Trader Joe’s orders a 6-week supply of its frozen organic chocolate waffles when stock on hand drops to 400 units.

1. Trader Joe’s orders a 6-week supply of its frozen organic chocolate waffles when stock on hand drops to 400 units. The lead time for this item is 4 weeks. Demand is normal with an average of 80 units per week and standard deviation of demand is estimated 50 units per week.
a. What level of customer service is Trader Joe’s providing to its distributors in terms of stock availability? What’s their average inventory of frozen organic chocolate waffles?
b. Trader Joe’s decides that 97.7% is an appropriate ratio of customers they can meet the demand of, in terms of that product. What will be their new safety stock and average inventory after such an improvement?
c. Trader Joe’s assumes that a customer who can’t find the product in the store is a lost customer and the cost of one lost customer is $16. The holding cost of the product in inventory is $8 per year. Then compare the two policies by calculating the total costs of holding and lost sales.

2. a. If we have some information about the demand, why don’t we simply hold inventory for the expected demand, wouldn’t this minimize the total cost, i.e., why do we hold safety stock?
b. What does an organization need to determine before deciding on its amount of safety stock?

3. You are a retailer, ordering your products from a producer and you just keep cyclical inventory (none of seasonal or safety stock inventories). You observe that your demand has increased recently, so your inventory has to be replenished more quickly, but you are not planning to change your lot size (Q).
a. What’s the impact of this on the amount of inventory you hold?
b. What’s the impact of this on the flow times?

4. Up, Up, and Away is a producer of kits and wind socks. Relevant data on a bottleneck operation in the shop for the upcoming fiscal year are given in the following table:
Item Kites Wind Socks
Demand forecast 30,000 units/year 12,000 units/year
Lot size 20 units 70 units
Standard processing time 0.3 hour/unit 1.0 hour/unit
Standard setup time 3.0 hour/lot 4.0 hour/lot

The shop works two shifts per day, 8 hours per shift, 200 days per year. There currently are 4 machines, and 75% capacity utilization is desired. How many machines should be purchased to meet the upcoming year’s demand?

5. A department store sells (among other things) sports shirts for casual wear. The salesman in charge of the men’s department knows that the demand for one of these shirts is fairly constant at 250 shirts per year. These shirts are obtained from the manufacturer who charges a delivery fee of $65, regardless of the number of shirts delivered. In addition, in-house costs associated with each order total $6.
The manufacturer charges $16.25 per shirt, but is willing to lower the price by 3 percent per shirt if the department will order 288 shirts each time. The holding costs are estimated to be 8.5% of the shirt cost.
Should the salesman recommend that the department store accept the offer of the quantity discount and larger order size? Please calculate.