Homework for Chapter 12
12-1.
12-6.
12-21.
12-25.
Hayes Electronics stocks and sells a particular brand of microcomputer. It costs the firm $450 each time it
places an order with the manufacturer fir the microcomputers. The cost of carrying one microcomputer in
inventory for a year is $170. The store manager estimates that total annual demand for the computers will be
1,200 units, with a constant demand rate throughout the year. Orders are received within minutes after
placement from a local warehouse maintained by the manufacturer. The store policy is never to have stockouts
of the microcomputers. The store is open for business every day of the year except Christmas Day. Determine
the following:
a. Optimal order quantity per order
b. Minimum total annual inventory costs
c. The number of orders per year
d. The time between orders (in working days)
The Simple Simon Bakery produces fruit pies for freezing and subsequent sale. The bakery, which operates 5
days a week, 52 weeks a year, can produce pies at a rate of 64 pies per day. The bakery sets up the pieproduction operation and produces until a predetermined number (Q) have been produced. When not
producing pies, the bakery uses its personnel and facilities for producing other bakery items. The setup cost
for a production run of fruit pies is $500. The cost of holding frozen pies in storage is $5 per pie per year. The
annual demand for frozen fruit pies, which is constant over time, is 5,000 pies. Determine the following:
a. The optimum production run quantity (Q)
b. Total annual inventory costs
c. The optimum number of production runs per year
d. The optimum cycle time (time between run starts)
e. The run length in working days
The office manager for the Gotham Life Insurance Company orders letterhead stationary 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: Determine the optimal order quantity and the total annual inventory costs.
Order Quantity (Boxes)
Price per Box
200-999
$16
1,000-2,999
$14
3,000-5,999
$13
6,000+
$12
The amount of denim used daily by The Western Jeans Company in its manufacturing process to make jeans is
normally distributed with an average of 3,000 yards of denim and a standard deviation of 600 yards. The lead
time required to receive an order of denim from the textile mill is a constant 6 days. Determine the safety
stock and reorder point if The Western Jeans Company wants to limit the probability of stockout and work
stoppage to 5 percent.
Answers for Chapter 12 Homework
12-1.
12-6.
12-21.
12-25.
Co = $450
Cc = $170/unit/yr
D = 1,200 units/yr
a.) Qopt = SQRT(2(450)(1200)/170) = 79.7 units
b.) TC = (450)(1200)/79.7 + 170(79.7)/2 = $13,550 per year
c.) D/Q = 1200/79.7 = 15.06 orders/yr
d.) Days/orders = 364/15.06 = 24.17 working days
operating days = 5(52) = 260 working days
p = 64 pies/day D = 5000 pies/yr
d = D/days = 5000/260 = 19.23 pies/day
Co = $500/run
Cc = $5/pie/yr
a.) Qopt = SQRT(2(500)(5000)/5/(1-19.23/64)) = 1,195.6 pies
b.) TC = 500(5000)/1195.6 + 5(1195.6)(1-19.23/64)/2 = $4,182/yr
c.) D/Q = 5000/1195.6 = 4.18 runs/yr
d.) Cycle Time = Q/d = 1195.6/19.23 = 62.17 working days
e.) Q/p = 1195.6/64 = 18.68 working days/run
D = 6500 boxes/yr
Co = $28/order Cc = $3/box/yr
Qopt = SQRT(2(28)(6500)/3) = 348 boxes
Q = 348 boxes, TC = $105,045
Q = 1000 boxes, TC = $92,682
Q = 3000 boxes, TC = $89,061
Q = 6000 boxes, TC = $87,030
Choose Q = 6000 boxes, with an annual total cost of $87,030.
d-bar = 3000 yrds/day
d = 600 yrds
L = 6 days
R = 3000(6) + 1.645(600)(6)1/2 = 20,418 yrds
Safety stock = 1.645(600)(6)1/2 = 2,418 yrds