(lecture held on 6/09/02)
Till now we have seen APP problems formulated as Transportation problems. But the Transportation LP can only be used for solving simple problems. Generally, these problems need to be formulated as LP problems, as illustrated by the following example:
Ex: Assume best demand estimates are as follows:
|
Jan |
5300 |
May |
4100 |
Sept |
7300 |
|
Feb |
5100 |
June |
4800 |
Oct |
7800 |
|
Mar |
4400 |
July |
6000 |
Nov |
7600 |
|
Apr |
2800 |
Aug |
7100 |
Dec |
6400 |
To adjust for the demand fluctuations as shown above, the management needs to make some decisions. These decisions can take the form of:
1. Hire & Fire: Changing workforce level by hiring or firing.
2. Overtime: Covering temporary shortages by overtime work.
3. Inventory: Storing some of the present surplus to cover future shortages.
All these measures have some extra cost associated with them as compared to the regular time production costs. These costs are:
1. Hiring: $300 per worker
2. Firing: $420 per worker
3. Overtime: ($20+regular production cost) per unit
4. Inventory Holding Cost: $8 per month
Also these measures are subject to some constraints which are require to be satisfied for production to be feasible:
1. Change of workforce level is restricted to at most 40 workers per month (up or down).
2. Each worker produces 20 units per month on regular time and will produce no more than 6 units per month on overtime.
3. At present there are 290 workers + no inventory.
4. Long range planning dictates a zero inventory by next December.