Question

A retailer purchases a certain type of chemical from a supplier on the following quantity discount schedule: • If the order amount is less than 100 kg.s, the supplier charges $30 per kg. • If the order amount is at least 100 kg.s and less than 500 kg.s, the supplier applies an incremental discount where the first 100 kg. costs $30 per kg. and the remaining amount costs $28 per kg. • If the order amount is at least 500 kg.s, the supplier applies an all-units discount and charges $28 per kg. for all units. The ordering cost is $100 per order and the retail owner assumes an annual holding cost based on the annual inflation rate which is 25%. The annual demand of this chemical to retailer is 800 kg.s and the demand rate stays constant in the planning horizon. Back-ordering is disallowed and both the retailer and the supplier works for 365 days in a year. Find the economic order quantity and the order cycle time (in days) that minimizes the total inventory cost. Calculate the minimum total annual inventory cost. Carry out the whole analysis and show all of your calculations. **how is the total cost calculated?**

Answer 1

<100	30
100-499	28	slab
>=500	28	all
O=Ordering cost	100
A=Annual Demand	800Kgs
C=Holding cost	25%	Price	30	7.50
			28	7.00
Case 1 Cost = 30
EOQ=√2AO/C	=√2(800)(100)/7.5
	146.0593
Case 2: Cost = 28
EOQ=√2AO/C	=√2(800)(100)/7
	151.1858
Assume order qty of 152
Total cost
No of orders	5.263158	800/152
Ordering Cost	526.3158	5*100
Carrying cost	556.75
For 1st 99 qty	371.25	99/2*7.5
For rest of the qty	185.5	(152-99)/2*7
Total cost	1083.066
Assume order qty of 155
Total cost
No of orders	5.16129	800/155
Ordering Cost	516.129	5*100
Carrying cost	567.25
For 1st 99 qty	371.25	99/2*7.5
For rest of the qty	196	(155-99)/2*7
Total cost	1083.379
Assume order qty of 150
Total cost
No of orders	5.333333	800/150
Ordering Cost	533.3333	5*100
Carrying cost	549.75
For 1st 99 qty	371.25	99/2*7.5
For rest of the qty	178.5	(150-99)/2*7
Total cost	1083.083
Assume order qty of 140
Total cost
No of orders	5.714286	800/140
Ordering Cost	571.4286	5*100
Carrying cost	514.75
For 1st 99 qty	371.25	99/2*7.5
For rest of the qty	143.5	(140-99)/2*7
Total cost	1086.179
Assume order qty of 160
Total cost
No of orders	5	800/160
Ordering Cost	500	5*100
Carrying cost	584.75
For 1st 99 qty	371.25	99/2*7.5
For rest of the qty	213.5	(160-99)/2*7
Total cost	1084.75

Based on the above Trail method, EOQ is 152 kgs.