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1 Journal of the Society of Korea Industrial and Systems Engineering Vol 27 No 4 pp23 32 December 2004 물류시스템에서수송주기와차량크기의결정 * Determination of the Transportation Cycle Time and the Vehicle Size in a Distribution System Suk-Hwa Chang Industrial Engineering Department University of Incheon This paper addresses a model for the transportation planning that determines the transportation cycle time and the vehicle size to minimize the cost in a distribution system The vehicle routing to minimize the transportation distance of the vehicles is also determined A distribution system is consisted of a distribution center and many retailers Products are transported from distribution center to retailers according to transportation planning A model is assumed that the time horizon is continuous and infinite and the demand of retailers is constant and deterministic Cost factors are the transportation cost and the inventory cost which the transportation cost is proportional to the transportation distance of vehicle when products are transported from distribution center to retailers and the inventory cost is proportional to inventory amounts of retailers A transportation cycle time and a vehicle size are selected among respective finite alternatives The problem is analyzed and a illustrative example is shown distribution system transportation cycle time vehicle size 1 서론1) *

2 장석화 Bramel and Simchi-Levi[22] Anily and Federgruen[23] Herer and Roundy[24] Viswanathan and Mathur[25] 2 [7] product-mix JIT push pull dock [6] 2 수송주기및차량크기의결정 21 모형형성 [18 19] ([1] [2] [3]) Labbe[4] Yang et al[5] [11] Jackson et al[20] Federgruen and Zheng[21]

3 물류시스템에서수송주기와차량크기의결정 < 1> pickup delivery 차량크기가선택되면그렇지않으면 수송주기가선택되면그렇지않으면 수송경로에서대리점방문후대리점를방문하면그렇지않으면 < 그림 1> 수송주기에대한수송및재고비용

4 장석화 (3) (3) (4) (4) < 1> (5) (6) 대안 < 표 1> 수송주기대안수송주기 1 (5) 1 (6) 1 (3) 2 3 (7) S-1 (8) S (1) (1) (7) - (8) (7) (2) (2) (10) (9) ( ) 2 (9) (10)

5 물류시스템에서수송주기와차량크기의결정 (10) for (11) for (12) (13) (14) < 그림 2(b)> 두차량을재고가 0인시점에분산하여수송 0 or 1 (15) and ( ) is a tour assignment (16) (10) (13) (14) (3) (9) (10) (17) (19) < 2(a)> (18) + (17) (18) (19) 1 1 < 2(a)> 0 < 2(b)> < 2b> 0 (20) (21) (20) (21) (21) (19) (21) [ < 그림 2(a)> 두차량을동일한시점에수송 + ]/2 (22)

6 장석화 (23) (24) + (23) [ + ]/ (24) P1 (a) (b) (c) (d) savings 알고리듬 P1 mimimize c 1 i [2 + ] + subject to for for or 1 and ( ) is a tour assignment Gillett and Miller[15] the sweep Wright and Clarke[16] savings heuristic [ ] savings heuristic 가차량경로계획알고리듬 1: 2 3: savings 4 savings savings 4 < 차량의수결정 3

7 물류시스템에서수송주기와차량크기의결정 P2 1 차량경로이차량에의해수송되면 그렇지않으면 차량 이사용되면 그렇지않으면 P2 minimize (25) subject to (26) (27) (28) 0 or 1 (29) 0 or 1 (30) (26) (27) P2 (31) 3 수치적예제 (28) (31) km 100km 10 2 [5 25] /km 100/km 135/km km/hour ( + ) < 3> < 3> 2 < 그림 2> 물류센터및대리점의배치

8 장석화 < 표 2> 대리점의위치좌표및수요량 대리점 위치좌표 (X Y) 수요량 / 일 대리점 위치좌표 (X Y) 수요량 / 일 1 ( 96 44) 9 16 (146 82) 21 2 (115 59) (108 13) 21 3 ( 8 11) ( 96 84) 13 4 ( 17 32) (117 23) 22 5 (127 62) ( 70 7) 12 6 ( 26 89) ( 35 33) 9 7 ( 6 96) ( 48 58) 15 8 ( 47 2) 9 23 (118 14) 9 9 (123 11) ( 95 87) ( 35 40) 8 25 ( 99 33) ( 88 10) 6 26 ( 81 49) (139 29) 7 27 (138 43) ( 50 68) 6 28 (117 26) ( 31 98) ( 49 98) ( 55 40) (111 97) (( )/ ) JIT < 3> < 4> < 4> 0 < 4> < 5> < 표 3> 수송주기와차량크기에따른물류비용 수송주기( 일) 차량크기 (50) 차량크기 (100) 차량크기 (150) 물류비용 평균물류비용/ 일 물류비용 평균물류비용/ 일 물류비용 평균물류비용/ 일

9 물류시스템에서수송주기와차량크기의결정 < 5> 1 < 4> < 표 4> 차량경로계획및수송시간 번호차량경로시간( 분) 번호차량경로시간( 분) < 표 5> 차량의수송일정 번호수송차량차량경로번호수송시간 결 론 참고문헌 [1] Turner WG Ghare PM and Foulds LR Transportation routing problem a survey AIIE Transactions Vol [2] Basnet C Clark DN and Foulds LR A decision support system approach to vehicle routing Control and Cybernetics Vol [3] Golden BL and Assad AA Vehicle routing methods and studies North-Holland Amsterdam 1988 [4] Labbe M Laporte G and Mercure H Capacitated vehicle routing on trees Operations Research Vol [5] Yang PC and Wee HM An arborescent inventory model in a supply chain system Production Planning & Control Vol [6] Fleischmann B Design of freight traffic networks Advanced in Distribution Logistics [7] Ballou RH Business Logistics Management 4th edition Prentice-Hall Inc 1999 [8] Kasilingam RG Logistics and transportation design and planning Kluwer academic publishers 1998 [9] Bramel J and Simchi-Levi D The logic of logistics Springer-Verlag New York Inc 1997 [10] Daganzo GF Logistics Systems Analysis Springer 1999 [11] McGavin E Schwarz LB and Ward J Two-interval inventory-allocation policies in a one-warehouse N-identical-retailer distribution system Management Science Vol [12] Chopra S and Meindl P Supply Chain Management Upper Saddle River New Jersey 2001 [13] Bertsimas D and Simchi-Levi D The new generation of vehicle routing research robust algorithms addressing uncertainty Operations Research Vol [14] Christofides N Vehicle routing In The Traveling Salesman Problem a Guided Tour of Combinatorial Optimization Lawler ELJK Lenstra A H G Rinnooy Kan and DB Shmoys(eds) John Wiley & Sons Ltd New York [15] Gillett BE and Miller LR A heuristic algorithm for the vehicle dispatching problem Operations Research Vol [16] Clarke G and Wright JW Scheduling of vehicles from a central depot to a number of delivery points

10 Operations Research Vol [17] Fisher ML Vehicle Routing In Handbook in Operations Research and Management Science the volume on Network Routing Ball M T L Magnanti CL Monma and GL Memhauser (eds) North- Holland Amsterdam [18] Graves SC and Schwarz LB Single cycle continuous review policies for arborescent production/inventory systems Management Science Vol [19] Roundy R 98%-effective integer-ration lot sizing for one-warehouse multi-retailer systems Management Science Vol [20] Jackson PL Maxwell WL and Muckstadt JA The joint replenishment problem with powers of two restrictions AIIE Transactions Vol [21] Federgruen A and Zheng YS The joint replenishment problem with general joint structures Operations Research Vol [22] Bramel J and Simchi-Levi D A location based heuristic for general routing problems Operations Research Vol ) [23] Anily S and Federgruen A One warehouse multiple retailer systems with vehicle routing costs Management Science Vol [24] Herer Y and Roundy R Heuristics for a one warehouse multi-retailer distribution problem with performance bounds Technical reports No 916 Cornell university Ithacha NY 1990 [25] Viswanathan S and Mathur K Integrating routing and inventory decision in one warehouse multi-retailer multi-product distribution systems working paper 1993 장석화

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