9.11 Discussion and Practice

1. Consider the following data for the most popular lens product by optical manufacturer Z-Lens:

   D	26,500	units/year
   sD	9,500	units/year
   L	0.08	years
   sL	0.03	years
   K	$1,250	per order
   h	$70	per unit per year
   p	$90	per unit

   1. Given this information, determine the optimal order quantity and the optimal reorder point.

   2. Now imagine that the company's key competitor goes out of business, leaving Z-Lens as the sole remaining seller of this particular type of lens. The lack of alternatives effectively reduces Z-Lens' stockout costs by 50%. How do you think will this affect the optimal order quantity and reorder point determined in part a) of this question? Will they increase or decrease? What is the intuitive rationale for these changes?

2. Dan’s Dog Diner (DDD) is a low-key restaurant selling hot dogs and a long-time neighborhood favorite. DDD keeps an inventory of its best-selling product, the foot-long Frankfurter, in the freezer and reorders as needed when inventory runs low. Specifically, Dan’s rule of thumb is to place another order when there are only 100 sausages left. Average daily demand is 30 units with a standard deviation of 10 units, and the average replenishment lead time is two days with a standard deviation of 1 day. Lately, Dan has noticed that he runs out of foot-long Frankfurters nearly three times a month, on average. Wanting to keep his customers happy, Dan decides to strive for a 99% in-stock rate moving forward. By how many units will Dan have to increase safety stocks to achieve this goal?

3. CraftMart, a small chain of arts and crafts stores in the U.S. Midwest, sells blue and green ribbons in its stores. The associated demand and lead time information is provided in the table below. In an effort to reduce inventory investments, the company is considering replacing blue and green ribbons by a single stock keeping unit (SKU), namely turquoise ribbons, since market research indicates that buyers of blue or green ribbons would be willing to switch to turquoise ribbons, such that total demand for this product would equal the sum of demands for blue and green ribbons. Since demands for blue and green ribbons are less than perfectly positively correlated, the standard deviation of demand is estimated to be 7,800 units only.

   	Blue Ribbons	Green Ribbons	Turquoise Ribbons
   D	23,000	14,000	37,000	units/year
   sD	6,500	3,500	7,800	units/year
   L	0.05	0.05	0.05	years
   sL	0.03	0.03	0.03	years
   In-stock rate		94%
   z		1.55

   1. What is the standard deviation of lead time demand for blue and green ribbons?

   2. How much safety stock does CraftMart need to hold for blue and green ribbons to achieve a 94% in-stock rate?

   3. How much safety stock would be needed for turquoise ribbons (after blue and green ribbons are discontinued)? What would be the percent reduction in safety stocks resulting from this consolidation?

   4. Imagine you are invited to present your findings to the company's executive officers. Please explain (in layman's terms), why this so-called SKU rationalization will be beneficial from a safety stock reduction perspective.

4. Rosie Reynolds is the owner of Rosie’s Roses, a flower shop located just off of the historic town square. Business has not been rosy lately (no pun intended). Sales have plummeted as disgruntled would-be customers frequently leave the store when their preferred flowers are not in stock. At the same time, costs have soared as Rosie has had to dispose of unsold flowers at an increasing rate. Rosie realizes that she needs help making smarter ordering decisions. Rosie buys roses at a wholesale market for $2.25 a piece and resells them for a unit price of $4.20. Any roses that go unsold are disposed of at a community bio-waste facility at a cost of $0.15 per unit. Looking at Rosie’s sales records from last month, you find that average daily demand is 62 roses with a standard deviation of 14 roses. How many roses should Rosie order each day?

5. At the annual board meeting, the CFO of ImPress, the publisher of Marketing & Insight (a trade magazine published monthly and distributed in Europe and North America), announces that the unit gross margin, i.e. the difference between the unit sales price and unit production costs has increased over the past two years (thanks to a decrease in production costs). However, the CFO admonishes you, the VP of Production and Supply Chain Management, that during the same time an increasing number of units have gone to waste at the end of each publication cycle, even though demand has not changed (in terms of both mean demand and demand variability). The CFO argues that profitability could be increased if production quantities were reduced to essentially eliminate excess inventories at the end of each month. Of course, you disagree. Drawing on your understanding of the newsvendor model, please educate the CFO and briefly explain why the observed increase in leftover inventory observed over the past two years is justified and actually contributes to greater profitability.

Additional Practice Questions