MIT2_854F10_lp_ex

MIT2_854F10_lp_ex - LP Example Stanley B. Gershwin...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: LP Example Stanley B. Gershwin Massachusetts Institute of Technology Consider the factory in Figure 1 that consists of three parallel machines. It makes a single product which can be produced using any one of the machines. The possible material ows are indicated. Assume that the cost ($/part) of using machine M i is c i , and that the maximum rate that M i can operate is i . Assume that c 3 > c 2 > c 1 > and let 3 = . The total demand is D . Problem: How should the demand be allocated among the machines to minimize cost? Intuitive answer: We want to use the least expensive machine as much as possible, and the most expensive machine as little as possible. Therefore If D 1 , x 1 = D, x 2 = x 3 = cost = c 1 D If 1 < D 1 + 2 , x 1 = 1 , x 2 = D 1 , x 3 = cost = c 1 1 + c 2 ( D 1 ) If 1 + 2 < D, x 1 = 1 , x 2 = 2 , x 3 = D 1 2 cost = c 1 1 + c 2 2 + c 3 ( D 1 2 ) LP formulation: min c 1 x 1 + c 2 x 2 + c 3...
View Full Document

Page1 / 7

MIT2_854F10_lp_ex - LP Example Stanley B. Gershwin...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online