Week 7

• All businesses and other organisations operate within constraints.
• Where just one limiting factor exists (analytical solution – ie we can calculate it)
• Where multiple limiting factors exist (graphical solution – ie we can draw it)
• When capacity constraints exist:

  1.Identify the limiting factor (scarce resource)

  2.Calculate the unit contribution for each product

  3.Note the number of units (kg., hours, litres…) each product uses of the scarce resource

  4.Divide contribution by usage to find out how you get the most contribution for the scarce resource

  5.Prioritise (most contribution per unit of scarce resource)6.Schedule production
• For multiple limiting factors (constraints) we need to use a quantitative technique called linear programming
• For two products and multiple constraints, a graphical solution is possible (this is what you need to be able to do)
• The same logic applies to multiple products and multiple constraints but we can’t solve it graphically and have to rely on computer software (we won’t do this but you need to be aware that it exists) – the problem is that we need more than two dimensional graph paper in this case!
• The same logic applies to multiple products and multiple constraints but we can’t solve it graphically and have to rely on computer software (we won’t do this but you need to be aware that it exists) – the problem is that we need more than two dimensional graph paper in this case!
• How to solve multiple limiting factors problems

  1. Formulate the problem algebraically, i.e. formulate the objective function  based on the contribution (that’s what you’re trying to maximise) and the input constraints (the limiting factors)
• How to solve multiple limiting factors problems

  2. Enter all input constraints into a graph. The solution lies in the area that is overlapped by all input constraints.
• How to solve multiple limiting factors problems

  3 Draw an objective function line. Extend it to the right until it touches the last corner of the solution area. This is the optimal solution, as it gives the biggest value of what you’re trying to maximise -  the contribution.
• How to solve multiple limiting factors problems

  4 Determine the exact optimum output by solving the simultaneous equations for the constraints at the optimal point.
• It is often possible to lift constraints by acquiring additional resources at a higher price
• Need to establish the change in contribution from obtaining one additional unit of resource (= shadow price)
• Companies often find their activities constrained in the short term
• They have to decide on the optimal production plan that will maximise contribution
• If a single limiting factor exists, we need to establish the contribution per scarce resource and prioritise products that make the best use of the scarce resource
• If we have multiple limiting factors and two products, a graphical solution is possible.
• We can use the shadow price to establish how much a company should pay to obtain additional resources