EXTRA PROBLEMS WITH SOLUTIONS

Example 10:

The ABC Co. is planning to stock a new product. The Co. Has developed the

following information:

Annual usage = 5400 units

Cost of the product = 365 MU/unit

Ordering cost = 55 MU/order

Carrying cost = 28% /year of inventory value held.

a Determine the optimal number of units per order

b. Find the optimal number of orders/year

c. Find the annual total inventory cost

Solution:

a. X0 = √2CB/zp = √2*5400*55/365*0.28 = ~76 units/order

b. N0 = C/X0 =5400 / 76 = ~71 orders/year

c. Ke= √2CBzp = √2*5400*55*365*0.28 = 7791.46 MU/year.

Example 11:

Holding costs are 35 MU/unit/year. The ordering cost is 120 MU/order and sales

are relatively constant at 400 month.

a. What is the optimal order quantity?

b. What is the annual total inventory cost?

Solution:

a. X0 = √2CB/E= √2*(400*12)*120/35 = 181.42 units/order

b. Ke= √2CBE= √2*(400*12)*120*35 = 6349.80 MU/year

Example 12:

Azim furniture company handles several lines of furniture, one of which is the

popular Layback Model TT chair. The manager, Mr. Farmerson, has decided to

determine by use of the EOQ model the best quantity to obtain in each order. Mr.

Farmerson has determined from past invoices that he has sold about 200 chair during

each of the past five years at a fairly uniform rate and he expects to continue at that rate.

He has estimated that preparation of an order and other variable costs associated with

each order are about 10 MU, and it costs him about 1.5 % per month (or 18% per year) to

hold items in stock. His cost for the chair is 87 MU.

a. How many layback chairs should be ordered each time?

b. How many orders would there be?

c. Determine the approximate lenght of a supply order in days?

d. Calculate the minimum total inventory cost

e. Show and verify that the annual holding cost is equal to the annual ordering cost

(due to rounding, show these costs are approximately equal)

Solution:

a. X0 = √2CB/Zp = √2*200*10 /0.18*87 = 15.98 =~16 chairs/order

b. N0 = C/X0 =200 /16= 12.5 orders/year

c. t0 = X0/C * 365 = 16 /200 *365 = 29.2 days

d. Ke= √2CBZp = √2*200*10*0.18*87 = 250.28 MU/year

e. N0 *B = 12.5 * 10 = 125 MU

X0/2*Zp = 15.98/2 * 0.18*87 = 125.1 MU

Example 13:

A. Leyla Tas has determined that the annual demand for #6 screws is 100000

screws. Leyla, estimates that it costs 10 MU every time when an order is placed. This

cost includes wages, the cost of the forms used in placing the order and so on.

Furthermore, she estimates that the cost of carrying are screw in inventory for a year is

one-half of 0.01 MU. Assume that the demand is constant throughout the year.

a. How many #6 screws should Leyla order at a time to minimize total inventory

cost?

b. How many orders per year would be placed? What would the annual ordering cost

be?

c. What would the average inventory be? What would the annual holding cost be?

Solution:

a. E= 0.01/2 = 0.005

X0 = √2CB/E

X0 = √2*100000*10 / 0.005 = 20000 screws/order

b. N0 = C/X0 = 100000/20000= 5 orders/year

Total ordering cost = N*B = 5*10 = 50 MU/year

c. Average inventory = x/2 = 20000/2 = 10000 units

Total holding cost = x/2*E= 10000 * 0.005 = 50 MU/year

B. It takes approximately 8 working days for an order of #6 screws to arrive once

the order has been placed. The demand is fairly constant, and on the average the store

sells 500 screws each day. What is the ROP?

Solution:

ROP = Ro= use rate * lead time = c*tlt = 500 screws/day * 8 days = 4 000 screws.

C. The manager believes that Leyla places too many orders for screws /year. He

believes that an order should be placed only twice/year. If Leyla follows her manager`s

policy, how much more would this cost every year over the ordering policy that she

developed, if only two orders were placed each year, what effect would this have on the

ROP?

Solution:

Twice a year = Ke= NB + X/2*E = 2*10 + 50000/2*0.005 = 20 + 125 = 145

5 times a year = Ke= √2CBE = √2*100000*10*0.005 = 100 MU

Extra cost for manager’s offer = 45 MU

No effect on ROP.

Example 14:

Ahmet Uslu experiences an annual demand of 220 000 MU for pro quality tennis

balls at the İzmir Tennis Supply Company. It cost Ahmet 30 MU to place an order and

his carrying cost is 18%. How many orders per year should Ahmet place for the balls?

Solution:

Example 15:

Ayşe Çalışkan,owner of Computer Village, needs to determine an optimal

ordering policy for Porto-Pro computers,annual demand for the computers is 28 000 MU

and carrying cost is 23 percent. Ayşe has estimated order costs to be 48 MU per order.

What are the optimal MU per order?

Solution:

Example 16:

EMU uses 96 000 MU annually of a particular reagent in the chemistry

department of the EMU estimates the ordering cost at 45 MU and thinks that the

university can hold this type of inventory at an annual storage cost of 22% of the

purchase price. How many months’ supply should the purchasing department order at on

time to minimize total annual cost of inventory?

Solution:

Example 17:

The ABC co.is planning to stock new product. The ABC co.has developed the

following information:

Annual usage = 5400 units

Cost of the product = 365 MU/unit

Ordering cost = 55 MU/order

Carrying cost = 28%/year of inventory value held

a) Determine the optimal number of units per order?

b) Find the optimal number of orders/year?

c) Find the annual total inventory cost?

Solution:

Example 18:

A local artisan uses supplies purchased from an overseas supplier. The owner

believes the assumptions of the EOQ model are met reasonably well. Minimization of

inventory cost is her objective. Relevant data, from the files of the credit firm, are annual

demand (C) = 240 units, ordering cost (B) = 42 MU/order, and holding cost = 4

MU/unit/year.

a) How many should she order at one time?

b) How many times per year will she replenish its inventory of this material?

c) What will be the total inventory costs associated with this material?

d) If she discovered that the carrying cost has been overstated, and was in reality

only 1 MU/unit-year, what is the corrected value of EOQ?

Solution:

a)

b)

c)

d)

Example 19:

Ground Coffee shop uses 3 kgs of a specialty tea weekly; each kg. costs 16 MU.

Carrying costs are 2 MU/kg/week because space is very scarce. It costs the firm 7 MU to

prepare an order. Assume the basic EOQ model with no shortages applies. Assume 52

weeks/year.

a) How many kgs should Ground to order at a time?

b) What is total annual inventory cost?

c) How many orders should ground place annually?

d) How many days will there be between orders(assume 310 operating days)?

Solution:

a)

b)

c)

d)

Example 20:

Holding costs are 35 MU/unit/year. The ordering cost is 120 MU/order, and

sales are reletively constant at 400/month.

a) What is the optimal order quantity?

b) What is the annual total inventory cost?

Solution:

Example 21:

ABC, a company that sells pump housings to other manufacturers, would like to

reduce its inventory cost by determining the optimal number of pump housings to obtain

per order. The annual demand is 1 000 units, the ordering cost is 10 MU/order, and the

average carrying cost per unit per year is 0.50 MU. Calculate EOQ .(i.e.the optimal

number of units per order).

Solution:

Example 22:

Lemar Supermarket sells about 200 000 kilos of milk annually. The milk is

purchased for 4 MU/kg. Holding costs are 1.40 MU/kg/yr. Each order costs 35 MU. If the

shelf life of the milk is only 5 days, how many kilos should be ordered at a time.

Solution:

With an EOQ of 3 162.28 kilos an order must be placed every 5.77 days. But the

shelf life is 5 days so some milk will start to go sour. Therefore

should be ordered every 5 days.

Example 23:

A building materials stockist obtains its cement from a single supplier. Demand

for cement is reasonably constant throughout the year. Last year the company sold 2 000

tonnes of cement. It estimates the costs of placing an order at around 25 MU each time

an order is placed and charges inventory holding at 20% of purchase cost. The company

purchases cement at 60 MU per tonne.

a) How much cement should the company order at a time?

b) Instead of ordering EOQ, why not a order convenient 100 tonnes?

Solution:

a) EOQ for cement

b) Total cost of ordering plan for

or we can calculate by

Total cost of ordering plan for

Result:

The extra cost of ordering 100 tonnes at a time is 1 100 MU-1095.454 MU= 4.55

MU. The production/operations manager therefore should feel confident in using the

more convenient order quantity.

Example 24:

# 2 pencils at the EMU bookstore are sold at a fairly steady rate of 60 per week.

The pencil cost the bookstore 0.02 MU each and sell for 0.15 MU each. It costs the

bookstore 12 MU to initiate an order and holding costs are based on an annual interet

rate of 25%. Determine the optimal number of pencils for the bookstore to purchase and

the time between placement of orders. What are the holding and setup costs for this item?

Solution:

Example 25:

A wholesaler has a steady demand for 50 items of a given product each month.

The purchase cost of each item is 6 MU and the holding cost for this item is estimated to

be 20% of the stock value per annum. Every order placed by the wholesaler cost 10 MU

in administration charges regardless of the number ordered?

Solution:

C = annual demand = 50x12 = 600 items

p = price unit = 6 MU

B = order cost = 10 MU

E = holding cost of one item per year = Zp= 0.20x6

An order size of 100 is used at an order frequency of

Example 26:

C = Demand/week = 400 unit.

P =Purchase price = 3 MU/unit

E = Holding cost = 2 MU/100 items/week

B = Order cost =12 MU/order

Solution:

An order size of 693 items is recommended

Example 27:

TT Beverage Co. is a distributor of beer, wine and soft drinks product. From a

main warehouse located in Magusa, TRNC, TT supplies nearly 1000 retail stores with

beverage products. The beer inventory, which constitutes about 40% of the company’s

total inventory, averages approximately 50 000 cases. With an average cost per case of

approximately 8MU, TT estimates the value of its beer inventory to be 400 000 MU.

The warehouse manager has decided to do a detailed study of inventory costs

associated with Sergio Beer, the # 1 selling TT beer. The purpose of the study is to

establish the “how-much to order,” and “when to order” decisions for Segio Beer that

will result in the lowest possible cost.

The manager found that the demand is constant and 2 000 cases/week.The cost of

holding for the TT beer inventory is 25% of the value of the inventory.

(Note that definding the holding cost as a % of the value of the product is

convenient, because it is easily transferable to other products)

TT is paying 32 MU/order regardless of the quantity requested in the order.

Suppose TT is open 5 days each week, and the manufacturer of Sergio Beer guarantees

2-day delivery on any order placed.

a) Find Economic Order Quantity.

b) Find reorder point.

c) How frequently theorder will be placed?

d) Find the cycle time?

e) Calculate minimum total inventory cost.

Solution:

a) Find EOQ

The use of an order quantity of 1824 cases will yield the minimum-cost inventory

policy for TT beer.

b) Find the reorder point

c) How frequently the order will be placed?

d) Find the cycle time.

The cycle time is 4.6 working days.

e) Calculate minimum total inventory cost.