Group 9 - Answer To Case Problem (Distribution System Design) P372

[샤오즈웨이（경영）]

Hello group members,

    By now  we didn't study Management Scinence Chapter 7 , So I am not very sure these answers are right or wrong. From question 2 to question 3, because the objective function's variable and constraint are so much, maybe you wil l feel a little uncomfortable when you see these answers.

Question 1

Costs of manufacturing: $426,710.00

Costs of distribution from plants to distribution centers:  $92,252.00

Costs of distribution from distribution centers to customer centers :  $101,808.00

Total costs:  $620,770.00

Question 2

Costs of manufacturing: $423,230.00

Costs of distribution from plants to distribution centers:  $85,292.00

Costs of distribution from distribution centers to customer centers :  $92,420.00

Total costs: $600,942.00

Savings: $19,828.00

Question3 

Costs of manufacturing: $423,230.00

Costs of distribution from plants to distribution centers, Los Angele , San Diego and San Diego:  $76,804.00

Costs of distribution from distribution centers to customer centers:  $53,500.00

Total costs:  $553,534.00

Savings:  $67,236.00

FIGURE (question1)

FIGURE (question2)

FIGURE (question3)

About  MS6.0exe

Question 1 :

Here  the objective function is olny the costs of manufacturing from plants to distribution centers  Sante Fe and Las Vegas + the cost of  distribution from plants to distribution centers  Sante Fe and Las Vegas)

that is Min 12.7A+14.7B+13.9C+11.2D

Question 2

objective function is the total costs

Min.12.7A+14.7B+13.9C+11.2D+13.7E+0.3F1+5.2F2+2.1F3+5.4F4+3.1F5+4.5F6+4.4F7+6F8+6F9+2.7F10+5.4F11+4.7F12+3.3F13+3.4F14

        +2.4F15+3.3F16+2.1F17+2.7F18+2.5F19

          F18                     F19          

          2.7                     2.5

Question 3

objective function is the total costs

Min.12.7A+14.7B+13.9C+11.2D+13.7E+0.3F1+5.2F2+2.1F3+5.4F4+3.1F5+4.5F6+4.4F7+6F8+6F9+2.7F10+5.4F11+4.7F12+3.3F13+3.4F14

        +2.4F15+3.3F16+2.1F17+2.7F18+2.5F19+14G1+10.3G2+10.7G3

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Change this Case Problem from Darby Company to SONY Company

EI paso ⇨ Osaka Japan, San Bernardino ⇨ Shanghai China, Ft. Worth ⇨ Busan, Santa Fe ⇨ Mokpo, Las Vegas ⇨Incheon, Dallas ⇨Yangsan, San Antonio ⇨Changwon, Wichita ⇨Gimhae, Kansas City ⇨Masan, Denver ⇨Daegu, Salt Lake City ⇨Daejeon, Phoenix ⇨Gwangju, Los Angeles ⇨Seoul, San Diego ⇨Suwon 

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The SONY Company manufactures and distributes MP3, then sale MP3 to S. Korea.

SONY Company has 2 plants.

One is in Shanghai China. The other one is in Osaka Japan.

The cost of each MP3 produced at the Japan is $10.5, And the production capacity is 30,000 quarterly.

The cost of each MP3 produced at China is $10.0, And the production capacity is 20,000 quarterly.(TABLE 1)

TABLE 1.

Plant	Cost	Production Capacity
China	$10.00	20,000
Japan	$10.50	30,000

SONY Company has 3 distribution centers in S. Korea.

One is in Pusan, one is in Pusan, one is in Mokpo, the other is in Incheon.

The cost of shipping a MP3 from each of the two plants to each of the tree distribution  centers is shown in Table 2. ( Note that no shipments are allowed from the China to Pusan )

TABLE 2.

Plant	Pusan	Mokpo	Incheon
Japan	$3.20	$2.20	$4.20
China	---	$3.90	$1.20

SONY Company has 9 customer zones in S.Korea. They are Yangsan, Changwon, Gimhae, Masan,

Deagu, Daejeon, Gwangju, Seoul and Suwon. The numbers of MP3s needed in each customer zone for the next quarter is shown in Table 3.

TABLE 3.

Customer Zone	Demand (MP3s)
Yangsan	6300
Changwon	4880
Gimhae	2130
Masan	1210
Deagu	6120
Deajeon	4830
Gwangju	2750
Seoul	8580
Suwon	4460

Demand at the Yangsan, Changwon, Gimhae and Masan customer zones is satisfied by Shipments from the Busan.

Demand at the Daegu, Daejeon and Gwangju customer zones is satisfied by Shipments from the Mogpo.

Demand at the Seoul and Suwon customer zones is satisfied by Shipments from the Incheon.

The cost of shipping from each distribution center to each customer zone is given in Table 4.

TABLE 4. ( note that some of the distribution centers cannot serve certain customer zones )

	Yangsan	Changwon	Gimhae	Masan	Daegu	Daejeon	Gwangju	Seoul	Suwon
Busan	$0.30	$2.10	$3.10	$4.40	$6	--	--	--	--
Mogpo	$5.20	$5.40	$4.50	$6	$2.70	$4.70	$3.40	$3.30	$2.70
Incheon	--	--	--	--	$5.40	$3.30	$2	$2.10	$2.50

Question

1.      What will SONY Company’s manufacturing and distribution costs be for the following quarter?

2.      If customers could be served by any of the distribution centers for which costs are available. Can costs be reduced? By how much?

3.      If SONY Company can send MP3 from Japanese Plant to Changwon directly with $3.5 each MP3, from Chinese plant to Seoul directly with $0.3 each MP3, and from Chinese plant to Suwan directly with $0.7 each MP3 (TABLE 5), Can costs be further reduced? By how much?

TABLE5

	Changwon	Seoul	Suwon
Janpan	$3.50
China		$0.30	$0.70

Answer to Question1

Min 12.7A+14.7B+13.9C+11.2D (note that  the objective function is only the costs of manufacturing from plants to distribution centers  Mokpo and Incheon + the cost of  distribution from plants to distribution centers  Mokpo and Incheon)

s.b. A+B≦15480 Osaka Japan

C+D≦20000 Shanghai China

A+C=13700 Mokpo

B+D=13040 Incheon

Answer to Question2

① Costs of manufacturing: 10.5A + 10.5B + 10.5E + 10C + 10D

② Costs of distribution from plants to distribution centers: 2.2A + 4.2B + 3.9C + 1.2D +3.2E

③ Costs of distribution from distribution centers to customer centers : 0.3F1 + 5.2F2 + 2.1F3 + 5.4F4 + 3.1F5 + 4.5F6 +4.4F7 + 6F8 + 6F9 + 2.7F10 + 5.4F11 + 4.7F12 + 3.3F13 + 3.4F14 + 2.4F15 + 3.3F16 + 2.1F17 + 2.7F18 + 2.5F19

Total costs=①+②+③: 12.7A + 14.7B + 13.9C + 11.2D + 13.7E + 0.3F1 + 5.2F2 + 2.1F3 +5.4F4 + 3.1F5 + 4.5F6 + 4.4F7 + 6F8 + 6F9 + 2.7F10 + 5.4F11 + 4.7F12 + 3.3F13 + 3.4F14 + 2.4F15 + 3.3F16 + 2.1F17 + 2.7F18 + 2.5F19

Min  12.7A + 14.7B + 13.9C + 11.2D + 13.7E + 0.3F1 + 5.2F2 + 2.1F3 +5.4F4 + 3.1F5 + 4.5F6 + 4.4F7 + 6F8 + 6F9 + 2.7F10 + 5.4F11 + 4.7F12 + 3.3F13 + 3.4F14 + 2.4F15 + 3.3F16 + 2.1F17 + 2.7F18 + 2.5F19

s.b.  F1+F2=6300 Yangsan

F3+F4=4880 Changwon

F5+F6=2130 Gimhae

F7+F8=1210  Masan

F9+F10+F11=6120 Deagu

F12+F13=4830 Deajeon

F14+F15=2750 Gwangju

F16+F17=8580 Seoul

F18+F19=4460 Suwon

E-F1-F3-F5-F7-F9=0 Busan

A+C-F2-F4-F6-F8-F10-F12-F14-F16-F18=0 Mokpo

B+D-F11-F13-F15-F17-F19=0 Incheon

C+D≦20000 Shanghai China

A+B+E≦30000 Osaka Japan

Answer to Question3.

① Costs of manufacturing: 10.5A + 10.5B + 10.5E + 10.5G1 +10C + 10D +10G2 + 10G3

② Costs of distribution from plants to distribution centers: 2.2A + 4.2B + 3.9C + 1.2D +3.2E

③ Costs of distribution from distribution centers to customer centers : 0.3F1 + 5.2F2 + 2.1F3 + 5.4F4 + 3.1F5 + 4.5F6 +4.4F7 + 6F8 + 6F9 + 2.7F10 + 5.4F11 + 4.7F12 + 3.3F13 + 3.4F14 + 2.4F15 + 3.3F16 + 2.1F17 + 2.7F18 + 2.5F19

④ Costs of distribution from plants to customer centers: 3.5G1 + 0.3G2 + 0.7G3

Total costs=①+②+③+④ : 12.7A + 14.7B + 13.9C + 11.2D +13.7E + 0.3F1 + 5.2F2 + 2.1F3 + 5.4F4 + 3.1F5 + 4.5F6 +4.4F7 + 6F8 + 6F9 + 2.7F10 + 5.4F11 + 4.7F12 + 3.3F13 + 3.4F14 + 2.4F15 + 3.3F16 + 2.1F17 + 2.7F18 + 2.5F19 + 14G1 + 10.3G2 +10.7G3

Min 12.7A + 14.7B + 13.9C + 11.2D +13.7E + 0.3F1 + 5.2F2 + 2.1F3 + 5.4F4 + 3.1F5 + 4.5F6 +4.4F7 + 6F8 + 6F9 + 2.7F10 + 5.4F11 + 4.7F12 + 3.3F13 + 3.4F14 + 2.4F15 + 3.3F16 + 2.1F17 + 2.7F18 + 2.5F19 + 14G1 + 10.3G2 +10.7G3

s.t.

  F1+F2=6300 Yangsan

F3+F4+G1=4880 Changwon

F5+F6=2130 Gimhae

F7+F8=1210  Masan

F9+F10+F11=6120 Deagu

F12+F13=4830 Deajeon

F14+F15=2750 Gwangju

F16+F17+G2=8580 Seoul

F18+F19+G3=4460 Suwon

E-F1-F3-F5-F7-F9=0 Busan

A+C-F2-F4-F6-F8-F10-F12-F14-F16-F18=0 Mokpo

B+D-F11-F13-F15-F17-F19=0 Incheon

C+D+G2+G3≦20000 Shanghai China

A+B+E+G1≦30000 Osaka Japan

[최지연(경영06)]

^ ^ *

[남혜린(경영)]

흠... ㅎ 2번이랑 3번이면... ㅎ 목요일날 만나서 다시 설명해주세요~ ㅋㅋ이거 참고해서 갈게요ㅎ

[배성수(경영)]

내 생각에는 제대로 푼거 같은데...^^;;;;일단 비용을 최소화 시킨 운송경로와 기존의 운송경로에서 큰 차이는 나지 않는다...2~3개의 경로만 바뀌고 나머지는 기존의 경로가 최소화 경로이다...그리고 바뀐 경로도 단위단 비용이 기존의 경로와 큰 차이가 나지 않는다 많이 나야 1달러 정도..그래서 19000달러 차이면 많은 차이 인거 같은데...^^;;;

[김해인(경영06)]

즈웨이 ~ 화이팅 ㅎ,ㅎ 언제발표해요 ?

[임효순(사학)]

샤오즈웨이 넘 수고했당..ㅠ

[이여진(운영자)]

^^ Gooooooood job!!!!

[김유나(운영자)]

와~쯔웨이!! 열씨미하구있엉??화이팅이야^^