MAD, MSE, and MAPE

  1. If you increase the value of the smoothing constant, what effect will it have on the exponential
    smoothing model? Explain.
  2. Selecting from MAD, MSE, and MAPE, which measure of forecast accuracy do you consider
    superior? Why?
  3. Explain in general terms how a safety stock level is determined in the Q system of inventory
    management using customer service level.
    Part 2: Problems
  4. AV City stocks and sells a particular brand of laptop. It costs the firm $525 each time it places an
    order with the manufacturer for the laptops. The cost of carrying one laptop in inventory for a year
    is $125. Demand for the laptops is reasonably constant over time, and the forecast is 5 units per
    day. The store operates 320 days per year.
    A. Determine the optimal order quantity per order and the number of orders per year.
    B. AV City assumed with certainty that the ordering cost is $525/order and the inventory
    carrying cost is $125/unit/year. However, the inventory model parameters are frequently
    only estimates that are subject to some degree of uncertainty. Consider four cases of
    variation in the model parameters as follows: (i) Both ordering cost and carrying cost are
    10% less than originally estimated; (ii) both ordering cost and carrying cost are 10% higher
    than originally estimated; (iii) ordering cost is 10% higher and carrying cost is 10% lower
    than originally estimated; and (iv) ordering cost is 10% lower and carrying cost is 10%
    higher than originally estimated. Determine the optimal order quantity and total inventory
    cost for each of the four cases. Prepare a table with values from all four cases and compare
    the sensitivity of the model solution to changes in parameter values.
  5. Akber is the manager of the One-stop Office Supply Company in Khobar. The company attempts
    to gain an advantage over its competitors by providing quality customer service, which includes
    prompt delivery of orders by truck or van and always being able to meet customer demand from its
    stock. To achieve this degree of customer service, it must stock a large volume of items on a daily
    basis at a central warehouse and at three retail stores in the city. Akber maintains these inventory
    levels by borrowing cash on a daily basis from AlRajhi Bank. He estimates that for the coming
    fiscal year, the company’s demand for cash to pay for inventory will be $15,000 per day for 310
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    working days. Any money he borrows during the year must be repaid with interest by the end of
    the year. The annual interest rate currently charged by the bank is 10%. Any time Akber takes out
    a loan to purchase inventory, the bank charges the company a loan origination fee of $1,150 plus
    2.5 points (i.e., 2.5% of the amount borrowed).
    Akber often uses EOQ analysis to determine optimal amounts of inventory to order for different
    office supplies. Now he is wondering if he can use the same type of analysis to determine the
    optimal borrowing policy. Determine the amount of the loan Akber should borrow from the bank,
    the total annual cost of the company’s borrowing policy, and the number of loans the company
    should obtain during the year. Also determine the level of cash on hand at which the company
    should apply for a new loan given that it takes 15 days for a loan to be processed by the bank.
    Suppose the bank offers Akber the following discount: on any loan amount equal to or greater than
    $500,000, the bank will lower the number of points charged on the loan origination fee from 2.5%
    to 2.00%. What would be the company’s optimal amount borrowed?
  6. You have invested in a stock mutual fund. You are considering liquidating and investing in a bond
    fund. You would like to forecast the price of the stock fund for the next month before making a
    decision. You have collected the following data on the average price of the fund during the past 20
    months.
    Month Fund Price Month Fund Price Month Fund Price
    1 63.25 8 65.12 15 70.12
    2 60.12 9 68.25 16 72.75
    3 61.75 10 65.50 17 74.12
    4 64.25 11 68.12 18 71.75
    5 59.38 12 63.25 19 75.50
    6 57.88 13 64.38 20 76.75
    7 62.25 14 68.62
    A. Using a four-month moving average, forecast the fund prices up to month 21.
    B. Using a four-month weighted average with the most recent month weighted 0.50, the next most
    recent month weighted 0.20, the third month weighted 0.20, and the fourth month weighted
    0.10, forecast the fund prices up to month 21.
    C. Compute an exponentially smoothed forecast using ? = 0.30 and forecast the fund prices up
    to month 21.
    D. Compare the forecasts in A, B, and C using MAD and indicate the most accurate method.
    E. Compare the forecasts in A, B, and C using MSE and indicate the most accurate method.
    F. Do you reach the same conclusion for both D and E? Why or why not?
    G. Using tracking signal, indicate whether or not the methods in A, B, and C are in control.

Sample Solution