4. Consider the following data for a Transportation Problem with 5 origins and 6
ID: 396773 • Letter: 4
Question
4. Consider the following data for a Transportation Problem with 5 origins and 6 destinations (Store 1-Store 6). The supply at each origin, demand at each store, and the unit costs are shown in the following table S/unit Dallas Denver Juarez uscon Wichita Demand Store 6Supply 1000 1500 2000 1000 1500 Store 1 Store 2Store 3 Store 4 Store 5 210 164 154 173 157 1300 156 217 152 112 123 96 126 104 1000 185 155 85 125 162 1300 145 232 125 169 154 1500 154 153 132 1200 187 1200 a. Solve the Transportation Problem to find the minimum cost shipping pattern Minimum Cost- Fill in the table with the optimal flows: Flows Dallas Denver Juarez Tucson Wichita Store 1 Store 2 Store 3| Store 4 Store 5 Store 6 Which origins do not send all their supply? Which destinations do not receive all their demand? b. Now suppose that there is to be an expansion at exactly one of the four origins Dallas, Denver, Tucson or Wichita that will increase its supply by 1000 units. (For example, Dallas could be expanded to have a supply of 2000.) Only one origin will be expanded. Which origin should be expanded to provide the lowest cost solution that satisfies all the demand? Origin to Expand by 1000 units -Explanation / Answer
To solve this problem use least cost method in transportation problem.
Step1: identify least cost in the matrix
$/ unit
Store1
Store2
Store3
Store4
Store5
Store6
Supply
Dallas
112
145
156
171
210
185
1000
Denver
123
154
217
232
164
155
1500
Juarez
96
83
152
125
154
85
2000
tuscon
126
153
177
169
173
125
1000
Wichita
104
132
187
154
157
162
1500
Demand
1000
1200
1200
1500
1300
1300
Juarez has least cost of 83, hence allocate first for Juarez. Store 2 has demand of 1200 and Juarez has supply of 2000. Hence 1200 can be supplied from Juarez. Hence store 2 demand becomes zero and Juarez supply becomes 800
$/ unit
Store1
Store2
Store3
Store4
Store5
Store6
Supply
Dallas
112
145
156
171
210
185
1000
Denver
123
154
217
232
164
155
1500
Juarez
96
83
152
125
154
85
800
tuscon
126
153
177
169
173
125
1000
Wichita
104
132
187
154
157
162
1500
Demand
1000
0
1200
1500
1300
1300
Step2: Fallow same method and try to match all the supply and demand. If there is a tie, allot cell which has maximum demand/supply. The final tables is shown below.
$/ unit
Store1
Store2
Store3
Store4
Store5
Store6
Supply
Dallas
1000
0
Denver
200
1300
0
Juarez
1200
800
0
tuscon
500
500
0
Wichita
1000
500
0
Demand
0
0
0
500
0
0
Now multiply demand with cost in table 1.
Minimum cost = $908,200
Which origin do not send any supply?
Since demand is more than supply, all stores should send supply. Hence there is no city with surplus supply.
Which destination do not receive all their demand?
Store 4
Which origin should be expanded to meet the demand completely?
For this look at column store4 and find which origin has lowest cost. That origin can be expanded.
The least is Juarez but that is not the store which company is looking for expansion. Hence look for next low cost origin i.e. Wichita. Hence Wichita can be expanded.
$/ unit
Store1
Store2
Store3
Store4
Store5
Store6
Supply
Dallas
112
145
156
171
210
185
1000
Denver
123
154
217
232
164
155
1500
Juarez
96
83
152
125
154
85
2000
tuscon
126
153
177
169
173
125
1000
Wichita
104
132
187
154
157
162
1500
Demand
1000
1200
1200
1500
1300
1300
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