Question

Case Study 3: ELYSIAN CYCLES                                      

Located in a major southwestern U.S. city, Elysian Cycles (EC) is a wholesale distributor of bicycles and bicycle parts. Its primary retail outlets are located in eight cities within a 400-mile radius of the distribution center. These retail outlets generally depend on receiving orders for additional stock within two days after notifying the distribution center (if the stock is available). The company’s management feels this is a valuable marketing tool that aids its survival in a highly competitive industry.

EC distributes a wide variety of finished bicycles, but all are based on five different frame designs, each of which is available in several sizes. Table 1 gives a breakdown of product options that are available to the retail outlets.

Table 1. Prices and Options of Available Bicycles

Frame Style	Available Sizes, in.	Number of Gears	Suggested List Price
A	16, 20, 24	10	$   99.95
B	16, 20, 24	15	124.95
C	16, 20, 24, 26	15	169.95
D	20, 24, 26	15	219.95
E	20, 24, 26	21	349.95

EC receives these different styles from a single manufacturer overseas, and shipments can take as long as four weeks from the time an order is made by telephone or Internet. Including the costs of communication, paperwork, and customs clearance, EC estimates that it incurs a cost of $65 each time an order is placed. The cost per bicycle is roughly 60 percent of the suggested list price for any of the styles available.

Demand for these bicycles is somewhat seasonal in nature, being heavier in spring and early summer and tapering off through fall and winter (except for a heavy surge in the six weeks before Christmas). A breakdown of the previous year’s business with the retail outlets usually forms the basis for EC’s yearly operations plan. A growth factor (either positive or negative) is used to refine further the demand estimate by reflecting the upcoming yearly market. By developing a yearly plan and updating it when appropriate, EC can establish a reasonable basis for obtaining any necessary financing from the bank. Last year’s monthly demand for the different bicycle styles that EC distributes is shown in Table 2

Table 2. Monthly Bicycle Demand

Frame Style
Month	A	B	C	D	E	Total
January	0	3	5	2	0	10
February	2	8	10	3	1	24
March	4	15	21	12	2	54
April	4	35	40	21	3	103
May	3	43	65	37	3	151
June	3	27	41	18	2	91
July	2	13	26	11	1	53
August	1	10	16	9	1	37
September	1	9	11	7	1	29
October	1	8	10	7	2	28
November	2	15	19	12	3	51
December	3	30	33	19	4	89
Total	26	216	297	158	23	720

Because of the increasing popularity of bicycles for recreational purposes and for supplanting some automobile usage, EC believes that its market might grow by as much as 25 percent in the upcoming year. There have been years when the full amount of expected growth did not materialize, however, so EC has decided to base its plan on a more conservative 15 percent growth factor to allow for variations in consumer buying habits and to ensure that it is not overstocked excessively if the expected market does not occur. Holding costs that are associated with inventory of any bicycle style are estimated to be about 0.75 percent of the unit cost of a bicycle per month.

Develop an inventory control plan for EC to use as the basis for its upcoming annual plan. Justify your reason for choosing a particular type (or combination of types) of inventory system(s). For your particular plan, specify the safety stock requirement if EC institutes a policy of maintaining a 95 percent service level.

Answer 1

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Because sales data is not available at the level of bicycle size (e.g. 18, 21, 23), the stock-keeping unit (SKU) will be identified by bicycle frame style (i.e., A, B, C, D, or E). It is assumed that orders for a particular frame style will be broken down into appropriate bicycle sizes based on current sales experience. Several possible inventory systems might be appropriate for Eysian Cycles. First we will consider two versions of the Continuous Review System. In the first, or disaggregate, case, an inventory system complete with EOQ and Reorder point will be designed for each bicycle frame style. In the second, or aggregate, case, all the bicycles will be considered together with only one order placed for a predetermined mix of bicycle frame styles. Finally, a Periodic Review System is proposed in which the periodic order will consist of a mix of bicycle styles based on current sales.

Continuous Review System (Disaggregate Version)

The economic order quantity for each bicycle frame style will be calculated using equation (3) with H = IC.

where:

D = Annual demand for last year increased by a 15 percent growth factor

S = Ordering cost of $65

I = Holding cost of 0.75 percent per month or 9 percent per year as a percentage of bicycle value

C = Wholesale cost of bicycle at 60 percent of suggested list price

Bicycle Style	Last Year’s Demand	Projected Demand (D)	Wholesale Cost (C)	EOQ	Order Interval (mos.)
A	26	30	59.97	27	12
B	216	248	74.97	69	3.3
C	297	342	101.97	70	2.5
D	158	182	131.97	45	3
E	23	26	209.97	13	6

The reorder point for each bicycle style is calculated based on the desire for a 95 percent service level. The lead-time to receive orders from the overseas manufacturer is stated as four weeks or approximately one month. It is assumed that the monthly demand data is normally distributed. From Appendix A we find that a standard normal deviate of 1.65 ensures 5 percent in one tail. Using equations (8, 9,and 11) the reorder point is calculated for each bicycle style.

However, because the lead-time (LT) is approximately one month the reorder point formula is simplified as below with s and m representing the monthly demand parameters.

The average monthly demand will be inflated by 15 percent to reflect anticipated growth. The standard deviation of the monthly demands will be calculated assuming dispersion from one year to the next will remain unchanged. Furthermore, a sample standard deviation is calculated using (n-1) because only 12 months of data is available.

Bicycle Style	Monthly Demand	Projected Demand	Standard Deviation	Safety Stock	Reorder Point
A	2.2	2.5	1.3	2.1	5
B	18.0	20.7	12.6	20.8	42
C	24.8	28.5	17.4	28.7	57
D	13.2	15.1	9.6	15.8	31
E	1.9	2.2	1.2	2.0	4

For comparison purposes the annual total cost of the inventory system is calculated using equation (2) with H = IC.

Bicycle Style	Projected Demand (D)	Wholesale Cost (C)	Order Quantity (Q)	Total Annual Cost ($)
A	30	59.97	27	145.08
B	248	74.97	69	466.40
C	343	101.97	70	638.77
D	182	131.97	45	530.12
E	26	209.97	13	252.83
			System Cost	2033.20

Continuous Review System (Aggregate Version)

Because one manufacturer furnishes all bicycles, consolidating all bicycle styles into one order saves ordering costs. Whenever an order is placed, it will contain a predetermined mix of bicycle styles. The order size of each style will be in proportion to its sales demand. The economic order quantity and reorder point is now based on the total demand for all bicycles irrespective of style.

The retail cost per bicycle of $170 used above is a weighted average based on annual sales.

The sample standard deviation for monthly demand used above is calculated from the last column of total monthly demand data.

Bicycle Style	Percent of Monthly Demand	No. of Units in EOQ	No. of Units in Safety Stock
A	3.6	4	2
B	30.0	32	21
C	41.3	45	28
D	21.9	24	15
E	3.2	3	2
	Totals	108	68

The number of units in the safety stock is taken directly from the previous calculations of safety stock by bicycle style.

The total annual system cost is calculated as:

Thus, in comparison with the disaggregate version, considerable savings in inventory system cost is achieved with some loss in controlling inventory levels by bicycle frame style. Because a fixed mix of styles is always ordered, the system will not respond to changes in demand for individual bicycle styles (possibly running out of stock of some styles and overstocking others).

Periodic Review System

The cost savings of aggregate ordering are retained and the ability to control inventory levels by bicycle style is achieved using the periodic review system. For the periodic review system, the stock level of each bicycle style will be reviewed and the needs for each will be aggregated into one order that may vary in quantity. The review period (RP) is based on the EOQ of 108 calculated above for the aggregate version of the continuous review system. An EOQ of 108 represents placing an order approximately every 1½ months because average aggregate monthly demand is 69. The target inventory level is determined using equation (13):

Bicycle Style	Percent of Monthly Demand	No. of Units in Target
A	3.6	10
B	30.3	84
C	41.3	115
D	21.9	61
E	3.2	9

For this system, every 6 weeks an inventory of all bicycle styles is undertaken. An order is placed to include the number of bicycle styles needed in each category to bring the existing inventory up to the target level for each

style. The aggregate order feature is preserved, but each order mix reflects the current sales of bicycles by style. The annual inventory cost for this system is equivalent to the aggregate continuous system, because the same EOQ is used. However, because the buffer stock is now 107 units compared to 68, some additional inventory holding cost is incurred. On an annual basis this extra cost is calculated to be (.09)(107-68)(170)(.60) = $358.02. This results in a total annual system cost of $1352.10.

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