The J. Mehta Company's production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is as follows:
|
Month
|
Demand for Stainless Steel Sinks
|
|
1
|
120
|
|
2
|
160
|
|
3
|
240
|
|
4
|
100
|
The Mehta firm can normally produce 100 stainless steel sinks in a month. This is done during regular production hours at a cost of $100 per sink. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices:
(1) he can produce up to 50 more sinks per month in overtime but at a cost of $130 per sink;
(2) he can purchase a limited number of sinks from a friendly competitor for resale (the maximum number of outside purchases over the four-month period is 450 sinks, at a cost of $150 each);
(3) Or, he can fill the demand from his on-hand inventory (i.e. beginning inventory). The inventory carrying cost is $10 per sink per month (i.e. the cost of holding a sink in inventory at the end of the month is $10 per sink).
A constant workforce level is expected. Back orders are NOT permitted (e.g. order taken in period 3 to satisfy the demand in later period 2 is not permitted). Inventory on hand at the beginning of month 1 is 40 sinks (i.e. beginning inventory in month 1 is 40 sinks)
a. Set up and formulate algebraically the above "production scheduling" problem as a TRANSPORTATION Model to minimize cost.
b. SOLVE using Excel solver (Provide a printout of the corresponding "Excel Spreadsheet" and the "Answer Report"). Also include a managerial statement that describes verbally the results.
Note: This problem can be formulated as multi-period production scheduling LP problem.However, if you try to formulate it this way then you will get ZERO as the problem requirement is to formulate it as a transportation problem.
Problem 2
A department has three machines available, and the new department manager must select one of the machines to assign to a new product line. The product line will consist of three slightly different products, A, B and C. Production requirements, machine capacities and setup costs are given in the following table:
|
Machine
|
Setup Cost
|
Production time per pound
|
Capacity (hours)
|
|
A
|
B
|
C
|
|
1
|
$150
|
4
|
3
|
5
|
1000
|
|
2
|
$120
|
3
|
2
|
4
|
800
|
|
3
|
$110
|
2
|
4
|
2
|
700
|
The revenue per pound on the three products is listed in the following table:
|
Product
|
Revenue
|
|
A
|
$13
|
|
B
|
$10
|
|
C
|
$12
|
a. Formulate algebraically this problem that will maximize the net profit taking into account an additional factor: At least 40 pounds of each product must be made.
b. Solve for the optimal solution and profit using Excel solver (Provide a printout of the corresponding "Excel Spreadsheet" and the "Answer Report"). Also include a managerial statement that describes verbally the results.
Problem 3
California Tours is planning a group bus trip that for the following candidate cities in the table below. Also included are the total costs for the group to visit those cities on the tour.
|
City
|
Cost($)
|
|
San Fransisco (SF)
|
5000
|
|
Oakland (OK)
|
4500
|
|
Palo Alta (PA)
|
3600
|
|
San Jose (SJ)
|
4100
|
|
San Mateo (SM)
|
3500
|
|
Concord (CO)
|
2500
|
|
Santa Cruz (SC)
|
3200
|
|
Monterey (MN)
|
4000
|
To plan the trip, three prioritized goals are listed below, in order of importance.
P1: Avoid spending more than $15000 for the total trip.
P2: Visit at least 5 cities.
P3: Include San Mateo in the tour.
a. Formulate a goal programming model that will help to determine the number of cities to include in the tour.
b. Find the optimal solution using Solver. (Provide a printout of the Answer report and theExcel spreadsheet formulation). Also include a managerial statement that describes verbally the results.