Inventory & MRP Practice Problems (Updated 02/24/2007 06:43 PM)

1.  MamaMia's Pizza purchases its pizza delivery boxes from a printer.  MamaMia's delivers an average of 200 pizzas monthly.  Boxes cost 20 cents each, and each order costs $10 to process.  Because of limited storage space, the manager wants to charge inventory holding at 30 percent of cost.  The lead time to obtain boxes from the printer is one week, and the restaurant is open 360 days per year.  Determine the economic order quantity, reorder point, number of order per year, and total annual cost.  If the printer raises cost of each box to 25 cents, how would these results change?

Solution:

Pizzas….

D = 2400 pizza/year

Co = $10/order

Ch = $0.20/unit*(0.3) = $0.06/unit

Q* = EOQ = ((2*D*Co)/Ch)^0.5 = ((2*2400*10)/0.06)^0.5 = 894 pizzas per order

Reorder point = r = 2400 pizza/year*1/360 year/day*7 days = 47 pizzas

Orders (or cycles) per year = 2400 pizza/year * 1/894 cycles/pizza = 2.7 cycles/year

Total annual inventory cost = TAC = order cost + holding cost = D*Co/Q + (Q/2)*Ch

TAC = 2400*10/894 + (894/2)*0.06 = 26.8 + 26.8 = $53.60 per year

NOTE that when TAC is calculated using Q*, annual ordering costs EQUAL annual holding costs—this is a good way to verify that you’ve done the math right.

It’s up to you to redo for $0.25/pizza unit cost. What happens when unit costs increase??

2. The XYZ Company purchases a component used in the production of automobile generators directly from the supplier.  XYZ's generator production, which is operated at a constant rate, will require 1,200 components per month throughout the year.  Assume ordering costs are $25 per order, unit cost is $2.00 per component, and annual inventory holding costs are charged at 20 percent.  The company operates 250 days per year, and the lead time is five days.

a) Compute the EOQ, total annual inventory holding and ordering costs, and the reorder point.

b) Suppose XYZ's managers like the operational efficiency of ordering in quantities of 1,200 units and ordering once per month.  How much more expensive would this policy be than your EOQ recommendation?  Would you recommend in favor of the 1,200 unit order quantity?  Explain.  What would the reorder point be if the 1,200 unit quantity was acceptable?

Solution:

Note that this is a realistic scenario!

a) First compute the "ideal" ordering quantity—the EOQ

Q* = ((2*14400*25)/(0.2*2))^0.5 = 1342 units

Reorder at r = 14400*5/250 = 288 units

TAC = 14400*25/1342 + (1342/2)*0.2*2 = 268 + 268 = $536

b) Now, check the TAC of chosen policy of Q = 1200 units per order

TAC = 14400*25/1200 + (1200/2)*0.2*2 = 300 + 240 = $540

As expected, chosen policy is more expensive than EOQ policy—but not by much. In real life, the chosen policy may be practically acceptable.

3.  Tele-Reco is a new specialty store that sells television sets, videotape recorders, video games, and other television-related products.  A new Japanese-manufactured videotape recorder costs Tele-Reco $600 per unit.  Tele-Reco's inventory carrying cost is figured at an annual rate of 22 percent.  Ordering costs are estimated at $70 per order.

a) If demand for the new videotape recorder is expected to be constant at a rate of 20 units per month, what is the recommended order quantity for the VCR?

b) What are the estimated annual inventory holding and ordering costs associated with this product?

c) How many orders will be placed per year?

d) With 250 working days per year, what is the cycle time for this product?

Solution:

a) How many VCRs to order?

D = 20*12 = 240 per year

Q* = ((2*240*70)/(0.22*600)^0.5 = 16 units

b) Annual order cost = 240*70/16 = $1053 Annual holding cost = (16/2)*0.22*600 = 1053

c) D/Q = 240/16 = 15 orders per year

d) Q/D = 250*16/240 = 16.6 days 

4. Given the parts list in Table 1, draw the bill of materials.

Table 1: Parts List

Solution:

Bill of Materials (a.k.a. "Product Tree):

Remember that each level of hierarchy portrays how many units go into ONE unit of the next level up. How many H’s go into one end item??

5.  The parts used in the manufacture of a toy car are shown in Figure 1.  Five hundred toy cars are needed by week 12.  Current inventory levels and lead times are shown in Table 2.

Figure 1: Toy Car Bill of Materials

Table 2: Toy Car Inventories and Lead Times

Solution:

An MRP table helps us determine how many to order, and when to place the order to ensure parts arrive in time for assembly.