계 량 분 석

1. 계 량 분 석 이 승 재 2011. 00. 00

2. 계량 분석 9 주차 Transportation & Transhipment Problem

3. 네모 필요할 때 쓸 양식 - 소제목용 Transportation Problem Contents DEFINITION APPLICATION THE TRANSPORTATION ALGORITHM THE ASSIGNMENT MODEL • PRODUCTION-INVENTORY CONTROL • DETERMINATION OF THE STARTING SOLUTION • ITERATIVE COMPUTATION OF TRANSPORTATION ALGORITHM • BALANCING OF THE T.M. • THE HUNGARIAN METHOD

4. Transportation Problem APPLICATION – Definition of the transportation model 수송계획이란 제품의 공급지와 수요지가 둘 이상 존재하고, 각 공급지로부터 각 수요지까지 단위당 수송비용이 알려져 있을 때, 총 수송비용을 최소로 하는 공급지와 수요지의 연결방법을 모색하는 것을 말한다. • :The amount of supply at source i • :The amount of demand at destination j • :Cost per unit • :The amount shipped

5. Transportation Problem Example MG Auto has three plants in L.A. , Detroit, and New Orleans, and two major distribution centers in Denver and Miami. The capacities of the three plants during the next quarter are 1000, 1500, and 1200 cars. The quarterly demands at the two distribution centers are 2300 and 1400 cars. The mileage chart between the plants and the distribution centers is given in Table 1. The trucking company in charge of transporting the cars charges 8 cents per mile per car. The transportation costs per car on the different routes, rounded to the closest dollar, are given in Table 2.

6. Transportation Problem Example • Minimize z = = 3700 cars

7. Transportation Problem Example - Solution

8. Transportation Problem Application – Production Inventory Control Example A company manufactures backpacks for serious hikers. The demand for its product occurs during March to June of each year. A company estimates the demand for the four months to be 100,200,180,and 300 units, respectively. The company uses part-time labor to manufacture the backpacks and , accordingly, its production capacity varies monthly. It is estimated that A company can produce 50, 180, 280, and 270 units in March through June. Because the production capacity and demand for the different months do not match, a current month’s demand may be satisfied in one of three ways. 1. Current month’s production 2. Surplus production in an earlier month 3. Surplus production in a later month In the first case, the production cost per backpack is 40. The second case incurs an additional holding cost of $0.50 per backpakc per month. In the third case, and additional penalty cost of $2.00 per backpack is incurred for each month delay. A company wishes to determine the optimal production schedule for the four months.

9. Transportation Problem Example - Solution

10. Transportation Problem The Transportation Algorithm – Determination of the starting solution 1. north-west corner method(북서코너법) Step1. 북서쪽의 구석부터 수요량과 공급량 비교 및 할당 Step2. 수요량과 공급량이 남아있는 칸에 할당 Step3. 남은 수송량의 할당 Step4. 최초 실행가능기저해 도출

11. Transportation Problem Transportation Problem Application – Production Inventory Control The Transportation Algorithm – Determination of the starting solution 2.Least- cost method

12. Transportation Problem Transportation Problem Application – Production Inventory Control The Transportation Algorithm – Determination of the starting solution 3. Vogel approximation method(VAM)

13. Transportation Problem Transportation Problem Application – Production Inventory Control The Transportation Algorithm – Determination of the starting solution 3. Vogel approximation method(VAM)

14. Transportation Problem Transportation Problem Application – Production Inventory Control The Transportation Algorithm – Determination of the starting solution 3. Vogel approximation method(VAM)

15. Transportation Problem Transportation Problem Application – Production Inventory Control The Transportation Algorithm – Determination of the starting solution 3. Vogel approximation method(VAM)

16. Transportation Problem The Transportation Algorithm – Iterative Computation of Transportation Algorithm

17. Transportation Problem The Transportation Algorithm – Iterative Computation of Transportation Algorithm for each basic xij for each nonbasic xij 개선지수가 모두 음수일때 최적해이다.

18. Transportation Problem The Transportation Algorithm – Iterative Computation of Transportation Algorithm

19. Transportation Problem The Transportation Algorithm – Iterative Computation of Transportation Algorithm

20. Transportation Problem The Transportation Algorithm -Balancing Of The Transportation Model

21. Transportation Problem The Transportation Algorithm -Balancing Of The Transportation Model

22. Transportation Problem The Transportation Algorithm -Balancing Of The Transportation Model

23. Transportation Problem The Transportation Algorithm -Balancing Of The Transportation Model 개선지수가 모두 음수 →최적값

24. Transportation Problem THE ASSIGNMENT MODEL - Definition of the assignment model • 주어진 과업들을 작업자에게 적절하게 배정하는 방법 • 각 공급지의 공급량 : 1 • 각 수요지의 수요량 : 1 The Hungarian method

25. Transportation Problem THE ASSIGNMENT MODEL Joe Klyne’s three children, John, Karen, and Terri, want to earn some money to take care of personal expenses during a school trip to the local zoo. Mr. Klyne has chosen three chores for his children: mowing the lawn, painting the garage door, and washing the family cars. To avoid anticipated sibling competition, he asks them to submit (secret) bids for what they feel is fair pay for each of the three chores. The understanding is that all three children will abide by their father’s decision a s to who gets which chore. Table summarizes the bids received. Based on this information, how should Mr. Klyne assign the chores?

26. Transportation Problem THE ASSIGNMENT MODEL

27. Transportation Problem THE ASSIGNMENT MODEL Total cost = 9+10+8=$27 (P1+P2+P3) + (q1+q2+q3) = (9+9+8) + (0+1+0) = $27

28. Transportation Problem THE ASSIGNMENT MODEL

29. Transportation Problem THE ASSIGNMENT MODEL Total cost =1+10+5+5=$21 (P1+p2+p3+p4)+(q1+q2+q3+q4) + (entry) = (1+7+4+5)+(0+0+3+0)+1=$21