Test 1 Review Problems and Solutions
A. Computational Questions
(i) Review computational examples in the lecture notes.
(ii) Study end-of-chapter problems in the textbook.
(iii) Study questions from the old exams.
Note on rounding:
General rule #1: In most cases, just use normal rounding. For example, 32.15 should be
rounded down to 32 if the final answer has to be an integer (e.g., order quantity). This
works for EOQ, EPQ and forecasting.
General rule #2: For all intermediate calculations, use the decimal numbers (2 or 3
decimal places will suffice). For example, one question asks you to calculate EOQ and
the total cost. Lets say that EOQ = 32.15. Then 32.15 will be rounded down to 32 in
your final statement of what the order quantity is. In order to calculate the total cost,
however, use 32.15 in the TC formula.
Exception: For example, EOQ = 32.15 and rounded down to 32. Lets say that the annual
demand is 1000. Based on these numbers, the number of orders = D/Q = 1000/32.15 =
31.1. Now, in the final statement, the optimal order quantity is 32, and if the number of
orders is 31, then the total demand satisfied = 3132 = 992, which is less than 1000. Only
in this kind of situation, the number of orders may be rounded up to 32 from 31.1, and
state in the final answer that 32 orders are necessary to satisfy all of demand based on
EOQ = 32.
A1. Textbook Computational Problems
Topic Textbook End-of-Chapter Problems
#13 use holding cost of $5/bag/year throughout; solution different from the textbook
#14 use holding cost of $5/bag/year throughout
#22 assume Q system
#5 use 1= D 1o start calculation for exponential smoothing
#6 use 1= D 1o start calculation for exponential smoothing
#9 solve the problem by the method shown in the lecture notes
#14 solve the problem by the method shown in the lecture notes
#21 also use MAPD and CE to compare two methods
1 A2. Computational Questions from Old Exams
1. You are given the following partial demand and forecast data for a product:
t):arter 4 5 6
Forecast (F ): 400 430 600
Demand (D )t 420 370 680
a) Compute a 3-quarter simple moving average forecast for quarter 7.
b) The actual demand for quarter 7 turned out to be 1060. Compute an exponentially smoothed
forecast for quarter 8 with = 0.15. Use the forecast for quarter 7 from part a).
c) Observing the actual demands for quarters 4 through 7, you are thinking about updating the value
of in part b). Would you choose a smaller or larger value than 0.15? Justify your answer briefly.
d) For the forecasts given in part a) (quarters 4 to 6) and the forecast computed in a) (quarter 7),
compute a measure of bias error. Is there any bias, and if so, has the forecast been biased low or
e) The product turns out to be popular homemade-style ice cream made in a small plant. The
complete demand data for years 1, 2, and 3 are given below. Compute the forecast for each of
quarters in year 4, given that the forecast for the total demand in year 4 is 2980 gallons.
Quarterly demand (in gallons)
Year Quarter 1 Quarter 2 Quarter 3 Quarter 4
1 350 710 950 420
2 370 680 1060 500
3 450 750 1020 570
2. The University Gift Shop purchases sweatshirts emblazoned with the school name and logo from a
vendor in Toronto. The vendor sells the sweatshirts to the Gift Shop for $34.99 apiece. Shipping from
Toronto to London costs $110 per order. When an order arrives, it has been estimated that receiving
and inspection tasks cost the Gift Shop $25. The annual holding cost for a sweatshirt is calculated as
11% of the purchase cost. The Gift Shop manager estimates that 3100 sweatshirts will be sold during
the upcoming academic year.
a) Determine the optimal order quantity using the basic EOQ model.
b) The vendor has recently offered a 3% discount on the purchase price if the Gift Shop orders 500
or more but less than 2000 at a time, and a 5% discount if the Shop orders 2000 or more at a time.
Would you take up one of these offers? If so, what is the new optimal order quantity, and if not,
why not? Use the same holding cost from part a) throughout this question.
c) Based on your answer in part b), how many orders will there be in a year? What is the annual
average inventory level?
d) Based on your answer in part b), what is the reorder point if the lead time is 3 business days?
Assume that there are 260 business days a year.
e) In parts a) and b), one type of the main inventory management costs has not been included in
calculating the optimal order quantity. What is it and why has it been left out?
2 3. Big Value Supermarket stocks Crunchies Cereal. The demand for Crunchies was 10,200 boxes in
year 6. The demand forecast for year 7 is calculated using exponential smoothing with = 0.12 (the
forecast for year 6 was 9500 boxes). It costs Big Value $80 per order of Crunchies and $0.85 per box
annually to keep the cereal in storage. The store manager wants to know what the optimal inventory
management policy is for Crunchies in year 7. Determine the optimal policy and describe it based on
a periodic review system. What is the total cost associated with the optimal policy, and what is the
average inventory level of Crunchies? Assume that Big Value operates 365 days per year.
4. ABC Computers assembles microcomputers from generic components. It purchases its colour
monitors from a manufacturer in Taiwan with a lead time of 21 days. Daily demand for monitors is
normally distributed with a mean of 3.5 monitors and a standard deviation of 1.7 monitors. ABC has
determined that the ordering cost is $325 per order, the annual holding cost is $25 per monitor, and
the stockout cost is $450 per lost sale. Currently ABC calculates the safety stock level for monitors
based on a 90% service level. If ABC is willing to spend 50% more on managing safety stock, what
service level could be achieved? The number of standard deviations is 1.28 for 90% service level,
1.65 for 95%, 2.05 for 98%, and 2.33 for 99%. ABC uses a continuous review system.
5. The manager of Petro North gasoline service station wants to forecast the demand for unleaded
gasoline next month so that the proper number of gallons can be ordered from the distributor. The
manager has accumulated the sales data and forecast accuracy measures during the past 10 months,
which are shown in the table below. Fill all blank spaces in the table labeled a through f.
Month 3-month Sales MAD MAPD MSE CE
Simple Moving (in gallons)
Feb N/A 1130 N/A N/A N/A N/A
Mar N/A 1360 N/A N/A N/A N/A
Apr N/A 1440 N/A N/A N/A N/A
May 1310.00 b 90.00 0.074 8100 90
Jun 1340.00 1670 210.00 d 58500 240.00
Jul 1443.33 1810 262.22 0.167 e 606.67
Aug 1566.67 1920 c 0.172 94072 960.00
Sep 1800.00 1630 262.00 0.159 81038 790.00
Oct a 1470 271.11 0.167 84245 f
Nov 1673.33 1510 255.71 0.159 76021 310.00
6. Richmond Street Microbrewery makes Western Beer, which it bottles and sells in its adjoining
pub/restaurant and by the case. It costs $1100 to set up, brew and bottle a batch of the beer. The
annual cost to store the beer is $2.75 per bottle. The annual demand for the beer is 16,000 bottles and
the brewery has the capacity to produce 28,000 bottles annually. The current production policy is to
continue producing the beer until the storage gets full. The storage holds a maximum of 750 bottles of
beer. Production starts again when the inventory of beer is depleted. The owners of the brewery are
considering an option of increasing the beer storage space to hold a maximum of 3000 bottles as part
of their expansion strategy for the next five years. Is this a good option in terms of the cost savings?
Why or why not? Comment also on the current policy of producing the beer until the storage is full.
What would be an optimal production policy for the brewery? Lastly, determine how many
production days are required for the optimal production policy (assume one year = 365 days).