3. Cat Lovers Inc. (CLI) is a distributor of a popular blend of cat food that se
ID: 364582 • Letter: 3
Question
3. Cat Lovers Inc. (CLI) is a distributor of a popular blend of cat food that sells $1.25 per can.
CLI sells 500 cans per week. It orders cans of cat food from Nutrious & Delicious (N&D), a
major supplier of pet foods. N&D sells cans to CLI at $0.5 per can and charges a flat fee of $20
per order for shipping and handling. CLI’s annual inventory holding cost rate is 25%. Currently,
the lead-time for an order is 6 weeks.
(6 points)
a) Find the optimal order quantity, the reorder point and the annual total cost associate
with it for CLI. On average, how many weeks of demand of this can food does CLI
hold in inventory under this policy?
(6 points)
b) If CLI is restricted to ordering in tier quantities where a tier has 20 cases and a case
has 96 cans, what is CLI’s optimal order quantity in tiers, reorder point and the
average annual total cost? (Hint: while order quantity is restricted to tiers, reorder
point should be in cans)
(13 points)
c) Suppose N&D offers two types of quantity discount plans in addition to $0.5 per can
plan. One is an all units discount that is based on order intervals (T), which is the
time between two orders placed by CLI, and the other one is an incremental quantity
discount. Below are the two quantity discount plans available to CLI:
All units order interval discount:
Order Interval(weeks)/Unit Cost (c)per Can
0<T< 6 0.5
6T<20 0.49
20T 0.48
Incremental quantity discount:Quantity Ordered(Cans)/Unit Cost (c)per Can
0<Q 3000 0.5
3000<Q5000 0.49
5000<Q10, 000 0.48
10,000<Q 0.47
Find the optimal order quantity, the reorder point and the total costs associated with these two
plans and identify the plan with the minimum total cost. Recall that order lead-time is 6 weeks
as before, irrespective of the discount plan.
Explanation / Answer
Weekly demand, d = 500
Annual demand, D = 500*52 = 26000
Ordering cost, K = 20
Item cost, C = 0.5
Holding cost, H = 0.5*25% = 0.125
Lead time, L = 6 weeks
a) Optimal order quantity, EOQ = (2DK/H) = (2*26000*20/0.125) = 2884
Reorder point, R = d*L = 500*6 = 3000
Total annual cost = (D/Q)*K + (Q/2)*H + D*C = (26000/2884)*20 + (2884/2)*0.125 + 26000*0.5 = $ 13,361
Average weeks of inventory = (Q/2)/d = (2884/2)/500 = 2.9 weeks
b) Number of cans in a tier = 20*96 = 1920 cans
Annual demand in tiers = 26000/1920 = 13.54
Annual Holding cost per tier = 1920*0.125 = 240
Optimal order quantity = (2*13.54*20/240) = 1.5 ~ 2 tiers
Reorder point is same as before = d*L = 3000 cans
(c)
(1) All units order interval discount:
i) With EOQ, order interval = 2884/500 = 5.8 weeks. Therefore, applicable price is 0.5
Total cost for EOQ policy = $ 13,361 (as determined in part (a)
ii) Order qty for order interval of 6 weeks = 6*500 = 3000
Total cost for 6 weeks order interval policy = (26000/3000)*20 + (3000/2)*0.49*0.25 + 26000*0.49 = $ 13,097
iii) Order qty for order interval of 20 weeks = 20*500 = 10000
Total cost for 20 weeks order interval policy = (26000/10000)*20 + (10000/2)*0.48*0.25 + 26000*0.48 = $ 13,132
The minimum cost is of 6 weeks order interval policy. Therefore, optimal order quantity = 3000 cans
Total annual cost = $ 13,097
(2) Incremental quantity discount:
i) With EOQ, applicable price is 0.5
Total cost for EOQ policy = $ 13,361 (as determined in part (a)
ii) Order qty =3001
Total cost for Q=3001 policy = (26000/3001)*20 + (3001/2)*0.49*0.25 + 26000*0.49 = $ 13,097
iii) Order qty =5001
Total cost for Q=5001 policy = (26000/5001)*20 + (5001/2)*0.48*0.25 + 26000*0.48 = $ 12,884
iii) Order qty =10001
Total cost for Q=10001 policy = (26000/10001)*20 + (10001/2)*0.47*0.25 + 26000*0.47 = $ 12,860
The minimum cost is of Q=10001 order policy. Therefore, optimal order quantity = 10001 cans
Total annual cost = $ 13,860
Reorder point is same as determined in part (a) in all the cases.
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