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1. The Marlin Company operates 50 weeks a year, and its cost of goods sold last year was $1,500,000. The firm carries six items in inventory: three raw materials, two work-in-process items, and one finished good. The following table shows company’s last year’s average inventory levels for these items, along with their unit values.

Category             Part Number    Average Inventory Units    Value per Unit
Raw Materials         RM-1                    1750                            $15
                              RM-2                    1500                           $25
                              RM-3                    2000                           $20

Work-in-process    WIP-1                     1500                           $40
                             WIP-2                     1200                           $50

Finished Goods        FG-1                     1000                           $75

a. Determine their average aggregate inventory value?

b. How many weeks of supply do the firm have?

c. What was their inventory turnover last year?

d. The turnover ratio is widely used as it is a common measure which links to the financial statements of the firm.  Discuss benefits and drawbacks of using this measure.

2. The Burdell Wheel and Tire Company assembles tires to wheel rims for use on cars during manufacture of vehicles by the automotive industry. Burdell desires to locate a low-cost supplier for the tires he uses in his assembly operation. The supplier would be choosen based on total annual cost to supply Burdell’s needs. Burdell’s annual needs are for 25,000 tires, and company operates 250 days a year. The following data are available for two suppliers being considered.

Supplier          Shipping     Annual Shipping    Price/unit    Annual Holding     Lead Time(days)     Annual

                      Quantity         Costs                                    Cost/unit                                    Administrative Cost      

Lexington Tire  2,000         $18,000                     $40            $8.00                        8                    $14,000
Irmo Auto        1,000         $24,000                     $41            $8.20                        5                    $18,000

Use the Total Cost Analysis for Supplier Selection, which supplier must Burdell select? Give details to justify your answer.

3. A manufacturer’s research and development centre should expand by building a new facility. The search has been narrowed to five locations, all of which are acceptable to management. The assessment of these sites is being made on the basis of the five subjective location factors that follow. Management has agreed to use a five-point scale (Excellent = 5, and Poor = 1) to quantify and compare their subjective opinions about the relative goodness of the sites. The weight reflects the significance of each factor in the decision.

Factor                       Weight    A    B    C    D    E
Labor climate                30       4    2     1    4    2
Proximity to markets    30       5    3     3    4    4
Quality of life                15       1    3     2    1    5
Proximity to suppliers   15       2    5     3    4    3
Taxes                          10       3    4     4    1    5

Compute the weighted score for each alternative. Which location will you suggest? Why?

4. A specialty coffeehouse sells Colombian coffee at a fairly steady rate of 78 pounds per week. The beans are purchased from a local supplier for $4.00 per pound. The coffeehouse estimates that it costs $45 in paperwork and labor to place an order for the coffee, and the annual holding cost is 15% of the purchasing price. (Use 52 weeks/year)

a. What is the economic order quantity (EOQ) for Colombian coffee?

b. What us the optimal number of orders per year?

c. What is the optimal interval (in weeks) between the orders?

d. Suppose that the coffeehouse’s present order policy is to buy beans every 8 weeks. The manager says that the ordering cost of S = $45 is only a guess. Hence, he insists on using the present policy. Find the range of S for which the EOQ you found in part a) will be preferable (in terms of a lower total replenishment and carrying costs) to the current policy of buying beans every 8 weeks.

5. A store has collected the following information on one of its products:
            Demand = 6,760 units/year
            Standard deviation of weekly demand = 18 units
            Ordering costs = $40/order
            Holding costs = $2/unit/year
            Cycle-service level = 90% (z for 90% = 1.28)
            Lead-time = 3 weeks
Number of weeks per year = 52 weeks

a. If the firm uses continuous review system to control the inventory, what will be its order quantity and reorder point?

b. Suppose that firm decided to change to the periodic review system to control the item’s inventory. The time between reviews, P, is estimated using the EOQ model. For the most recent review, an inventory clerk checked the inventory of this item and found 300 units. There were no scheduled receipts or backorders at the time. Find out how many units must the firm order.

6. Observed monthly sales of a popular brand tennis shoe at a medium-sized sports store at the town’s mall over the first six months of the year are given in the following table.

Month      Jan    Feb    Mar    Apr    May    June    July    Aug
Demand    27    32      30      45     36      40       38    42

a. Use a three-month moving average method to forecast the sales for the months April through September. Also compute the mean squared error (MSE) based on the sales and forecasts for months April through August. 

b. If the forecast for January was 25, determine the forecast for sales for the months February through September using an exponential smoothing method with α = 0.30. Also compute the mean squared error (MSE) based on the sales and forecasts for months April through August. 

c. Which method would you recommend based on MSE? Why?

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