Analytical Models in DSS
A company that assembles electronic alarm systems requires three component parts: C1, C2, and C3. In-house production costs are estimated to be $15 per unit for part C1, $18 per unit for part C2, and $ 20 per unit for part C3. It requires 0.16 hours of machining time and 0.1 hours of finishing time to produce to each unit of part C1 in-house; 0.3 hours of machining time and 0.2 hours of finishing time to produce to each unit of part C2 in-house; and 0.25 hours of machining time and 0.3 hours of finishing time to produce to each unit of part C3 in-house.
Because of contractual obligations the company needs 6,000 units each of parts C1, C2, and C3 in the upcoming week. It has only 3000 hours of machining time and 2400 hours of finishing time available over this period. Since its limited production capacity prevents it from satisfying its entire demand for these parts through in-house production alone, the company also needs to purchase some quantities of these parts from external suppliers.
Two external suppliers are available - Supplier A and Supplier B. Supplier A can supply at most 1000 units of C1 at a cost of $16 per unit, at most 1500 units of C2 at a cost of $20 per unit, and at most 1000 units of C3 at a cost of $24 per unit. Supplier B can supply at most 1200 units of C1 at a cost of $18 per unit, at most 2000 units of C2 at a cost of $22 per unit, and at most 1000 units of C3 at a cost of $23 per unit.
For your convenience, the information presented above is summarized in the table below.
|
Part
|
Cost per unit
|
Quantity
|
Capacity (units)
|
Hours required per unit
|
|
In-house
|
Supplier A
|
Supplier B
|
Required
|
Supplier A
|
Supplier B
|
Machining
|
Finishing
|
|
C1
|
$ 15
|
$ 16
|
$ 18
|
6000
|
1000
|
1200
|
0.16
|
0.10
|
|
C2
|
$ 18
|
$ 20
|
$ 22
|
6000
|
1500
|
2000
|
0.30
|
0.20
|
|
C3
|
$ 20
|
$ 24
|
$ 23
|
6000
|
1000
|
1000
|
0.25
|
0.30
|
|
|
|
|
|
|
|
|
Available (hours)
|
|
|
|
|
|
|
|
|
Machining
|
Finishing
|
|
|
|
|
|
|
|
|
3000
|
2400
|
The company uses a decision support system to determine the optimal production and purchase plan for parts C1, C2, and C3 so as to meet their needs (contractual obligations in the upcoming week) at minimum cost. It also uses the decision support system to perform sensitivity analysis.
a) What is the minimum cost attainable under the optimal plan?
The company has located a third supplier (New-Supplier) who can supply at most 100 units of part C1 in the upcoming week, but the purchase price is subject to negotiations. What is the maximum price that the company should be willing to pay New-Supplier for each unit of C1? Justify your answer. Assume that all demands, prices, and availability of resources remain unchanged.