Linear programming

Question 1

What are limiting factors?

Answer 1

1. Materials
2. Employees (Labour)
3. Quotas (particular for products for particular customer regardless of whether in best interests
4. Time

Question 2

What does linear programming do?

Answer 2

It takes all the limiting factors and produces a ratio of production. This ratio will maximise contribution. Resources can then be allocated effectively.

Question 3

How to calculate linear programming?

Answer 3

1. Objective variable (TC) = Calculate maximum contribution (sum of contribution for each product)
2. Specify constraints
3. Put controls in place - a non negativity constraint = n > 0
4. Plot on graph to find maximum contribution
5. x axis = no of N units, y axis = no of M units
6. To find x axis you would do the total constraint (e.g. 300 labour hours) divided by Xn (X hours for each n unit) = X. Then do same for Unit M on Y axis and can plot line
7. Anything to the right of that line is not feasible. Labour hours are not available
8. Repeat for other constraints e.g. materials
9. If there is a min contract quantity, draw that as a straight line on the graph. This will narrow the feasible region
10. Lower objective line to lowest equation possible. I.e. we have 60n + 80m which can become 3n + 4m (divided by 20). Plot this line on the graph and push that line as far too the right as possible WITHIN the feasible region
11. The furthest point possible is the optimal point

Question 4

What are the limitations of linear programming?

Answer 4

1. Indivisibility of variables - can’t use half a resource. Often the answer is .5 of something for instance
2. Imperfect linear relationships e.g. costs and production. Assumes it will always be consistent i.e a machine will always be able to produce 55 products an hour
3. Only one objective function - whether to minimise costs, maximise profit etc. But you can’t combine, would have to do each linear graph again
4. Assume constant returns. Assumes you will always have a certain amount of demand for certain products
5. Complicated with many variables. Could be 100s of different factors!
6. Very time consuming adding time and cost
7. If using technology, it is still relying on the human element - they are still inputting the figures. Complex software is also very expensive

Question 5

What are the benefits of linear programming?

Answer 5

1. Can use technology to save time and costs, present more clearly and easier to record and distribute
2. Allows for identification of limiting factors
3. Can find the maximum product mix for maximum contribution
4. For multiple limitations - very unlikely to have only one!

Question 6

What are the non financial considerations of devising a product mix?

Answer 6

Ethics - where do the ingredients or materials come from? e.g. palm oil

Value of the product - some profits aren’t very profitable but are needed e.g. gluten free bread

Demand - High contribution does not mean high profit - there might not be the demand for it!

Time - perm vs temp i.e. if price of raw materials rises for a period of time. Would change prod mix in the short term

Competitors - Drive down demand. About to release a bread and the comp is about to bring out something better thereby reducing demand for our product