QM B Lego Simplex Scenario You

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QM B Lego Simplex

Scenario • You manufacture tables and chairs. Small brick • Tables and chairs are manufactured from small and large bricks. Large brick

Lego Simplex Data • Table – 2 large bricks – 2 small bricks – $16 profit • Chair – 1 large bricks – 2 small bricks – $10 profit

Lego My Simplex Resources • You have 8 small bricks and 6 large bricks

The Goal • How many tables and how many chairs should be produced to maximize profit? Buzz Group Question 1 Groups of 3 -4

One possible solution Is this solution optimal? Profit = 3*16 = $48 Give up a table (-$16) Make two chairs (+20) Improves the solution by $4. So the above solutions is not optimal.

Optimal Solution 2 tables 2 chairs Profit: $52

Formulate as an LP Buzz Group: Question 2 Be sure to: Define variables Write the objective function Write the constraints Include non-negativity constraints

Formulate as an LP T – number of tables to produce C – number of chairs to produce Max 16 T + 10 C Subject to: 2 T+ C 6 2 T+2 C 8 T 0, C 0 Large bricks Small bricks Non-negativity

Graphical Insight 2 T+2 C 8 2 T+ C 6

At the optimal solution: • What if one more large brick becomes available? Buzz Group: Question 3

What would you be willing to pay for the brick? • Take a chair apart: (-10) • Make a table: (+16) • Pay a maximum of $6. This is the shadow price for large bricks – the increase in the objective function if one more unit of the resource, large bricks, becomes available.

How many large bricks should you buy at $6? • If we have yet another additional large bricks (8 altogether), then we can take apart the second chair and make a table. ($6 improvement). • If we add one more large brick (9 altogether), can we make another table?

Allowable increase • The number of additional large bricks that are worth the shadow price of $6 is 2.

Sensitivity Analysis • Shadow Prices – increase in the objective function if one more unit of the resource becomes available • Allowable increases – amount that the resource can increase and have the shadow price stay the same; – if outside the allowable increase, change RHS and re-run.

Sensitivity Report

Think-pair-share: Stratton – Sensitivity Analysis • What is the optimal product mix? • What is the unused capacity of each resource? • An additional labor hour is available. Where should that labor hour be assigned? • An additional 8 labor hours are available. Where should these labor hours be assigned? • The material manager has found an additional 2 pounds of additive mix for $1. 20 per pound. Should he procure this additional mix?

Stratton Sensitivity Analysis • What is the optimal product mix 3 packages of Pipe 1 6 packages of Pipe 2 • What is the unused capacity Extrusion hours: 0 Packaging hours: 0 Additive mix: 4 of each resource: hours pounds

Stratton Sensitivity Analysis • An additional labor hour is available, where should that labor hour be assigned? Packaging – for every additional hour of packaging, profit increases $11 (up to a 2 hours increase)

Stratton Sensitivity Analysis • An additional 8 labor hours are available. Where should these labor hours be assigned? Need to re-run the model since 8 hours is larger than the allowable increase for both labor hour constraints.

Stratton Sensitivity Analysis • The material manager has found an additional 2 pounds of additive mix for $1. 20 per pound. Should he procure this additional mix? No, the current optimal solution does not use all of the additive mix that is available.

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