Question

Compare the optimum delivery quantities for, (a) a policy in which stock-out is permitted, (b) A policy in which stock out must not occur; demand = 650 per month, cost of holding =$ 5 per annum, setup cost = $1250 cost of stock-out = $2 per item per month. What is the maximum setup cost can be accepted under policy (b) if the total cost per month associated with this policy is not exceeded the total cost per month of policy (a).

Answer 1

(a) a policy in which stock-out is permitted

Annual demand, D	7800	units
Holding cost, Ch	$5	per year
Setup cost, Co	$1,250
Stockout cost, Cb	$24	per year
Optimal Order Qty, Q	2,171	= SQRT((2DCo/Ch)*(Ch+Cb)/Cb)
Maximum Backorder units, S	374	= QCh/(Ch+Cb)
Average Inventory level, V/2	743	= (Q-S)^2/2Q
Number of orders	4	= D/Q
Number of backorders	32	= S^2/2Q
Total Cost	$ 8,983	= (V/2)*Ch + (D/Q)*Co + (S^2/2Q)*Cb

(b) a policy in which stockout must not occur

Q = SQRT(2DS/H) = SQRT(2*7800*1250/5) = 1975

Total annual cost of this policy = (D/Q)*S + (Q/2)*H = (7800/1975)*1250 + (1975/2)*5 = $ 9,874

Total cost of policy b is higher by = 9874 - 8983 = $ 891

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Using goal seek function, in excel, maximum setup cost = $ 1034.5