Posted: November 4th, 2015

1.    A large bakery buys flour in 25 kg bags. The bakery uses an average of 4,860 bags a year. Preparing an order, receiving the shipment, and paying the invoice costs \$10 per order. Annual holding cost is \$5 per flour bag.
a.    Determine the economic order quantity. 2p
b.    What is the average number of bags on hand (i.e., average cycle inventory) if EOQ is used? 1p
c.    How many orders per year will there be if EOQ is used? 1p
d.    Calculate the total annual cost of ordering and holding flour for EOQ. 2p
e.    If ordering cost were to increase by 50 percent per order, by what percentage would the EOQ change? 2p

2.    A fresh produce distributor uses 800 nonreturnable packing crates a month, which it purchases at a cost of \$5 each. The manager has assigned an annual holding cost of 25 percent of the purchase price per crate. Ordering cost is \$28 per order. Currently the manager orders 800 crates at a time. How much could the firm save annually in ordering and holding costs by using the EOQ?  7p

3.    The manager of a car wash has received a revised price list from the vendor of the liquid soap, and a promise of a shorter lead time for deliveries. Formerly the lead time was four days, but now the vendor promises a reduction of 25 percent in that time (i.e., new lead time is 3 days). Annual usage of soap is 4,500 litres. The car wash is open 360 days a year. Assume that daily usage of soap is Normal, and that it has a standard deviation of two litres per day. The ordering cost is \$10 per order and annual holding cost rate is 40 percent of unit cost. The revised price list is shown below.

a.    What order quantity is optimal? 8p
b.    What ROP is appropriate if the acceptable risk of a stock-out is 1.5 percent? 2p

4.    Given the following information:
Expected demand during a lead time = 300 units
Standard deviation of demand during a lead time = 30 units
Demand during a lead time is Normally distributed
a.    Determine the safety stock needed to attain a 1 percent risk of stock-out during a lead time.  2p
b.    Would a stock-out risk of 2 percent require more or less safety stock? Explain. 2p
5.    Experience suggests that usage of copy paper at a small copy centre can be approximated by a Normal distribution with a mean of five boxes per day and a standard deviation of one-half box per day. Two days are required to fill an order for paper. Ordering cost is \$10 per order, and annual holding cost is \$10 per box.
a.    Determine the economic order quantity, assuming 250 workdays a year. 2p
b.    If the copy center reorders when the paper on hand and on order is 12 boxes, calculate the risk of a stock-out during a lead time. 3p
c.    If a fixed-interval of seven days, instead of the EOQ/ROP, is used for reordering, what shortage risk does the copy center incur if it orders 36 boxes when the amount on hand is 12 boxes? 3p

6.    A hospital reorders size 7 surgical gloves when the supply on hand and on order falls to 18 units (pairs). Lead time for resupply is three days. Given the typical usage over the last 10 days below, what service level is achieved with the hospital’s reorder policy? 6p

7.    A stockroom manager must set up inventory ordering procedures for two new items, P34 and P35. P34 can be ordered at any time, but P35 can be ordered only once every four weeks. The company operates 50 weeks a year, and the weekly usage rate for each item is normally distributed. The manager has gathered the following information about the items:

a.    At what inventory level should the manager reorder P34? 3p
b.    Calculate the economic order quantity for P34. 2p
c.    Calculate the order quantity for P35 if 110 units are on hand at the time the order is placed. 4p

8.    Calculate the total cost for each of the following aggregate plans using these unit costs:

Regular output = \$40
Overtime = \$50
Subcontract = \$60

Inventory per month = \$10

a.    7p

b.    7p

c.    (Refer to part b.) After complaints from some workers about working overtime every month during the first half of the year, the manager is now considering adding some temporary workers for the second half of the year, which would increase regular output to a steady 350 units a month, not using any overtime, and using subcontracting to make up the shortage. Determine the total cost of this plan. 7p
9.
a.    Given the following forecasts and steady regular output of 550 every month, what total cost would result if overtime is limited to a maximum of 40 units a month, and subcontracting is limited to a maximum of 10 units a month? Unit costs are:  7p
Regular output = \$20         Back order per month = \$18
Overtime = \$30
Subcontract = \$25
Inventory per month = \$10

b.    Suppose back orders are not allowed. Modify your plan from part a to accommodate this as economically as possible. The limits on overtime and subcontracting remain the same. 7p

10.    A small distiller produces whiskey. The salesperson has developed the following forecasts for demand (in cases) for the next six months.

Use the following information:

Develop the minimum cost plan using level output/workforce, supplemented with each of the following, and compute the total cost for each plan. Which plan has lower total cost?

a.    Use overtime (up to 1,000 cases per month). Hint: Use OT in a three-month period. 8p
b.    Use a combination of overtime (500 cases per month maximum) and part-time labour (500 cases per month maximum). Hint: Use OT in a five-month period, supplemented with part-time production. 7p

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