Question

The office manager for the Gotham Life Insurance Company orders letterhead stationery from an office products firm in boxes of 500 sheets. The company uses 6,500 boxes per year. Annual carrying costs are $3 per box, and ordering costs are $28. The following discount price schedule is provided by the office supply company: Order Quantity (in boxes) Price per Box 200-999 $16 1000-2999 14 3000-5999 13 6000+ 12 a. Determine the optimal order quantity and the total annual inventory cost. b. Determine the optimal order quantity and total annual inventory cost for boxes of stationery if the carrying cost is 20% of the price of a box of stationery. Please put answers in the excel format.

			ORDERING	ORDERING	ORDERING	ORDERING
			EOQ	1,000	3,000	6,000
		=
Average inventory =
Annual carrying cost =
Number of orders =
Annual order cost =
Total inventory purchase cost
Total inventory cost =

Answer 1

a) Calculating optimal order quantity or EOQ :

EOQ = where A is Annual demand in units, B is ordering cost(per purchase order) and C is holding cost per unit, per year.

Where A = 6,500 boxes utilized per year

B = $28 and C = $3 per box, per year

EOQ =

   =

   =

   =348.33 i.e EOQ = 348 units

Computation of total annual inventory cost :

Particulars	Ordering	Ordering	Ordering	Ordering
	EOQ i.e 348	1,000	3,000	6,000
Average inventory	174	500	1,500	3,000
Note: This is the sum of opening stock and closing stock divided by 2. Here it is sum of order size and closing inventory is zero, divided by 2.	i.e 348/2	i.e 1000/2	i.e 3,000/2	i.e 6000/2
Annual Carrying cost(In $)	522	1,500	4,500	9,000
	i.e 174*3	i.e 500*3	i.e 1,500*3	i.e 3000*3
Number of orders	19	7	3	2
Note : Number of orders is total boxes purchased for the year, divided by ordering quantity	i.e 6500/348 = 18.68. Hence no. of orders is the next whole number i.e 19	i.e 6,500/1,000 = 6.5. Hence no. of orders is the next whole number i.e 7	i.e 6,500/3,000 = 2.17 i.e 3	i.e 6,500/6000 = 1.08 i.e 2
Annual order cost(In $)	532	196	84	56
	i.e 19*28	i.e 7*28	i.e3*28	i.e 2*28
Total Inventory Purchase cost(In $)	5,568	14,000	39,000	72,000
(No. of boxes * price per box)	i.e 348*16	i.e 1000*14	i.e 3000*13	i.e 6000*12
Total Inventory cost(In $)	6,622	15,696	43,584	81,056
(Total inventory purchase price + Annual Carrying cost + Annual order cost)	i.e 5,568 + 522 + 532	i.e 14,000+1,500+196	i.e 39,000+4,500+84	i.e 72,000+9,000+56

b) EOQ when carrying cost is 20% of price of box of stationery :

Therefore carrying cost is 20% of $16 = $3.2

EOQ =

=

=337.26 i.e 337 units

Computation of total annual inventory cost :

Particulars	Ordering	Ordering	Ordering	Ordering
	EOQ i.e 337	1,000	3,000	6,000
Average inventory	169	500	1,500	3,000
Note: This is the sum of opening stock and closing stock divided by 2. Here it is sum of order size and closing inventory is zero, divided by 2.	i.e 337/2	i.e 1000/2	i.e 3,000/2	i.e 6000/2
Annual Carrying cost(In $)	541	1,600	4,800	9,600
	i.e 169*3.2	i.e 500*3.2	i.e 1,500*3.2	i.e 3000*3.2
Number of orders	19	7	3	2
Note : Number of orders is total boxes purchased for the year, divided by ordering quantity	i.e 6500/337 = 19.29. Hence no. of orders is the next whole number i.e 20	i.e 6,500/1,000 = 6.5. Hence no. of orders is the next whole number i.e 7	i.e 6,500/3,000 = 2.17 i.e 3	i.e 6,500/6000 = 1.08 i.e 2
Annual order cost(In $)	560	196	84	56
	i.e 20*28	i.e 7*28	i.e 3*28	i.e 2*28
Total Inventory Purchase cost(In $)	5,568	14,000	39,000	72,000
(No. of boxes * price per box)	i.e 348*16	i.e 1000*14	i.e 3000*13	i.e 6000*12
Total Inventory cost(In $)	6,669	15,796	43,884	81,656
(Total inventory purchase price + Annual Carrying cost + Annual order cost)	i.e 5,568 + 560 + 541	i.e 14,000+1,600+196	i.e 39,000+4,800+84	i.e 72,000+9,600+56