Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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The Makonsel Company is a fully integrated company that both produces goods and sells them at its retail outlets. After production, the goods are stored in the company's two warehouses until needed by the retail outlets. Trucks are used to transport the goods from the two plants to the warehouses, and then from the warehouses to the three retail outlets. Using units of full truckloads, the following table shows each plant's monthly output, its shipping cost per truckload sent to each warehouse, and the maximum amount that it can ship per month to each warehouse. To Unit Shipping Cost Shipping Capacity From Warehouse 1 Warehouse 2 Warehouse 1 Warehouse 2 Output Plant 1 $425 $560 125 150 200 Plant 2 $510 $600 175 200 300 For each retail outlet (RO), the next table shows its monthly demand, its shipping cost per truckload from each warehouse, and the maximum amount that can be shipping per month from each warehouse. To Unit Shipping Cost Shipping Capacity From RO1 RO2 RO3 RO1 RO2 RO3 Warehouse 1 $470 $505 $490 100 150 100 Warehouse 2 $390 $410 $440 125 150 75 Demand 150 200 150 150 200 150 Management now wants to determine a distribution plan (number of truckloads shipped per month from each plant to each warehouse and from each warehouse to each retail outlet) that will minimize the total shipping cost. (a) Draw a network that depicts the company's distribution network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. (b) Formulate this problem as a minimum cost flow problem by inserting all the necessary data into this network (c) Use Excel Solve to solve this problem.
Transcribed Image Text:The Makonsel Company is a fully integrated company that both produces goods and sells them at its
retail outlets. After production, the goods are stored in the company's two warehouses until needed
by the retail outlets. Trucks are used to transport the goods from the two plants to the warehouses,
and then from the warehouses to the three retail outlets.
Using units of full truckloads, the following table shows each plant's monthly output, its
shipping cost per truckload sent to each warehouse, and the maximum amount that it can ship per
month to each warehouse.
From
To
Plant 1
Plant 2
From
To
Unit Shipping Cost
Warehouse 1
Warehouse 2
Demand
Warehouse 1
$425
$510
RO1
$470
$390
Warehouse 2
$560
$600
150
Unit Shipping Cost
For each retail outlet (RO), the next table shows its monthly demand, its shipping cost per
truckload from each warehouse, and the maximum amount that can be shipping per month from each
warehouse.
RO2
$505
$410
200
Warehouse 1
this network.
(c) Use Excel Solve to solve this problem.
RO3
Shipping Capacity
$490
$440
150
125
175
RO1
100
125
Warehouse 2
150
150
200
Shipping Capacity
RO2
150
Output
200
300
150
200
RO3
100
75
150
Management now wants to determine a distribution plan (number of truckloads shipped per
month from each plant to each warehouse and from each warehouse to each retail outlet) that will
minimize the total shipping cost.
(a) Draw a network that depicts the company's distribution network. Identify the supply nodes,
transshipment nodes, and demand nodes in this network.
(b) Formulate this problem as a minimum cost flow problem by inserting all the necessary data into
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