Operation management
QUESTION 1:
Exercise 1
A small firm produces two qualities of a product – Standard and De-Luxe. The contribution per unit is £100 for the Standard and £300 for the De-Luxe.
Each model requires 1 hour per unit in the machine shop and 40 machining hours are available per week. The Standard model can be assembled and finished in 2.5 hours per unit but the De-Luxe takes 10 hours per unit. There are 200 hours per week available for assembly and finishing.
Market research suggests that the maximum weekly sales of the De-Luxe model will be 18 units.
The products use a special component, of which only 1,200 are currently available per week. Each Standard unit uses 25 components and each De-Luxe unit needs 50. You are required to:
(a) analyse the current position and recommend a weekly production plan, showing the contribution.
Whilst keeping to the De-Luxe sales limit, the firm would like to maximise contribution and realises that this may mean paying more to increase the supply of some of the resources required. It is not possible to increase the machining hours but assembly hours and the number of components can be increased as follows:
Resource Additional amount above existing prices to increase supply
Assembly hours £12 extra per hour for hours above 200
Component £1 extra per component for components above 1,200
Decision Variables X1 = Quantity of product Standard to produce, X2 = Quantity of product De-Luxe to produce.
Objective function Maximise 100X1 + 300X2 (contribution)
Constraints
Subject to
Machining Hour X1 + X2 ≤ 40 hours
Assembling and Finishing 2.5X1 + 10X2 ≤ 200 hours
Components 25X1 + 50X2 ≤ 1200 components
Product De-Luxe X2 ≤ 18 units
Where X1, X2 ≥ 0 (non-negativity constraints) Plotting the contribution line
Consider the equation 100X1 + 300X2 = 1800
If X1 = 0 then X2 = 6
If X2 = 0 then X1 = 18
The red line represents the contribution line based on the above equation. A parallel line is
Exercise 1
A small firm produces two qualities of a product – Standard and De-Luxe. The contribution per unit is £100 for the Standard and £300 for the De-Luxe.
Each model requires 1 hour per unit in the machine shop and 40 machining hours are available per week. The Standard model can be assembled and finished in 2.5 hours per unit but the De-Luxe takes 10 hours per unit. There are 200 hours per week available for assembly and finishing.
Market research suggests that the maximum weekly sales of the De-Luxe model will be 18 units.
The products use a special component, of which only 1,200 are currently available per week. Each Standard unit uses 25 components and each De-Luxe unit needs 50. You are required to:
(a) analyse the current position and recommend a weekly production plan, showing the contribution.
Whilst keeping to the De-Luxe sales limit, the firm would like to maximise contribution and realises that this may mean paying more to increase the supply of some of the resources required. It is not possible to increase the machining hours but assembly hours and the number of components can be increased as follows:
Resource Additional amount above existing prices to increase supply
Assembly hours £12 extra per hour for hours above 200
Component £1 extra per component for components above 1,200
Decision Variables X1 = Quantity of product Standard to produce, X2 = Quantity of product De-Luxe to produce.
Objective function Maximise 100X1 + 300X2 (contribution)
Constraints
Subject to
Machining Hour X1 + X2 ≤ 40 hours
Assembling and Finishing 2.5X1 + 10X2 ≤ 200 hours
Components 25X1 + 50X2 ≤ 1200 components
Product De-Luxe X2 ≤ 18 units
Where X1, X2 ≥ 0 (non-negativity constraints) Plotting the contribution line
Consider the equation 100X1 + 300X2 = 1800
If X1 = 0 then X2 = 6
If X2 = 0 then X1 = 18
The red line represents the contribution line based on the above equation. A parallel line is