Assume that the following quantity discount schedule is appropriate. If annual demand is 120 units, order costs are $20 per order, and the annual holding cost is 25% of price, what order quantity would you recommend?
Order Size Unit Cost
0 to 49 $30.00
50 to 99 $28.50
100 or more $27.00
Given
Annual demand D = 120
Ordering cost S = 20
Holding cost H = 25% of price
Range | Cost C | Holding cost H | EOQ | |
0 to 49 | 30 | =30*0.25 = 7.5 | Feasible | |
50 to 99 | 28.5 | = 28.5*0.25 = 7.125 | Not feasible | |
100 or more | 27 | = 27*0.25 = 6.75 | Not feasible |
First is Feasible because it is with in the range of 0 to 49 and and the remaining are not feasible because EOQ is not with in the range of 50 to 99 and 100 or more. So 25 is the order quantity but we are not getting more discount. So we calculate total cost at Q = 25, Q = 50 and Q = 100
Total cost = Total purchase cost + Annual holding cost + Annual ordering cost = CD + (Q/2)H + (D/Q)S
At Q = 25
Total cost = 30*120 + ( 25/2)*7.5 + (120/25)*20 = 3789.75
At Q = 50
Total cost = 28.5*120 + ( 50/2)*7.125 + (120/50)*20 = 3646.125
At Q = 100
Total cost = 27*120 + ( 100/2)*6.75 + (120/100)*20 = 3601.5
Total cost is less at Q = 100
So I recommend order quantity of 100
Assume that the following quantity discount schedule is appropriate. If annual demand is 120 units, order...
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