Inventory Management: Balancing Costs and Avoiding Stockouts

Posted on Feb 2, 2025 in Social Education

6-4. Storing large quantities of inventory can eliminate shortages and stockouts. On the other hand, storing large quantities of inventory can significantly increase the cost of carrying or holding inventory. Therefore, a delicate balance must be sought between increased carrying costs and shortages and stockouts. In determining how much inventory a company should have on hand to avoid shortages and stockouts, the overall objective is to minimize carrying costs and shortage or stockout costs.

6-11. The assumptions made in the production run model are the same assumptions made in the economic order quantity with the exception that the instantaneous receipt of inventory assumption is eliminated. Thus, the assumptions are that the demand is known and constant, the lead time is known and constant, quantity discounts are not allowed, ordering cost and carrying cost are the only variable costs, and stockouts and shortages can be completely eliminated.

6-12. When the daily production rate becomes very large, the production run model becomes identical to the economic quantity model. This is because the fraction d/p approaches zero as the production rate becomes very large.

6-20. d = 100,000; c_o = $10; c_h = $0.005

a.

b. Number of orders per year

Total ordering cost = 5($10) = $50 per year

c. Average inventory

Total holding cost = 10,000(0.005) = $50 per year

6-21. ROP = 8 days × (500 screws/day) = 4,000 number 6 screws

6-25. d = 500 sandals; c_o = $10

If q* = 100,

c_h = $1, which is 20% of cost.

If c_h = 10% of $5 = $0.50,

6-26. Optimal order quantity is proportional to the square root of the ordering cost.

When c_o = $10, q* = 20,000 screws

6-27.

a.

b. Average inventory

Annual holding cost

c. Number of orders per year

Annual ordering cost

d. Total cost = $187.5 + $187.5 + 2500(15) = $37,875

e. With 250 days per year, and 10 orders per year, the number of days between orders = 250/10 = 25 days.

f. ROP = d × l = (2500 units per year/250 days per year) × 2 = 20 units

6-28.

a. Daily demand = 2500/250 = 10 units per day

b.

c. 324.92/50 = 6.5 days.

Inventory sold = (10 units/day)(6.5 days) = 65 units.

d. Maximum inventory level = q(1 – d/p) = 324.92(1 – 10/ 50)= 259.94

Average inventory = 0.5(maximum inventory level) = 0.5 (259.94) = 129.97

Annual holding cost = (average inventory) c_h = 129.97 (1.48) = $192.35

e. Number of production runs = d/q =2500/324.92 = 7.694

Annual setup cost = (d/q)c_s = 7.694(25) = $192.35

f. Including the cost of production, the annual cost is $192.35 + $192.35 + 2,500(14.80) = $37,384.71

g. ROP = d × l = 10 × 0.5 = 5 units

6-29.

a. Total cost = ordering cost + holding cost + purchase cost

= 46.88 + 725 + 36,250 = $37,021.88

b. Since the lead time has changed, the ROP also changes.

ROP = d × l = (10) × 3 = 30 units

c. The lowest cost is $37,021.88, so he should order 1,000 units each time an order is placed.

6-36. d = 1,000; unit cost = $50; c_o = $40; c_h = 0.25 × unit cost

With discount, unit cost = (1 – 0.03) × $50 = $48.50

Which should be adjusted to minimum orderable quantity (i.e., 200).

Original total cost = $51,000

Discount cost

Therefore, North Manufacturing should take the discount.