A 2-Phase Metaheuristic Approach for Time-Sensitive Manufacturing and Transportation Execution System

Transcription

1 STR/03/030/MET A 2-Phase Metaheurstc Approach for Tme-Senstve Manufacturng and Transportaton Executon System W. D. Ln, W. L. Lee and G. Y. Lm Abstract Wth the surge n the avalablty of real-tme manufacturng and transportaton resources nformaton, requrements for advanced ntellgent real tme decson-mang technques are mperatve. Ths research s focused on developng dynamc real tme demand responsve decson-mang technques to address the current and future needs n the feld of advanced synchronzed manufacturng and transportaton executon systems. In ths report, a model, whch consders the batchng process at the plants and the truc delveres to varous stes, s developed and solved by a two-phase soluton approach, whch ncludes the use of search technques, wthn a Metaheurstcs framewor. To acheve global optmalty, we consder the applcaton of a Tabu Search (TS), Guded Local Search (GLS) and a hybrd Guded Tabu Search (GTS) for further soluton enhancement n the second stage. Based on an example, the proposed strategy s able to show sgnfcant mprovement. Keywords: Manufacturng, Transportaton, Resource consoldaton, Meta-heurstcs 1 BACKGROUND Manufacturng and transportaton are two closely lned and dependent actvtes n a value chan. Fnshed goods need to be delvered to customers n an effcent and cost-effectve way to close the loop of proft mang. Otherwse, not only undelverable fnshed goods ncur nventory cost but also the customer servce level n terms of delvery would be spoled. To the extreme, some pershable or tme crtcal goods requre strct just-n-tme delvery. If the company drectly focuses on mprovng the effcency of ths segment, customer servce wll mprove. When customers receve hgh qualty and predctable servce whether pc-up or delvery they wll reward the company wth more busness. The company ncreases ts cash flow by the proft on these ncreased revenues. On the other hand, poor executon n outbound logstcs s a leadng cause of lost orders. Another, more nsdous symptom of poor customer servce adds to your cost as well. Ths s when operatonal mscues cause you to expedte or jump-through-hoops to prevent losng an order. If you have to dspatch a specal truc for that order or press a crew nto overtme servce, t eats nto your proftablty. Predctablty equates to revenue and proftablty. Executng well n the last leg of the supply chan means ncreased customer loyalty n the form of revenue and margn. To tacle such challenges, ths research project nvestgates novel approaches of ntellgent real-tme synchronzed manufacturng and transportaton coordnaton and control for tme-crtcal manufacturng and transportaton applcatons. In the ntal stage of ths research, a prototype Metaheurstcs-based Dynamc Demand Responsve Integrated Manufacturng and Transportaton Executon System wth ntegraton to advanced GIS/GPS (Geographc Informaton Systems/Global Postonng Systems) has been developed. The system features nclude responsve capabltes whch contnuously mae adjustment to meet predefned objectve functons n the control of real-tme manufacturng processes, handlng multple constrants and condtonal changes, statc and dynamc real-tme schedulng and optmzaton of vehcle routngs, real-tme vehcle tracng n a dscrete manner throughout the ntended route to enable optmum route computaton. The ey benefts of such a system are (1) Reduced total manufacturng and transportaton tme and cost; (2) Realtme dynamc demand-responsve to changes from customers, manufacturng process and transportaton actvtes; (3) Enhanced customer servce level; (4) Increased Return of Assets (ROA). An excellent busness example that hghlghts the necessty to combne plannng of manufacturng and transportaton actvtes s demonstrated by the Ready Mxed Concrete (RMC) ndustry. It s understandable that cement, once mxed and processed nto concrete, s a hghly pershable tem, as t requres mmedate delvery and pourng. Due to ths unque property, a buld-up of nventory tems to meet or even predct customer s fluctuatng demands s smply nfeasble. Therefore, the actvtes of the producton facltes and transportaton resources should be scheduled concurrently n order to satsfy customers orders n the rght tme and amount and at the lowest cost. Ths report ams to develop cost-effectve planttruc tnerares for the local RMC companes on a daly bass by solvng a model that character- 1

2 ses the RMC batchng and delvery operatons usng a two-phase soluton approach. 2 OBJECTIVE The objectves of ths report are therefore twofold: To develop a model that smultaneously consders the schedulng of the producton and delvery operatons n the RMC ndustry and To develop a producton-dspatchng schedule by solvng the model. 3 METHODOLOGY Constrant Programmng (CP) s a paradgm for representng and solvng a wde varety of problems ncludng Combnatoral Optmsaton Problems (COP) usng enumeratve technques such as branch and bound, and depth-frst search, enhanced by Constrant Propagaton an nherent CP technque. Whle the language can express COPs wth comparatve ease, ts optmsng search technque may not be deal for some COPs. However, replacng that wth search technques, whch nclude metaheurstcs, may be more approprate for COPs such as Vehcle Routng Problems wth Tme Wndows (VRPTW) due to ts effcacy n fndng near-optmal solutons for practcal sze problems. On metaheurstcs, Tabu Search (TS) [1], whch uses short and long-term memory (the tenure lst) to avod cyclng and orent the search towards unexplored regons of the soluton space, s a popular technque for conductng global searches, partcularly for VRPTW. Examples of ths context can be found n [2-4]. Another metaheurstc, whch s nvestgated n ths research, s Guded Local Search (GLS). Ths method orgnated from [5]. Smlar to TS, GLS paradgm s a memory-based approach, whch augments the true cost functon wth a penalty term based on the proxmty of the search to other prevously vsted local mnma, thus encouragng dversfcaton. Hybrdsaton of metaheurstcs s also nvestgated and a representatve example for VRPTW s provded by [6] where Genetc Algorthms, Smulated Annealng, and Tabu Search are combned. 3.1 The ready mx concrete ndustry Characterstcs of the product and resources of ths ndustry and ther mplcatons are hghlghted pror to the presentaton of the modellng approach. Product Characterstcs Upon hydraton, concrete must be delvered and poured wthn 1.5 hours for maxmum effectveness and strength. As such, travellng tme s lmted to a maxmum of 30 mnutes due to ths condton. Plant Characterstcs Each plant has ownershp of a fleet of trucs to serve specfc demand areas. Based on the orders receved, plants mplement ther ndvdual schedulng based on the avalable number of trucs. Ths defnes the delvery capacty of a plant, whch s often lmtng because the drvers and truc operatng costs are varable, allowng adjustments to be made to match the demand for the day. Consequently, delvery capacty, charactersed largely by truc avalablty, plays a decsve role n determnng the ablty to fulfl orders and consequently, n achevng tmelness n delveres, whch s an essental crteron n ths concrete busness. Demand Characterstcs Arrval of orders s random from a plant s perspectve, thus relably predctng any plant s worload for the day s not an easy tas. At tmes, large quanttes would be requested and thus would requre an unnterrupted supply of concrete. Ths may te up a consderable number of trucs and may even requre trucs to be on standby. Thus, arrangements wth nearby plants for addtonal capacty or as bacups may be necessary. Customers also tend to be prudent snce they are charged accordng to the amount ordered. Therefore, they would order less than requred and then rely on a few extra delveres placed on short notces to complete ther placement. The plant would then need to moblse empty trucs qucly to provde such servces. Note that once the frst delvery for a partcular order s ntated, the entre quantty demanded must be delvered. 3.2 Modellng consderatons From the characterstcs hghlghted, n order to produce and delver concrete cost-effectvely and relably, the schedulng of the producton and delvery jobs s seen as a prerequste tas. However, we tentatvely assume that order assgnment to plants s pre-determned; each plant has a strng of orders, ready to be dspensed to 2

3 ther trucs for executon. Consequently, we place the emphass of our modellng approach on truc schedulng. Thus, the optmal assgnment of jobs to vehcles based on the orders already generated for each plant s consdered. On that bass, snce truc avalablty governs the ablty to fulfl (more) orders, we show that t s more benefcal to pool these transport resources together to serve not only ther desgnated plants (thus ther demand regons) but across all plants (Fg. 1). Further, we consder that the consoldaton may tae place a gather pont, where vehcles would begn and end collectvely (after the completon of ther tass) All orders and ther necessary nformaton are nown wthn the plannng horzon. Full trucload s assumed.e. a vehcle delvers one load wthn the tme wndow, whch s strctly respected. Each truc s assgned to a specfc plant/ depot and could be used repeatedly durng the day. The operatng hours, brea-tmes and overtmes of the vehcles (drvers) are not consdered. Model Formulaton In order to formulate the mathematcal model, we frst defne the notaton. Vehcle A B A Customer orderid 32 Sets LOADING Plant0 Customer orderid 15 Customer orderid 12 Plant2 V = the complete set of nodes, {o(), 1, 2,, n, d()}. UNLOADING N = the complete set of tas nodes, {1, 2,, n} Plant1 Fg. 1. An llustraton for demonstratng resource poolng concept. N = the subset of tas nodes assgned to truc K. K = the set of trucs, {1,, K } We demonstrate that ths strategy can mnmse both total cost and more mportantly, the number of trucs used, leadng to an enhanced ablty to fulfl more orders (on real tme bass) and thus operatonal effcency would ncrease. 3.3 Delvery tas schedulng An order can be regarded as a boong of trucs to do a sequence of related delvery jobs. Also, each order s consttuted by a set of suborders wth each havng a demand quantty equvalent to the capacty of a truc. Each suborder s equvalent to a tas for a truc. It entals a truc to load at a specfc plant and then delver to ste. Ths tas ncorporates a plant-ste par or genercally, an orgn-destnaton par where pcup and delvery actvty s performed by the truc at a specfc tme. The pcup tme can be nferred from the delvery tme specfed. Each truc s assgned a sequence of tass, servng only one suborder at a tme. For nstance, begnnng at ts depot, plant, a truc loads at the plant specfed n the frst tas to be delvered to the ste specfed n the same tas. After tas, tas j s carred out. The truc would return to the depot plant m upon completon of all ts assgned tass. Pror to presentng the model, a set of underlyng assumptons s spelt out: A = the complete set of arcs, {(, j):, j V, j} G = the networ, (V, A ) Parameters r = number of trucs avalable at plant K. [e, l ] = tme wndow for node, V. c j = arc cost for performng tas j mmedately after performng tas by truc K, (, j) A t j = travel tme between the endng locaton of tas and the startng locaton of tas j, (, j) A, K. s = servce tme at node, N. Decson Varables j (bnary) = 1 f truc uses arc (, j), and 0 otherwse. T = tme at whch truc reaches node V. The problem s to mnmse total cost 3

4 K ( j) A cj, j () 1 s.t. K j :(, j ) A j = 1 : (, j) A j : ( j, ) A j ( T + s + t T ) 0 e T j l o r j j j = 0 j: ( o( ), j ) A ( ), j K N ( 2) j N, K () 3 (, j) A K, V, K (, j) A K, The objectve functon sees to mnmse the total cost and also the mnmsaton of the fleet sze. Constrant (2) ensures that each tas s accomplshed once. Constrants (3) and (4) are networ constrants ensurng that the nflow to sn node d() balance wth the outflow from source node o() n the networ G. The number of vehcles avalable at depot K s ndcated by r. Hence, a soluton to ths model provdes r schedules equvalent to the number of trucs at depot K. Relaton (5) states that the start of servce tme at node j (or the arrval tme at the depot f j = d()) must be greater or equal to the start of servce tme at node (or the departure tme from the depot f = o()). Constrant (6) s the tme wndow restrctons wthn whch servce must tae place, whle constrant (7) ndcates that flow varable are bnary. The resultng formulaton s as an adaptaton from the multple travellng salesman problem or m-tsptw formulaton havng a mult-commodty networ flow structure. 3.4 Soluton methodology A two-phase constructon and mprovement approach s adopted to develop a feasble schedule n realstc computatonal tme. ( 4) () 5 ( 6) ( 7) The frst stage conssts of generatng a feasble ntal soluton usng common VRP heurstcs. We consder frst the savngs algorthm poneered by [7]. Subsequently, ths soluton s enhanced through the applcaton of a local-search procedure, whch s based on a set of mprovement heurstcs descrbed n [8]. Each heurstc n ths set teratvely modfes the ntal soluton by swappng one or a subset of customers wthn and between routes (n the soluton) and ths s quantfed as a move. These moves collectvely produce a so-called neghbourhood. The local search procedure then chooses a legal, costreduced soluton from ths neghbourhood. Further, the local search can ether accept a soluton that results from the frst legal cost decreasng move or one that has the lowest cost (best accepted search) amongst the neghbourhood. Typcally, the local search procedure produces solutons that are optmal only on a local bass. To acheve global optmalty, we consder the applcaton of a Tabu Search (TS) n [1], Guded Local Search (GLS) n [9] and a hybrd, Guded Tabu Search (GTS) for further soluton enhancement n the second stage. The hybrd case s desgned and offered by ILOG Dspatcher 3.2. We then consder the followng combnaton of heurstcs to nvestgate ther effectveness n solvng the proposed model (Table 1). Table 1. Dfferent combnaton of soluton approaches. No. Heurstcs Used 1 st Stage 2 nd Stage Route- Buldng Local Optmal Global Optmal 1 Savngs Frst Accept None 2 Savngs Frst Accept TS 3 Savngs Frst Accept GLS 4 Savngs Frst Accept GTS 5 Savngs Best Accept TS 6 Savngs Best Accept GLS 7 Savngs Best Accept GTS The frst combnaton s consdered wth the ntenton of comparng the qualty of soluton derved wth and wthout the applcaton of metaheurstcs n the second phase. We would also le to nvestgate the effect of the two acceptance modes. The results and dscusson are provded n the next secton. 4 RESULTS & DISCUSSION A benchmar set of problems from [10], whch conssts of 56 sets of 100-customer data, s selectvely employed for testng purposes. For demonstraton purposes, Solomon C101 problem set s used. However, modfcatons are necessary to adapt to the proposed model. For example, the data s desgned for only one depot (plant) whereas our model entals multple depots. Therefore, x-y coordnates of addtonal depots have to be sutably ncluded nto the data. Fg. 1 llustrates the dstrbuton of 100 customer 4

5 orders and 8 plants over a [100,100] square area. Table 3. Dstrbuton schedules for eght plants. Plt Plan In Table 4, the ndvdual cost of the plans and the number of trucs needed to perform accordng to the plans descrbed n Table 3 are gven. The total cost s therefore $ and the total number of vehcle requred s 13. Fg. 2. Dstrbuton of depots & customers over [100,100] square grd. Table 2 shows producton sequences of the plants. These plans consder the plant capacty constrants and tme-wndow constrants and are developed by usng the nearest plant frst assgnment rule. The numbers n each cell reflect the customer s order ID and are assocated wth a producton tme-wndow, whch s derved from the delvery tme-wndow by consderng the travel tme between the plant and the customer ste. Table 2. Producton schedules for eght plants. Sequence Plant To show that our proposed strategy s better than the ncumbent (n the ndustry), we set up a scenaro where resources.e. trucs are restrcted to serve only ther desgnated plants. Consequently, we could treat the eght plants as ndvdual bodes. In ths case, schedulng orders for trucs of each plant results n a dstrbuton plan depcted n Table 3. We show only the vehcle plans of those plants whose dstrbuton plans dffer from the sequence reflected n the producton schedules. The hghlghted parts reflect the changes made. In the routes, the vehcles should begn and end at the depot, whch s not ncluded n the schedules. Table 4. Costs and number of trucs used per plant. Cost No. of Plant ($) Trucs Used Table 5 summares the results from applyng the dfferent soluton approaches lsted n Table 1. Compared to the unshared case, on average, total cost s reduced by 13.6% ($702.91) to $ and the number of trucs used s also reduced by 28.6% (four fewer trucs) to nne. Thus, our proposed strategy s proven to be better than the unshared case consdered n those terms. Table 5. Results usng dfferent soluton approaches. No 1 st Stage 1 Savngs 2 Savngs 3 Savngs 4 Savngs 5 Savngs 6 Savngs 7 Savngs Heurstcs Used 2 nd 3 rd Total Cost ($) CPU Tme (sec) No. of Veh Used Stage Stage Frst None Frst TS Frst GLS Frst GTS Best TS Best GLS Best GTS

6 To explan the approach to nterpretng the dstrbuton plans usng the proposed strategy, the result from the applcaton of GLS are shown n detal n Table 6. Usng Plan 1, for nstance, a typcal tas, for example, (P)3 to (S)32, means that a vehcle s supposed to go to plant 3 to load and then delver to customer 32. All vehcles starts and ends at the gather pont as shown n Fg. 1. As for the entre plan, t means that the nne vehcles have to alternate between the plants and customer stes. Thus, all vehcles are shared between plants for servng customer stes across varous regons. On algorthmc aspect, the applcaton of purely the local search procedure requres the least CPU tme (141 seconds) and nne vehcles, but has the hghest cost ncurred ($4810.2) as shown n Table 5. Ths s because none of the metaheurstcs that encourage a global search s appled for further cost mnmsaton. For a global search technque that stres a balance between a reasonably good objectve value and computatonal effcency, GLS n frst accept mode s a lely choce ndcated n Table 5; a (lowest) total cost of $ and nne vehcles s acheved wthn 583 seconds of CPU tme. Ths soluton has an mprovement of 15.9% over the base scenaro n terms of total cost and 23.1% for the number of vehcles used. Further nvestgaton s nonetheless requred to evaluate ts effcacy on larger problems. Table 6. Dstrbuton plan for proposed scenaro. Vehcle Plan Tas P S P S P S P S P S P S P S P S P S CONCLUSION Ths report ams to synchronze the manufacturng and transportaton actvtes for the RMC ndustry wth consoldated vehcle resources by solvng a developed model resemblng m- TSPTW usng a two-phase soluton approach, whch s partally based on Metaheurstcs framewor. A modfed nstance of the Solomon benchmar problem set s solved. Results show that resource poolng acheves an average 28.6% mprovement n number of trucs used over the unshared case. In addton, Guded Local Search n frst-accept mode s consdered the most effectve metaheurstc n searchng for a global soluton for the model wthn reasonable computatonal tme. 6 INDUSTRIAL SIGNIFICANCE Our solutons wll beneft certan ndustres sector nvolvng tme senstve manufacturng and logstcs operatons. More and more companes are heavly rely on E-Commerce sales (e.g.dell Computer) as ther maretng strategy. Such companes often promsed to delver goods wthn even narrowng tme-wndows to ther customers norder to reman compettve. Other examples of tme-crtcal operatons are fresh food supplers, concrete producton, and ntegrated logstcs servce provders, e.g. Logstcs, Postal Delvery Servces, etc. REFERENCES [1] F. Glover and M. Laguna, Tabu Search, Kluwer, Boston, (1997). [2] J. Brandao, Metaheurstc for the Vehcle Routng Problem wth Tme Wndows n Meta Heurstcs: Advances and Treads n Local Search Paradgms for Optmzaton, Kluwer, Boston, MA, pp , (1998). [3] W.C. Chang and R.A. Russell, A Reactve Tabu Search Metaheurstc for the Vehcle Routng Problem wth Tme Wndow, IN- FORMS Journal of Computng, Vol. 9, pp , (1997). [4] M. Clst, Plant Modellng for the Concrete and Asphalt Industres, Proceedngs of the 36th Annual Conference of the ORSNZ 2001, Unversty of Canterbury, Chrstchurch, New Zealand, (2001). [5] P.J. Klby, P. Prosser and P. Shaw, Guded Local Search for the Vehcle Routng Problem wth Tme Wndows, n Metaheurstcs: Advances and Trends n Local Search Paradgms for Optmsaton, S. Voss, S. Martello, I.H. Osman and C. Roucarol (Eds), pp , Kluwer, Boston, (1998). [6] J.F. Cordeau, G. Desaulners, J. Desrosers, M.M. Solomon and F. Soums, VRP wth Tme Wndows, n The Vehcle Routng Problem, P. Toth and D. Vgo (Eds), pp. 6

7 , (2002). [7] G. Clare and J.W. Wrght, Schedulng of Vehcles from a Central Depot to a Number of Delvery Ponts, Operatons Research, Vol. 12, pp , (1964). [8] C.W. Feng, H.T. Wu, Usng Genetc Algorthms to Optmse the Dspatchng Schedule of RMC Cars, Proceedngs of the 17th IAARC/CIB/IEEE/IFR, Internatonal Symposum on Automaton and Robotcs n Constructon, 17th ISAREC 2000, Nat. Tawan Unv., pp , (2000). [9] B. De Bacer, V. Furnon, P. Shaw, P. Klby and P. Prosser, Solvng Vehcle Routng Problems Usng Constrant Programmng and Metaheurstcs, Journal of Heurstcs, Vol. 6(4), pp , (2000). [10] K.L. Hoffman, When Real-Tme Plannng and Dspatchng s Essental: the Schedulng Nghtmare of Pershable Objects, (2002), [11] J. Somrlj, Optmsaton of Cement Supply and Ready-Mxed Concrete n Yugoslava, Proceedngs of the ERMCO 1983, London, England, (1983). 7