Question

Problem 13-14 A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.20 per stone for quantities of 600 stones or more, $8.60 per stone for orders of 400 to 599 stones, and $9.10 per stone for lesser quantities. The jewelry firm operates 111 days per year. Usage rate is 18 stones per day, and ordering costs are $49. a. If carrying costs are $3 per year for each stone, find the order quantity that will minimize total annual cost. (Do not round Intermediate calculations. Round your final answer to the nearest whole number.) Order quantity stones b. If annual carrying costs are 31 percent of unit cost, what is the optimal order size? (Do not round Intermediate calculations. Round your final answer to the nearest whole number.) Optimal order size stones c. If lead time is 4 working days, at what point should the company reorder? (Do not round Intermediate calculations. Round your final answer to the nearest whole number.) Reorder quantity stones

Answer 1

a) Order quantity of 600 minimizes total cost.

Annual demand, D = 18*111	1998
Order cost, Co	$49
Quantity	1-399	400-599	600+
Cost, C	$9.10	$8.60	$8.20
Holding cost , Cc	$3.00	$3.00	$3.00
EOQ = sqrt(2DCo/Cc)	255.48	255.48	255.48
Considered Order quantity - Q for calculation	255.00	400.00	600
	EOQ within range so Q = 255	Consider min 400 to get price discount	Consider min 600 to get price discount
Order size	1-399	400-599	600+
Product cost = D*Cost, Different Costs	$18,181.8	$17,182.8	$16,383.6
Holding cost = (Q/2) * Cc, Differenct Q as mentioned above	$382.50	$600.00	$900.00
Ordering cost = (D/Q) * Co	$383.93	$244.76	$163.17
Total cost = Sum of above 3	$18,948	$18,028	$17,447
			Lowest Cost

b) Optimal order size is still 600 stones

Annual demand, D = 18*111	1998
Order cost, Co	$49
Quantity	1-399	400-599	600+
Cost, C	$9.10	$8.60	$8.20
Holding cost , Cc = 31%*C	$2.82	$2.67	$2.54
EOQ = sqrt(2DCo/Cc)	263.46	271.01	277.54
Considered Order quantity - Q for calculation	263.00	400.00	600
	EOQ within range so Q = 263	Consider min 400 to get price discount	Consider min 600 to get price discount
Order size	1-399	400-599	600+
Product cost = D*Cost, Different Costs	$18,181.8	$17,182.8	$16,383.6
Holding cost = (Q/2) * Cc, Differenct Q as mentioned above	$370.96	$533.20	$762.60
Ordering cost = (D/Q) * Co	$372.25	$244.76	$163.17
Total cost = Sum of above 3	$18,925	$17,961	$17,309
			Lowest Cost

c) Reorder quantity = Lead-time * average demand = 4*18 = 72 stones