblem for twin-shuttle AS/RS as a minimum-cost perfect match-ing problem and presented a polynomial-time exact algorithm.Oliveira 5 and Figueiredo et al. 6 modelled the truck loadoperations on an AS/RS warehouse as a job shop scheduling prob-lem (JSP) with recirculation 5. Oliveira 5 assumed identicalprocessing times to transport pallets independently of the locationD. Cinar et al. / Applied Soft Computing 52 (2017) 566574 569of the aisle and the truck. Figueiredo et al. 6 extended the problemby considering different processing times and solved it by geneticalgorithms with random keys representation. Both Oliveira 5 andFigueiredo et al. 6 assumed that a pallet can be retrieved from oneaisle previously decided by WMS, considering the proximity to thedocking bay. In this study, this assumption is extended by consid-ering alternative aisles for pallets. The selection of the aisle wherethesimultaneously.tothethistigated.encountered4.schedulingorinlationminSCSSkCCXYSCCTable 2Notation for MIP.Indices:i loads (i, iprime L)j pallets (j, jprime P)k forklifts (k F)of the preceding pallet of the same load is finished. Constraints (8)and (9) give the completion time for each load and batch, respec-tively. Constraints (10)(14) represent the binary constraints andsign restrictions for decision variables.The model given by (1)(14) is an adjusted version of the oneproposed by zgven et al. 24 for FJSP. This problem can be mod-elled as a FJSP in which the loads are considered as jobs, the palletsof a load are regarded as the operations of jobs, and the forklifts usedto remove the retrieving items to the trucks are seen as machines.Minimization of the makespan (transportation time) is the objec-tive, as this allows minimization of the throughput time of ordersand maximization of the efficiency of the warehouse.In FJSP, more than one operations cannot be processed on amachine at the same time. Moreover, there are technological con-straints for all jobs which satisfy the precedence relations betweenpallets. In the warehouse, forklifts can carry only one pallet at a cer-tain time like the machines in FJSP. Similarly, there is a receivingorder of pallets for each load that should be guaranteed. No palletcan be loaded before the former one. In other words, overlappingthe transportation of pallets of the same load is not allowed. Theorder of pallets of each load can be taken into account as techno-logical constraints.In the warehouse, loads can be realized simultaneously andshould be ended inside the time window determined by WPS. Allpallets are retrieved is determined with truck load schedulingSo the problem consists of both selection of an aisleretrieve the pallet, which is currently performed by WMS, andscheduling of pallets transportation from collector to truck. Inway, the benefit of combining these two operations is inves-No study which addresses this problem as a FJSP has beenin the scope of this study.Modelling AS/RS warehouses as FJSPIn this section, a MIP formulation for the truckload operationproblem is presented. We do not consider cross-dockingorder picking to produce a pallet. The assumptions consideredthis study are given as follows:an order is formed by only (complete) pallets of products that arestored in the warehouse.an S/R machine is faster to put a pallet on the collector than aforklift to remove a pallet and an S/R machine operates in advanceof the forklift,a collector works as a buffer with capacity for several pallets,the flow of pallets in the collector (gravity roller conveyor) followsthe FIFO rule,an S/R machine takes zero units of time to put a pallet in thecollector.The notation used hereafter is given in Table 2. The MIP formu-for truckload operations scheduling is given as follows:Cb(1)subject tosummationdisplayk FijXijk= 1 i L, j Pi(2)ijk+ Cijk MXijki L, j Pi, k Fij(3)ijk Sijk+ tijk M(1 Xijk) i L, j Pi, k Fij(4)ijk Ciprimejprimek MYijiprimejprimeki iprime, j Pi, jprime Piprime , k Fij Fiprimejprime (5)iprimejprimek Cijk Mparenleftbig1 Yijiprimejprimekparenrightbigi iprime, j Pi, jprime
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