question archive Canning Transport is to move goods from three factories to three distribution centers
Canning Transport is to move goods from three factories to three distribution centers
Subject:Operations ManagementPrice:2.87 Bought7
Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below.
| Source | Supply | Destination | Demand |
| A | 200 | X | 50 |
| B | 100 | Y | 125 |
| C | 150 | Z | 125 |
| Shipping costs are: | |||
| Destination | |||
| Source | X | Y | Z |
| A | 3 | 2 | 5 |
| B | 9 | 10 | -- |
| C | 5 | 6 | 4 |
| (Source B cannot ship to destination Z) | |||
Answer the following questions:
A. Draw the network model.
B. What is the Linear Programming Model? (Be sure to include it in the correct form identifying the objective function and all constraints.
C. How many units should be moved from each source to each destination and what is the optimal value of the objective function? Solve using Excel Solver.
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Answer:
A) Network diagram is as follows:
B) Decision variables:
Xij = Quantity shipped from Source i (=A,B,C) to destination j (=X,Y,Z)
Objective: Min 3Xax + 2Xay + 5Xaz + 9Xbx + 10Xby + 5Xcx + 6Xcy + 4Xcz
s.t.
Xax + Xay + Xaz <= 200
Xbx + Xby <= 100
Xcx + Xcy + Xcz <= 150
Xax + Xbx + Xcx = 50
Xay + Xby + Xcy = 125
Xaz + Xcz = 125
Xij >= 0
C)
Solution of the LP model using Excel solver is as follows
Formula: J2 =SUMPRODUCT(B2:I2,$B$10:$I$10) copy to J2:J8
Shipment plan from source to destination is as follows:
A to X = 50
A to Y = 125
C to Z = 125
Shipment is zero on all other routes.
Optimal objective value = 900
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