The J. Mehta Company’s productionmanager is planning a series of one-month production periods forstainless steel sinks. The forecasted demand for the next fourmonths is as follows:
Month | Demand for Stainless Steel Sinks |
1 | 120 |
2 | 160 |
3 | 240 |
4 | 100 |
The Mehta firm can normally produce 100stainless steel sinks in a month. This is done during regularproduction hours at a cost of $100 per sink. If demand in any onemonth cannot be satisfied by regular production, the productionmanager has three other choices:
he can produce up to 50 more sinks per month in overtime but ata cost of $130 per sink;
he can purchase a limited number of sinks from a friendlycompetitor for resale (the maximum number of outside purchasesover the four-month period is 450 sinks, at a costof $150 each);
Or, he can fill the demand from his on-hand inventory (i.e.beginning inventory). The inventory carrying cost is $10 per sinkper month (i.e. the cost of holding a sink in inventory at the endof the month is $10 per sink).
Back orders are NOT permitted (e.g. order taken in period 3 tosatisfy the demand in later period 2 is not permitted). Inventoryon hand at the beginning of month 1 is 40 sinks (i.e. beginninginventory at month 1 is 40 sinks)
Set up and formulate algebraically the above “productionscheduling” problem as a TRANSPORTATION Model tominimize cost.
