Chapter 12 - Linear programming Flashcards
When are linear programming techniques used?
if faced with 2+ limiting factors
What does linear programming involve?
Construction of a mathematical model to represent the decisions problem
What are the steps of linear programming?
- Define variables
- State objective function
- State constraints
- Draw graph
- Find optimal solution
What does the objective function express?
Total contribution made from 2 products
How are constraints displayed?
As equations
What does an iso-contribution line show?
All combinations of x and y that provide the same total value for the objective function
What is the aim of the minimisation problem?
Find a total cost line touching the feasible polygon at a tangent as close to the origin as possible
What are binding constraints?
Max availability of the resource related to those constraints being used
Resource being used = resource available
What are non-binding constraints?
Constraints not fully used at the optimal solution point
Resource being used > resource available
What is slack?
Amount of a resource that’s under-utilised when the optimum plan is implemented
Why is slack important?
Beacuse unused resources can be put to another use
What is slack when the constraint is binding?
0, known as a scarce resource
What is the shadow price?
Max premium on price that the organisation would pay for the extra resource
How are shadow prices for a critical constraint calculated?
- Take the equations of the lines that intersect at the optimal point, +1 unit and leave critical constraint unchanged
- Use simultaneous equations to derive new optimal solution
- Calc revised optimal contribution and compare to original
- Increase from original is the shadow price
What are the limitations of linear programming?
- Linear relationship must exist
- Assumes single quantifiable objective
- Too complex to solve manually when there are lots of variables
- Assumes variables are completely divisible
- Assumes static situation
- Assumes short-term scenario
What are the advantages of using spreadsheets?
- Easy to use
- Quick data processing
- Reduce errors
- Quick reporting/analysis
What are the disadvantages of using spreadsheets?
- Sharing violations
- Unable to identify input errors
What type of non-financial data will be relevant to choosing the optimal product mix?
- Customer value placed on a product
- Competitor plans
- Length of time resource will be scarce
- Expected demand
- Ethical impacts of removing a product
What does the shadow price of labour mean?
Contribution increased by shadow price per hour for each extra hour of labour obtained
How is the shadow price calculated using contribution?
Contribution per unit/material used
What resources have a shadow price?
Only resources that meet at the optimal point
Line crosses R line
How is the iso-contribution line formulated?
Contribution of each product
Ignore fixed overhead
How can the max material be deduced from a graph?
- Where line crosses horizontal axis
- Gives R value
- R x material
Do binding constraints always have a shadow price?
Yes
