(2) Find an optimal solution for the following transportation problem To Valley Tow S Malin an Yonkers M Pinburgh 350 Madison (M) 58 ||$15 To Valley (5) Yonkers (3 Pittsburgh Using the Stepping Stone method to find en optimal plan. Tow 310 1,250 The above feasible plan is obtained by applying the Northwest Corner Rale (.g. 300 from M to F, etc.), and its total cost 350(58)+50(510)+150(512)+250(54)+200(311)+250(514)-51100 58 Junctio S $15 $10 Burg $14 400 Buy MB: 6-11-12-10 T: 5.12+10-8 600 P 15-14-11-12-10-8-2 PT: 6-14-11-12-2 11-14-11-4-4 250 Demand 450 the "most negative index" We focus on cell PT (index=9). Its closed path is PT to PB to 18 to YT, and back to PT. To increase the quar PT, we need to adjust PB down, 18 up, and 17 down. Therefore, the next improved plan is The improvement indices bel are determined as follows: nowM first, then sows and P MJ9-4-12-10-2
(2) Find an optimal solution for the following transportation problem To Valley Tow S Malin an Yonkers M Pinburgh 350 Madison (M) 58 ||$15 To Valley (5) Yonkers (3 Pittsburgh Using the Stepping Stone method to find en optimal plan. Tow 310 1,250 The above feasible plan is obtained by applying the Northwest Corner Rale (.g. 300 from M to F, etc.), and its total cost 350(58)+50(510)+150(512)+250(54)+200(311)+250(514)-51100 58 Junctio S $15 $10 Burg $14 400 Buy MB: 6-11-12-10 T: 5.12+10-8 600 P 15-14-11-12-10-8-2 PT: 6-14-11-12-2 11-14-11-4-4 250 Demand 450 the "most negative index" We focus on cell PT (index=9). Its closed path is PT to PB to 18 to YT, and back to PT. To increase the quar PT, we need to adjust PB down, 18 up, and 17 down. Therefore, the next improved plan is The improvement indices bel are determined as follows: nowM first, then sows and P MJ9-4-12-10-2
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:(2) Find an optimal solution for the following transportation problem.
Town
To Valley
FROM
Madison
(M)
Yonkers
(1)
Pittsburgh
(P)
Demand
FROM
Madison
(M)
Yonkers
Pittsburgh
FROM
3.50
Madison
(M)
Yonkers
FROM
$8
350
Madison
(M)
Yonkers
(1)
Pittsburgh
$5
SIS
350
Valley
(5)
$8
$5
$15
Using the Stepping-Stone method to find an optimal plan.
Tol Valley
Town
Junction
(7)
$8
Pittsburgh
Demand
350
Part (a) Find the new TC=
$5
$15
50
350
The above feasible plan is obtained by applying the Northwest Corner Rule (e.g., 300 from M to V, etc.), and
its total cost = 350($8) +50($10)+150($12) +250($4)+200($11) +250($14) = $11.800,
150
$8
200
$5
The improvement indices below
are determined as follows:
Supply row M first, then sows Y and P)
MJ: 9-4+12-10-2
400 MB: 6-11+12-10=-3
rv: 5-12+10-8-5
600 PP: 15-14+11-12-10-8-2
PT: 6-14+11-12-
PA 11-14+11-4-4
Demand
350
200
the "most negative index"
We focus on cell PT (index=-9). Its closed path is: PT to PB to YB to YT, and back to PT. To increase the quantity in
PT, we need to adjust PB down, YB up, and YT down. Therefore, the next improved plan is:
To
Munction
$15
50
150
$10
$12
50
150
200
$6
Town
200
$10
Part (e) Determine the next improved plan.
To Valley
Town
(1)
$12
$6
$10
$12
$6
$10
Junction
S
$12
250
$6
Demand
350
Part (d) Find the new TC=
Part (1) is the current solution optimal?
250
250
250
59
$4
250
250
250
$9
$4
$11
59
54
Junction
(5)
$9
$4
Burg
(8)
200
$11
250
450
Explain
200
250
450
$11
Burg
(8)
350
$6
314
100
450
Burg
(8)
450
$11
$14
Burg
(8)
$6
$11
$14
Supply
400
56
||$11
$14
600
250
1,250
250
1.250
Supply Row Mf first, then rows Y and P
400
600
Part (b) Find the indices (show steps)
250
1,250 Asterisk the "most negative index"
(show steps)
Supply
400
600
Part (e) Find the indices (show steps)
Row M first, then rows Y and P
250
1,250 Asterisk the "most negative index"
(show steps).
(hint: see Online Module 8, p.M8-4).
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