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Bama Drinks Company: an inventory case portfolio.(Instructor's Note)



Suggested Answers to Case Questions

1. Which inventory costs might Natalie be calling expensive?

Inventory holding costs. This includes cost of capital or investment in inventory cost. Here the instructor can introduce the concept that not having inventory is costly too. It can lead to the loss of customers, expediting, discounts, etc. This issue is important for discussing the differences in backordering costs and the discussion about different demand classes in the second part of the case.

2. What does Natalie mean by saying that they use a 90% fill rate?

Fill rate is the fraction of demand that is met without backorders or lost sales (Silver et al. 1998). For an inventory management course alternative service measures, e.g., fraction of cycle without stockouts or ready rate, can be discussed.

3. Which inventory policy is Bama Drinks using?

At this time, the company uses an order-point, s, and order-up-to quantity, S. This is known as an (s, S) policy. This system is frequently encountered in practice (Silver et al. 1998, p. 239). Silver et al. note that values for s and S are usually set arbitrarily. An inventory management class could address how to obtain reasonable values for s and S.

4. What are some alternative inventory policies that Bama Drinks could use?

At this time, the instructor can introduce a variety of policies; (s, Q), (s, S), (R, S), and (R, s, S). These policies are defined by order-point, s; order-up-to quantity, S; order quantity, Q; and review period length, R. For the introductory operations management class we address the conceptual difference between continuous versus periodic review and order quantity versus order-up-to level. For an inventory management class this can lead to a more in-depth discussion.

5. Which changes to Bama Drinks' inventory policy do you suggest?

We note that experiencing a few stock-outs might not justify changing the company's inventory policy. However, if analyses indicate that there is a systematic problem, changing the reorder point or safety stock levels would be appropriate.


Suggested Answers to Case Questions

1. For the moment ignore the freight cost. Using the economic order quantity (EOQ) model, determine the inventory order quantity that would provide the lowest total inventory ordering, and holding cost?


Where D= annual demand, S = ordering cost, and H = the cost to hold one unit of average inventory for one year.


2. Now including the freight cost what is the economic order quantity that would provide the minimum total inventory, holding, and freight cost? Does adding in the freight cost make much of a difference in the economic order quantity? Does the EOQ increase or decrease? Is that what you expected?

To show how freight cost should be handled we need return to the total inventory cost model (ignoring the product cost since it is constant).

TC = 1/2QH + (D/Q)S + (D/Q)F

Where: Q = the economic order quantity and F = the freight cost per shipment (regardless of size)

Therefore, EOQ = [square root of 2D(S + F)]/H EOQ = [square root of 2*(20,600)*(25 + 100)]/2 = 1,014.89 cases.

Assuming the freight cost is constant, including the freight cost per order or shipment makes a significant difference in the EOQ. It can make the EOQ much higher. One way to reduce the EOQ is to imbed the freight cost into the product selling price.

3. Using your answer to question (1), what would be Bama's total inventory ordering and holding cost for the year?

TC = 1/2QH + (D/Q)S

TC = 641.87 * 2.50 + 20,600*25 = $802.34 + $802.34 = $1,604.68

4. Again using your answer to question (1), how many orders should Bama place per year?

The number of orders per year = D/Q = 20,600/641.87 = 32.09 orders per year or one order every 250/32.09 = 7.79 days.

5. Given a lead time of three days at what inventory level should Bama place an order?

r = d* L

Where, r = the reorder point, d = the daily demand, and L = the lead time; in this case the number of days of lead time

r = (20,600/50*5) * 3 = 247.20 cases

6. Assuming: (1) a case of soft drinks requires 2.5 square feet of floor space and, (2) the case stacking conditions mentioned in the case, what is the maximum amount of storage space (floor space) Bama would need in its warehouse to store inventory?

The maximum inventory Bama should have in its warehouse is the moment the EOQ quantity arrives. This is at 641.87 or 642 cases. If each case requires 2.5 square feet of storage space, this is 1,605 square feet. Stacked three cases high this would result in a need for 1,605/3 = 535 square feet of floor storage space needed.


Suggested Answers to Case Questions

1. Is Bama experiencing a pattern of seasonality in its sales or are the seasonal fluctuations just random?

As shown by the Line Chart of Raw Sales the company is indeed experiencing seasonality in its sales. Typically, sales are at the low point for the year in the first quarter and rise to a pronounced spike in the fourth quarter. Thus, Bama should indeed forecast sales for 2009 and adjust them for seasonality.


2. If sales are indeed increasing per year and the company sales are experiencing seasonality what should the expected sales figures for 2009 be? And, how should the expected sales figures be determined?

This question assumes that students have an understanding of forecasting techniques. If forecasting is not covered in a prior course, students can study the forecasting topic in the OM course before inventory. With basic knowledge of forecasting techniques, the students should be able to forecast seasonally adjusted sales for the 2009 year. Perhaps the easiest method for forecasting sales that exhibit seasonality is to use the annual method. In this technique the students total the sales for each year. The yearly totals become the dependent variables and the years (1, 2, 3, etc.) are the independent variables. Linear regression is then used to determine the equation for this time series and in this case is used to forecast the total sales for 2009.

For this case the linear regression equation was determined to be:

Y = 11,667.93 + 1605.5(Year)

This regression helped explain 81% (R2) of the variation in the annual sales. While other mathematical formulations (e.g., a chart and regression function for a quadratic function is provided.) may better represent the relationship, for pedagogical purposes the linear expression seemed sufficient.

Next, the percent that each quarter represents of annual sales is determined. This is done by totaling the sales over all years for each quarter. The total sales over all years per quarter are divided by the total sales over all the years. Once these percents are determined, each is then multiplied by the total sales projected for (in this case) 2009. Next seasonalized sales by quarter for 2009 have been projected. Bama would also have an idea of how much each quarter (on average) represents of annual sales. These figures are provided in the table below.
Quarterly Sales as Proportion of Annual Sales

 Q1      0.1975
 Q2      0.2272
 Q3      0.2184
 Q4      0.3569

Seasonalized Sales Projected Quarterly Sales (2009)

 Q1     4,523.24
 Q2     5,204.97
 Q3     5,003.13
 Q4     8,174.83
Total   22,905.73

Thus, using this technique the projected, seasonalized sales of cases (rounded off) for 2009 are:
Quarter 1        4,523
Quarter 2        5,205
Quarter 3        5,003
Quarter 4        8,175

3. If inventory policies are tied to expected future sales, not past sales, what should Bama's inventory policies be for 2009?

Bama should adjust its inventory policies for 2009 for two reasons: sales are increasing and they have definite seasonality in their sales. Assuming sales are relatively constant within each quarter, they should calculate and use an EOQ for each quarter based on the projected, seasonalized, quarterly sales for 2009. The EOQ calculations shown on the Data Sheet were determined using the following EOQ formula adjusted for quarterly sales.

EOQ each quarter of 2009 = [square root of (2*(quarterly demand)*($25)]/($2.50/4))

This produces the quarterly EOQs for 2009 (rounding up):
Quarter 1    602
Quarter 2    645
Quarter 3    633
Quarter 4    809

Had the EOQ been based on the entire 2009 sales it would have been:

EOQ = [square root of (2*(22,906)*(25)]/(2.50)) = 676.8 or 677

This would indeed explain Natalie's comment that inventories seemed overstocked in early quarters and insufficient in later periods.


Suggested Answers to Case Questions

1. Which changes can Bama Drinks make to the inventory policy to increase service levels?

In this case, the company measures service level with fill rate (see question 2). The fill rate can be improved by increasing safety stock (SS) or by increasing the reorder point (s). A company keeps SS because of the stochastic nature of demand. Hence, when the variability of the lead time demand has increased it would be appropriate to increase SS. This in turn would also increase the reorder point since the reorder point = lead time demand + safety stock. When the lead time demand increases, it is appropriate to increase the reorder point. If the variation has not changed, the safety stock levels remain the same.

2. What trade-offs should be considered when setting service levels?

The fill rate balances the costs of having too much inventory (holding costs) versus not having enough inventory (shortage costs). The service level is set based on the relative costs of holding inventory, r, and the cost of being short of inventory per unit time (B3). The optimal fill rate is then; P2 = B3 / (B3 + r). (Silver et al. 2001, p. 245).

3. Based on Jamison's comment above, design a new inventory policy for Bama Drinks.

Jamison indicates that he would like to recognize the difference in customer importance in the new policy. Hence, he eludes to establishing demand classes.

Keep separate inventories

Many organizations have recognized that they need different inventory policies for different customer groups. Not utilizing the differences in service requirements among customers and therefore using an aggregate service level is costly (e.g. Deshpande et al. 2003). When the aggregate service level is too low customers will be lost. When the service level is too high for some demand classes, the company invests too much in inventory.

In practice, some companies have physically separated the inventory while others have created different SKUs for the various demand classes. A drawback of these approaches is that the company does not take advantage of inventory pooling (Deshpande et al. 2003).

Multiple Demand Classes

The multiple demand class issue becomes important when different groups of customers, or demand classes, have different service restrictions with the supplier e.g., costs of lost sales, backordering costs, differing service level contracts. When inventory is low, it is then reasonable to reject the demand from less valuable classes (Ha 1997). Hence, the company rations inventory. One way to ration inventory among demand classes is the use of rationing points, or critical levels, ([c.sub.i]) (e.g., Arslan et al. 2007)). If inventory is below the critical level of a demand class, any demand from this demand class will be backordered. Demand from the higher priority demand classes will still be satisfied when it occurs. Hence, a company can have on-hand inventory and backorders at the same time.

The multiple demand classes approach is presented in figure 1 below. In the figure, the company is using an (s, S) policy, like Bama Drinks.


Where, [c.sub.i] is the critical level, L is the replenishment lead time, and S is the order up to level in the (s, S) policy.


For an inventory management class an interesting follow-up discussion can address the issue of deciding which backorder should be filled first when a replenishment arrives. Also, if replenishment is insufficient should (a) backorders for lower priority demand classes or (b) inventory for higher priority demand classes be replenished first? These issues are also important discussions in the literature (e.g., Arslan et al. 2007).


Arslan, H., S. C. Graves, & T. A. Roemer (2007). A single product inventory model for multiple demand classes. Management Science 53 (9), 1486-1500.

Deshpande, M. A. Cohen, & K. Donohue (2003). A threshold inventory rationing policy for service-differentiated demand classes. Management Science 49 (6), 683-703.

Ha, A. Y. (1997). Inventory rationing in a make-to-stock production system with several demand classes. Management Science 43 (8), 1093-1103.

Kleijn, M. J. & R. Dekker (1998). An overview of inventory systems with several demand classes. Econometric Institute Report 9838/A.

Nahmias, S. & W. S. Demmy. 1981. Operating Characteristics of an Inventory System with Rationing. Management Science 27 (11), 1236-1245.

Silver, E. A., Pyke, D.F. & R. Peterson. (1998). Inventory management and production planning and scheduling (Third Edition). New York, NY

Marco Lam, York College of Pennsylvania

Benjamin Neve, The University of Alabama

Roger J. Gagnon, North Carolina A&T State University
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Title Annotation:Instructor's Note
Author:Lam, Marco; Neve, Benjamin; Gagnon, Roger J.
Publication:Journal of the International Academy for Case Studies
Article Type:Case study
Geographic Code:1USA
Date:Nov 1, 2010
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