Job Shop Layout n n Objective function = minimise ∑ ∑ Aij Dij Cij for all i≠j
i=1 j=1 Where:
Aij = the activity level from department i to department j; i=1,…,n and j=1,…,n, where n is the number of departments
Dij = distance from department i to department j
Cij = the cost per unit distance from department i to department j
Make or Buy Decisions Test 1. Cost Difference Cost Difference = (make - buy-in) = [(VC x Q) + FC]-[(P x Q)]
Test 2. Break-even Quantity The breakeven quantity (QB/E) is:
QB/E = FC (P - VC)
Where:
VC = Variable cost/unit if produced within the company
P = Purchase price per unit if purchased from a supplier
FC = Fixed costs associated with producing the part or item within the company
Q = Quantity produced or required (i.e. the volume)
Total cost of production = (VC x Q) + FC
Total cost of buying in = (P x Q)
Location Models Centre of Gravity Method: To determine the coordinates of the optimum location, the following equations are used:
and
Where: = quantity to be transported to destination i
= x coordinate of destination i
= y coordinate of destination i
= x coordinate of centre of gravity
= y coordinate of centre of gravity
Cost-Volume Analysis Location Model Linear equation: y = mx + c
i.e. Total Cost = (Variable cost x number of units) + Fixed costs
Profit = Sales – Total Cost
Crossover points:
y1 = m1x + c1 Eqn 1
y2 = m2x + c2 Eqn 2
Where:
m = variable cost;
c = fixed cost;
x = quantity Q (note x can be replaced by Q)
Crossover point of two linear equations is where y1 = y2, that is:
m1x + c1 = m2x + c2 Substituting for x with Q gives:
m1Q + c1 = m2Q + c2 Solving for Q at the crossover point gives:
m1Q - m2Q = c2 - c1 Q (m1-m2) = c2 - c1 Q = (c2 - c1)/(m1 – m2)
