Problem 5 A small computer manufacturing company forecasts the demand over the n

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

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