# Question: Five jobs need to be done on a certain machine

Five jobs need to be done on a certain machine. However, the setup time for each job depends upon which job immediately preceded it, as shown by the following table:

The objective is to schedule the sequence of jobs that minimizes the sum of the resulting setup times.

(a) Design a branch-and-bound algorithm for sequencing problems of this type by specifying how the branch, bound, and fathoming steps would be performed.

(b) Use this algorithm to solve this problem.

The objective is to schedule the sequence of jobs that minimizes the sum of the resulting setup times.

(a) Design a branch-and-bound algorithm for sequencing problems of this type by specifying how the branch, bound, and fathoming steps would be performed.

(b) Use this algorithm to solve this problem.

## Answer to relevant Questions

Consider the following nonlinear BIP problem: Maximize Subject to xj is binary, for j = 1, 2, 3, 4. Follow the instructions of Prob. 12.7-2 for the following IP model: Minimize Z = 2x1 + 3x2, Subject to And x1 ≥ 0, x2 ≥ 0 x1, x2 are integer. (a) Solve this problem graphically. (b) Use the MIP branch-and-bound algorithm ...Use the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve the following MIP problem interactively: Minimize Z = 5x1 + x2 + x3 + 2x4 + 3x5, Subject to and xj ≥ 0, for j = 1, 2, 3, 4, 5 xj is integer, for j = 1, ...Apply the procedure for tightening constraints to the following constraint for a pure BIP problem: x1 – x2 + 3x3 + 4x4 ≥ 1. Consider the following problem: Maximize Subject to x1 ∈ {3, 6, 12}, x2 ∈ {3, 6}, x3 ∈ {3, 6, 9, 12}, x4 ∈ {6, 12}, x5 ∈ {9, 12, 15, 18}, all these variables must have different values, x1 + x3 + x4 + 25.Post your question