Problem 1 (26 points)
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
1
2
3
4 Demand for Stainless Steel Sinks
120
160
240
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 at month 1 is 40 sinks)
a. Set up and formulate algebraically the above “production scheduling” problem as
a TRANSPORTATION Model to minimize cost. (16 points)
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. (10 points)
Note: This problem can be formulated as a multiperiod production scheduling LP
problem. However, DO NOT try to formulate it this way as the problem requirement
is to formulate it as a transportation problem.
