2. Question
• Hatcher Enterprises uses a chemical called Rbase in production operations at fie
divisions. Only 6 suppliers of Rbase meet Hatchers quality control standards. All 6
suppliers can produce Rbase in sufficient quantities to accommodate the needs of
each division. The Quantity of Rbase needed by each Hatcher division and the
price per gallon charged by each supplier as follows:
Demand Price
Division (1000 of gallons) Supplier per gallon ($)
1 40 1 12.6
2 45 2 14
3 50 3 10.2
4 35 4 14.2
5 45 5 12
6 13
3. Question-Contd.
• The cost per gallon ($) for shipping from each supplier to each division is provided in the
following table.
Supplie
r
Division 1 2 3 4 5 6
1 2.75 2.5 3.15 2.8 2.75 2.75
2 0.8 0.2 5.4 1.2 3.4 1
3 4.7 2.6 5.3 2.8 6 5.6
4 2.6 1.8 4.4 2.4 5 2.8
5 3.4 0.4 5 1.2 2.6 3.6
• Hatcher believes in spreading its business among suppliers so that the company will
be less affected by supplier problems (e.g. labor strikes or resource availability).
Company policy requires that each division have a separate supplier.
– a. For each supplier-division combination, compute the total cost of supplying the divisions demand.
– b. Determine the optimal assignment of suppliers to divisions.
4. Solution
• Total Demand = sum of demand from all the divisions = 215 gallons.
• Supply by each supplier, 1 to 6 is equal therefore = 215/6 = 35.833 gallons.
• Formulate the solution in Excel using the below formulas in each cell –
Demand
"=SUM(B3:
G3)" 40
45
50
35
45
"=SUM(B3:B7)"
Supply 35.83333 35.83333 35.83333 35.83333 35.83333 35.83333
"=SUM(B1
"=B13*B3+B14*B4+B15*B5+B16*B6+B17*B7" 0:G10)"
Suppliers
Divisions 1 2 3 4 5 6
1 2.75 2.5 3.15 2.8 2.75 2.75
2 0.8 0.2 5.4 1.2 3.4 1
3 4.7 2.6 5.3 2.8 6 5.6
4 2.6 1.8 4.4 2.4 5 2.8
5 3.4 0.4 5 1.2 2.6 3.6
5. Solution
• Using the solver options as –
• Changing Cells
– Shaded portion in previous slide
• Constraints –
– Sum of supply = Total supply
– Sum of demand = Total demand
• The solution is shown below, indicating the least transportation cost as
$476.67. The break-up of division to supplier quantities are listed below –
– Division 1 supplies 35.8 units to Supplier3 & 4.17 units to Suplier4
– Division 2 supplies 35.8 units to Supplier1 & 9.17 units to Supplier6
– Division 3 supplies 14.1 units to Supplier2 & 35.8 units to Supplier4
– Division 4 supplies 8.3 units to Supplier2 & 26.7 units to Supplier6
– Division 5 supplies 13.3 units to Supplier2 & 31.7 units to Supplier5
• Total Cost = Quantity * price (of the chosen division to supplier
combination) + Transportation cost
• Cost = 2673.333 + 476.6667 = $3150
6. Sensitivity Analysis
• Adjustable Cells –
– The Suppliers who are not being served by Division1 can be serviced to the tune
of 1.4 to 2.8 gallons of Rbase as the minimum and maximum. The cost per unit
will increase by 1.4 to 2.8 if these suppliers that have been omitted by the
solution are serviced.
– For those suppliers who are being serviced as per the solution, there is no more
demand remaining that can be served by divisions 1 to 6. Therefore there will
be no alteration in the cost.
7. Sensitivity Analysis- Contd.
• Constraints interpretation-
– Suppliers
• There is no more Rbase remaining to be supplied to Suppliers 1 to 6.
• An increased supply of 8.3 gallons can be made to Supplier1. This will increase the per unit cost by $0.6 .
• An increased supply of 35.83 gallons can be made to Supplier2. This will decrease the per unit cost by $0.2 .
• An increased supply of 4.17 gallons can be made to Supplier3. This will increase the per unit cost by $2.4.
• Supplier 4 cannot take any more supply. His capacity is maximized.
• An increased supply of 13.3 gallons can be made to Supplier5. This will increase the per unit cost by $2.
• An increased supply of 8.3 gallons can be made to Supplier6. This will increase the per unit cost by $0.8 .
– Division
• The divisions increase their capacity to supply anymore Rbase.
• A reduction in capacity of 4.17 gallons can be made by Division1. This will increase the profit by $0.75.
• A reduction in capacity of 8.3 gallons can be made by Division2. This will increase the profit by $0.2.
• A reduction in capacity of 35.8 gallons can be made by Division3. This will increase the profit by $2.8.
• A reduction in capacity of 8.3 gallons can be made by Division4. This will increase the profit by $2.
• A reduction in capacity of 13.3 gallons can be made by Division5. This will increase the profit by $0.6 .
