Integer Programming(IP) · What is it? Making decisions with IP Exclusion between choices Exclusion between constraints Solutions through branch and bound P Characteristics Solving Binary IPs Solving mixed ips and Lps Naive approach: rounding a simple way to solve an ip might be to round the non-integer solution to the nearest feasible integer. In practice, try it! In theory this idea makes no sense at all Consider Maximize Z=21x,+11x, Subject to7x1+4x2≤13 x1≥0,x2≥0,x1,x2 Integer Optimal solution x is(13/7, 0)Integer Programming (IP) • What is it? • Making decisions with IP – Exclusion between choices – Exclusion between constraints • Solutions through Branch and Bound – IP Characteristics – Solving Binary IPs – Solving Mixed IPs and LPs Naïve approach: rounding • A simple way to solve an IP might be to round the non-integer solution to the nearest feasible integer. In practice, try it! • In theory, this idea makes no sense at all. Consider • Optimal solution x* is (13/7,0) 0, 0, , integer Subject to 7 4 13 Maximize 21 11 1 2 1 2 1 2 1 2 x x x x x x Z x x t t  d