Problem 5 A small computer manufacturing company forecasts the demand over the n
ID: 3306898 • Letter: P
Question
Problem 5 A small computer manufacturing company forecasts the demand over the next n months to be di, i = 1, 2 , n. In any month it can produce r units, using regular production, at a cost of b dollars per uni. By using overtime, it can produce additional units at c dollars per unit, where c > b. The firm can store units from month to month at a cost of s dollars per unit per month. Formulate the problem of determining the production schedule that minimizes cost as a LP. Shortages are not permitted.Explanation / Answer
Solution:
In any month compnay can produce r units.
Next n month are as follows: 1, 2,3, 4, 5 .... n
Demand: d1 , d2 , ... dn
Production: x1, x2, ... xn
stock: d1 - x1 ; d2 - x2 ; .... dn - xn = i-1j=1 (di -xi )
The problem can be formulated as follow:
Minimize n i=1 max ((bxi + i-1 j=1 ( di xi ) , bxi + (c-b) (xi -r) +i-1 j=1 ( dj xj ) )
subject to
xi + n i=1 (dj xj ) di
di 0