COMMERCE 3QA3 Lecture Notes - Lecture 15: Feasible Region, Snottsta And Vreta Stones, Linear Programming Relaxation

• School: McMaster University
• Department: Commerce
• Course: COMMERCE 3QA3
• Professor: John Miltenburg

Document Summary

Many problems require some decision variables to have integer values. So b = 0. 57, u = 300. 37, etc. are not okay, but b = 1, u = 330 are okay. Sometimes it is sufficient to round non-integer solutions; e. g. u = . 37 rounds down to u = . For example, suppose the decision variable is b = 1 if we launch new product b, and b = 0 if we do not launch new product b. Then if b = 0. 57, which rounds to b = 1, does not tell us for sure whether or not we should launch new product b. Linear programming problems are called pure integer programming (ip) problems if all decision variables must have integer values. They are called mixed integer programming (mip) problems if some but not all decision variables must have integer values. Variables are called general integer variables if the(cid:455) take a(cid:374)(cid:455) positi(cid:448)e i(cid:374)teger (cid:448)alue i. e. (cid:1004), (cid:1005), (cid:1006), , 9(cid:1009)(cid:1004), 9(cid:1009)(cid:1005), .