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Forecast Comparisons in Inventory Management
Cost-effective maintenance ofan appropriate inventory ofsupplies for the clinical laboratory requires the ability to forecast demands and make decisions about how much to order and when to order. The purpose ofthis study was to retrospectively compare three forecasting methods (moving average, exponential smoothing, and linear-regression analysis) with an existing method ofspecifying a minimal quantity on handforfive items in a clinical chemistry laboratory. The most cost-effective method was the moving average forecast using monthly review intervals, order generation based on an equation employing both safety stock and current inventory, and a safety stock quantity equal to the lead time.
From the Department of Pathology, Greater Baltimore Medical Center, Baltimore, Md (Dr Noel), and the School of Allied Medical Professions, The Ohio State University, Columbus, Ohio (Dr Snyder). Dr Snyder is now with Indiana University School of Medicine, Indianapolis, Ind. Reprint requests to Indiana University School of Medicine, Division of Allied Health Sciences, Indiana University Medical Center, Coleman Hall, Suite 120,1140 W Michigan St, Indianapolis, IN 46223 (Dr Snyder).
lthough supply costs are not as significant an expense item as salaries and wages in clinical laboratories, these costs represent the single largest nonpayroll expense in the total budget.1 Supply costs include the purchase price of the unit, the cost of placing a purchase order, and the carrying costs associated with maintenance of an adequate inventory.2 While the purchase price of many laboratory supplies continues to escalate, the laboratory manager can exercise costcontainment techniques that minimize the cost of maintaining an inventory. The primary purpose for maintaining an inventory of laboratory supplies is to guard against compromising patient care by possibly extending a patient's hospital stay or delaying treatment or surgery because reagents and supplies are not available on demand.3 Inventory management bridges two independent operations— production of laboratory tests when they are needed and purchase of reagents and supplies when this activity is most convenient.4 Since individual inventory items are constantly being used, the challenge to laboratory managers is to forecast how much to order and when to order while keeping requisition and inventory costs at a minimum.5 The purpose of this study was to compare three forecasting methods for inventory management retrospectively with a currently used method for selected items in a large clinical chemistry laboratory.
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nventory Replenishment Systems and Opposing Cost Pressures Before describing the forecast methods compared in this study, it is appropriate to describe inventory behavior in replenishment systems and the relationship between opposing cost pressures. Figure 1 displays an example of a simple,fixed-quantityreplenishment system with a known demand of ten chemistry reagent kits (units) per week.6 On this basis, the usual demand is 44 units per month (10 kits/week X 52 weeks -^ 12 months). Lead time is defined as the time required from the initiation of the purchase by the laboratory until new stock arrives. This is usually determined by reviewing historical performance of the time it takes the institution to process a purchase order and consulting the vendor on delivery schedules. In this example, the lead time is 30 days. Review period is a designated time when the quantity of supplies on hand are counted and a new order potentially initiated. The review period in the example is also 30 days, or once a month, that someone reviews the quantity of stock on hand and initiates a new order. The dotted line in thefigurerepresents ordered inventory. On the basis of the usual demand of 44 units per month and the 30-day lead time for supplies to arrive once ordered, the order quantity is 44 units each month when the stock review is done. As a precautionary measure, a safety stock may be maintained to guard
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Steven A. Noel, PhD, MT(ASCP), and John R. Snyder, PhD, MT(ASCP)SH
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120 10080Units 604020 0
safety stock 15
30 45 60 75 90 105 120 A A A Time in Days
Fig 1. Inventory behavior of afixed-quantityreplenishment system with known consumer demands.
against an unexpected increase in demand or delay in the arrival of new reagents. Again, this is usually estimated from historical data; in this example the safety stock is set at 20 units. Some replenishment systems initiate a purchase order at the review time regardless of the balance of stock available when the demand is unknown, while other systems change the order quantity so that a maximum quantity is not exceeded. Usually inventory behavior in the clinical laboratory is more complex, and a single replenishment system inadequately explains the difficulty in controlling costs associated with inventory management. As stated earlier, two decisions must be made: how much to order and when to order. The opposing costs associated with each of these decisions are shown in Fig
chase order can range from $25 to $50 in a health care institution, although some institutions have reported costs ranging from $60 to $108.* Carrying Costs Carrying costs are costs associated with holding supplies in inventory from the time an item is purchased until it is used. These costs include taxes and insurance related to inventory, rental, or depreciation of space and fixtures devoted to inventory, security, and janitorial costs to
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where D indicates demand (annual usage in units); P, purchasing costs (cost in dollars of placing an order); I, inventory cost (annual carrying cost expressed as a percentage of inventory cost); and C, cost per unit.
»
high
2.i
Ordering Costs Costs associated with placing a purchase order include direct and indirect expenses such as stationery, postage, and telephone costs involved in order preparation, accounting, and paying the invoice. There are also payroll costs related to review, purchasing, expediting, receiving, inspection, and warehousing of supplies. While a precise measurement of these costs is generally not possible, a reasonable approximation can be made for purposes of comparison. The cost of an average pur-
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Total relevant costs s' Carrying cost
Cost \
\
1
\
1
\ i
low
S
S
•
s
** ***
1
\
*
*•*
^
Economic j order quantity
low
high Supply Quantity
Fig 2. Opposing cost pressures in inventory management.
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Ordering cost
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maintain the storage space, shrinkage, and obsolescence of supplies due to nonmovement, excess, and outdating, and the interest costs of money tied up in inventories.5 Carrying costs are stated as a percentage of the actual unit cost, usually 20%to30%.« From Fig 2, it is evident that ordering costs per unit decrease as the size of the order in number of units increases. It is also evident that carrying costs per unit increase as the size of the order increases. To minimize ordering costs, the manager must place fewer orders; to minimize carrying costs, the manager must keep inventory as low as possible. The challenge then is tofinda balance between ordering cost pressures for large inventories and carrying cost pressures for small inventories, a balance resulting in the lowest order cost and carrying cost. To find this optimum balance, the laboratory manager can calculate the economic order quantity (EOQ) for an item by considering the total relevant cost, the sum of the two opposing costs. The EOQ for a given item can be calculated as follows: 2DP EOQ= IC
Lead Time=30 days Usual Demand*44 units/month Order Quantity • 45 units Safety Stocks20units Review Period-30 days (A)
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orecast Methods Cost-effective inventory management techniques can take advantage of the replenishment system and opposing cost pressures concepts if an accurate system to forecast demand exists. Many traditional methods of inventory control and forecasting project the future based on past experience. Three such forecasting methods were selected for comparison in this study—moving average, exponential smoothing, and linear-regression analysis. Each of these methods is based on statistical averages of historical supply use. The number of review periods used in the calculations is at the discretion of the analyst; six review periods were uniformly chosen for each of the following forecast method descriptions. Moving Average This forecast method predicts demand for the current ordering period by calculating a simple average of use for the past six review periods. The term moving describes the fact that as the next review period occurs, only data from the previous six periods are used in the calculation. Therefore, the average changes because the earliest period data have been dropped. The moving average is a good forecasting technique for items with stable use. If a trend toward increased or decreased usage occurs, however, the method lacks accuracy. Stafford has described a modified moving average technique that includes the following four subset
strategies: (1) demand for last quarter equals demand for next quarter, (2) demand for the same quarter a year ago equals demand for the same upcoming quarter; (3) demand for the next quarter equals demand for last quarter, plus a determined percentage increase; and (4) demand for the next quarter equals demand for the same quarter a year ago, plus a determined percentage increase.7 In this fashion, the historical average is adjusted based on increased demand and a comparable usage period.
period. Abscissa values are the number of items used for the corresponding periods. The slope and y-intercept are determined from the given data, and the forecast is calculated for the current or seventh period as Y7 = (slope X 7)+y-intercept. The existing method for ordering supplies in the chemistry laboratory where this study was done required a manager to review and record stock on hand on a weekly basis. If stock fell below a predetermined volume, the sum of the average used in the past 2 weeks and a 1-week safety stock, an order was initiated equivalent to 1 week's usage.
Exponential Smoothing Exponential smoothing is a calculation of a weighted average, with the most recent period assigned the greatest weight, followed by an exponential decrease of the weight for each preceding period. With this method, usage data for each of the past six periods are multiplied by an exponentially decreasing factor, and the sum of the six products becomes the exponential average or forecast. For example, the number of items used in the most recent period is multiplied by 0.4, the next preceding period by 0.24, until the sixth period where usage data are multiplied by 0.031. The sum of all factors is equal to one. Usage data for this calculation "moves" as with the moving average method. Because use is weighted, exponential smoothing corrects for increased or decreased usage trends.
ethod In this study, the three forecasting methods described above were compared with an existing method of inventory management using five items. Amounts of each item used in 1985 and the starting inventory for that year were required for the analyses. Other analytical variables included order generation, amount of safety stock (demonstrated only with the moving average forecast method), and ordering internal length (review period). The variations of each forecast method are listed in Table I. A computer program, written in Applesoft Basic, facilitated the calculation process and order generations for this study.
Linear-Regression Analysis Linear-regression analysis calculates a demand forecast based on the slope and intercept of the "best-fit" line for usage data during the past six review periods. The period numbers (1 through 6) are ordinate values, with six as the most recent
Order Generation Order generation refers to the method used to calculate the volume to be ordered incorporating elements of forecast demand, safety stock, and current inventory. As displayed in Table I, ten approaches to inventory management were
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Table I: Experimental Design: Variables for Each Forecasting Method Design Number
Forecast Method
Order Generation
Current 1 2
Minimum stock Moving average Moving average Moving average Moving average Exponential smoothing Exponential smoothing Exponential smoothing Linear regression Linear regression Linear regression
(SS+F)-CIV (SS+F)-CIV (SS + F)-CIV ROP/EOQ (SS+F)-CIV {SS+F)-CiV ROP/EOQ (SS+F)-CIV (SS+F)-CIV ROP/EOQ
3 4 5 6 7 8 9 10
Quantity of Safety Stock Avg 1 wk Avg 1 wk Avg 4 wk
Avg 4 wk Avg 4 Avg 4 Avg 4 Avg 4 Avg 4 Avg 4 Avg 4
wk wk wk wk wk wk wk
Interval Length 1 1 1 1 1 1 1 1 1 1 1
wk wk wk mo mo wk mo mo wk mo mo
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From this equation, it should be evident that the optimum order size increases as D (annual usage) or P (ordering costs) gets larger or as I (inventory cost) and C (cost per unit) get smaller. When purchasing inventory in quantities that minimize the total of both ordering and carrying costs, the laboratory manager must also guard against depleting the in-house inventory, thus incurring a stockout cost.2 Clearly when a stockout occurs, provision of service is interrupted and patient care may be jeopardized. Stockout costs include both a loss in revenue and additional costs associated with initiating and receiving a rush order. While the manager cannot predict precisely the quantity of supplies that will be used during a given reorder period, establishing a measurable volume of safety stock should minimize the potential for stockouts.4
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For each of the ten forecast approaches (designs) for ordering, the interval length (review period) was varied, either 1 week or 1 month. Manipulation of this variable demonstrates potential stock-out situations necessitating rush orders. Cost Analysis Cost analysis was used as the definitive method for comparing the amounts ordered for each experimental ordering method. Ordering costs were the actual costs of units ordered based on current cost/unit values. Ordering costs were calculated by multiplying the cost/unit by the quantity of units ordered. Carrying costs, expenses incurred by having items in stock, were calculated by multiplying the order cost by 0.3 (30%). The cost of processing a requisition, the ordering cost, was calculated by multiplying the number of orders by $50. Total annual cost for one item is the sum of the or-
dering costs, carrying costs, and purchasing costs for that item for the year. The grand total is the sum of total costs for all five items for the year. esults and Comment The number of units ordered for each item, the annual number of orders, and the number of rush orders are listed in Table II. The current ordering method used in the clinical chemistry laboratory generated fewer orders than most methods included in the experimental design. Over-ordering, however, particularly for item 2 (60 units/year) and item 3 (84 units/year) increased the total carrying costs for these items. Cost analysis results, including cost savings or losses when compared to the current ordering method, are included in Table III. Over-ordering for items 2 and 3, as described above, caused the grand total
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Table II: Annual Order Data for the Five Items Included in the Comparison' Design Number
Item 1, A-B-C
Item 2, A-B-C
Item 3, A-B-C
Item 4, A-B-C
Item 5, A-B-C
Totals, A-B-C
Current
8-15-2 12-14-2 9-14-1 8-11-1 5-15-1 11-17-1 9-14-1 5-15-1 9-16-1 9-14-1 5-15-1
4-60-0 19-27-4 11-27-1 10-29-0 2-28-0 9-26-1 9-30-0 2-28-0 11-28-1 9-30-0 2-28-0
4-84-1 18-39-2 14-46-0 10-48-0 2-72-0 16-53-0 10-49-0 2-720 16-47-0 10-50-0 2-72-0
2-26-1 7-15-1 6-19-0 5-22-0 1-26-0 6-20-0 5-23-0 1-26-0 7-21-0 5-24-0 1-26-0
4-40-0 22-34-3 18-43-0 10-45-0 3-48-0 19-47-0 9-45-0 3-48-0 18-41-0 9-41-0 3-48-0
22-225-4 78-129-12 38-149-2 43-155-1 13-189-1 61-163-2
1 2 3 4 5 6 7 8 9 10
42-161-1 13-189-1 61-153-2 42-159-1 13-189-1
'A indicates number of orders placed; B, number of units ordered; and C, number of rush orders required.
Table III: Cost Analysis Summary for Each of Five Items With Different Forecasting Designs Design
Total Cost for Each Item, $
Number
1
Current 1 2 3 4 5 6 7 8 9 10
6,718 6,496 6,347 5,033 6,568 7,710 6,347 6,568 7,189 6.347 6,568
2 1,331 1,459 1,059 1,047 1,193 940 1,016 1,193 1,079 1,016 1,193
3
4
5
Grand Total Cost, $
1,783 1,635 1,571 1,405 1,457 1,799 1,424 1,457 1,686 1,443 1,457
1,114 935 1,041 1,108 1,064 1,080 1,147 1,064 1,169 1,186 1,064
2,563 3,109 3,441 3,159 2,986 3,727 3,109 2,986 3,322 2,872 2,986
13,509 13,634 13,459 11,752 13,268 15,256 13,043 13,268 14,445 12,864 13,268
* Forecasting design more costly than current minimum stock method.
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Cost Savings/ (Losses) From Current Method, $
( 125)* 50 1,757 241 (1,747)*
466 241 ( 936)*
645 241
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compared with the system currently used by the clinical chemistry laboratory. With the three demand forecast methods, orders are generated using one of two techniques. In thefirsttechnique, the order was calculated using the following simple equation: order=safety stock plus forecast demand minus current inventory ([SS+F] - CIV). Safety stock was predetermined as listed in Table I, and the current inventory was the volume on hand during the most recent count. The second technique for order generation was based on two calculated parameters, the reorder point (ROP), and the economic order quantity (EOQ). The reorder point was calculated as follows: ROP=SS+(F X LT), where SS indicates safety stock quantity; F, forecast demand; and LT, lead time. When the current inventory falls below the reorder point, the economic order quantity is ordered for the item.
Most of the other methods showed a savings by comparison with the current method with the exception of design methods 1,5, and 8. The additional costs for these methods resulted from a variable common to each: the 1-week review period. Too many orders were generated, and considering $50 per order acquisition charge, these methods were economically inefficient. The 1-month review interval for inventory and ordering demonstrated clear superiority in this study. When comparing forecast methods independent of the order generation formula and review interval variables, moving average is least expensive. For design methods 2,3, and 4, the average cost savings was $683. Average cost differences for the set of experimental smoothing methods (5,6, and 7) and linear-regression methods (8,9, and 10) showed losses of $347 and $17, respectively. By comparison with experimental smoothing and linear-regression methods, the annual number of orders, and the total amount ordered for most items were less using the moving average methods. The moving average methods were found best suited in this study, since annual usage of the five items varied randomly around a similar average. Trends toward increasing or decreasing usage were not observed with these data. No changes were observed among the three forecast methods (4,7, and 10) using
Table IV: Cost Savings Correlation of One Costly Item (1) With Grand Total Savings (r = .962) Design Method
Item 1 Cost Savings/(Losses) From Current Method, $
Grand Total Cost Savings/(losses) for All Five Items, $
1 2 3 4 5 6 7 8 9 10
222 371 1,685 150 (992) 371 150 (471) 371 150
( 125) 50 1,757 241 (1,747) 466 241 (936) 645 241
the ROP/EOQ order generation formula. Orders were generated with different review periods, but annual units ordered and cost totals were equal for each method. These same ROP/EOQ order generation methods were more expensive to use than the methods using the equation (SS+F)—CI V for order generation (3,6, and 9). By cost-analysis comparison, design methods 3,6, and 9 had an average cost savings of $956 as compared to $241 for the ROP/EOQ methods. The annual number of orders was significantly decreased when using ROP/EOQ, but the quantity ordered far exceeded that ordered by the methods using the safety stock plus forecast demand minus the current inventory formula. Because of the greater number of units on hand, holding costs for the ROP/EOQ design methods were higher. The quantity of safety stock used in the order calculations significantly altered ordering quantities and the number of orders generated per year. Design method 1 had a safety stockequaltoal -week average, whereas the safety stock for design method 2 was calculated as the average weekly use of an item times the number of weeks in the lead time (assumed to be 4 weeks). Both design methods used the moving average to forecast demand. Cost analysis comparison of these two methods revealed only a $ 175 difference in favor of design method 2. Fewer units were ordered using design method 1; however, more orders were generated, increasing the ordering cost. The reason for the increased number of orders was that the stock quantity fell to zero several times
throughout the year so that rush orders were necessary. Twelve rush orders were generated for design method 1, whereas design method 2 required only two rush orders. A safety stock quantity that equals the average use for the length of the lead time appears most cost efficient. Interestingly, experimental ordering for item 5 never resulted in a cost savings regardless of the variables used. This phenomenon reflects favorably on the current ordering accuracy by the laboratory for this item. Also, a positive correlation was noted between the grand total cost savings and savings in total cost for item 1 (Table IV). The coefficient of correlation (r) for these data is 0.962, an excellent correlation between the two groups of data due in pan to the comparably high cost of item 1 ($324) to that of the other items ($14.50 to $45.45). Results of grand total cost savings favor a bias toward item 1; however, small savings were also realized with items 2 through 4 forseveral methods.
onclusion The "best" method in this study, based on cost analysis comparison with the method currently used, is the moving average forecast, design method 3. This method used monthly review intervals, order generation using the equation of safety stock plus forecast demand minus current inventory when the safety stock quantity equaled the average length of the lead time. Methods that used 1-week intervals were less cost effective than those using
C
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cost for the current method to be greater than most of the experimental design methods. The current method's total annual cost was $13,509. The largest savings ($1,757) was generated by experimental design method 3, moving average with a 1-month interval length and order generation based on a 4-week safety stock plus forecast demand minus the current inventory on hand. Eleven units of item 1 were ordered by design method 3, only three units less than that ordered by the current system. However, since the cost of this item was high ($324/unit), a small difference in quantity ordered resulted in a large expense difference. When incorporating the 30% holding cost, lower annual costs resulted from a decreased ordering cost for all items except item 5. The number of orders generated by design method 3 was greater than that of the current method, but the additional ordering expense was offset by ordering and holding costs of over-ordered stock for items 2 and 3.
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References 1. Seawell LV: Hospital Financial Accounting Theory and Practice, 2nd ed. Chicago, 111, Healthcare Financial Management Association, 1987, pp 389-395. 2. Bates RT, Buelt JE: Inventory control, in Cleverley WO (ed): Handbook of Health Care Accounting and Finance, Rockville, Md, Aspen Systems Corporation, 1982, pp 525-356. 3. Inventory Control Systems for Laboratory Supplies, Villanova, Pa: National Committee for Clinical Laboratory Standards, vol 3, No 5,1983, pp 166-209. 4. Louvan GE: Inventory management, in Ben-
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nington JL, Boer GB, Louvan GE, et al (eds): Management and Cost Control Techniques for the Clinical Laboratory, Baltimore, Md, University Park Press, 1977,pp 311-323. 5. Sattler J: A Practical Guide to Financial Management of the Clinical Laboratory, Oradell, NJ, Medical Economics Company, 1980, pp 56-65. 6. Eizenga GL, Snyder JR: Inventory management and cost containment, in Snyder JR, Larsen AL (eds): Administration and Supervision in Laboratory Medicine, Philadelphia, Pa, Harper and Row Publishers, 1983, pp 511-539. 7. Stafford AC: Inventory control through focus forecasting. MLO 1985;17:49-53. Downloaded from https://academic.oup.com/labmed/article-abstract/21/2/91/2641802 by guest on 20 November 2018
the 1-month review time. Using the equation (SS+F)—CIV to calculate the order was less expensive than using the ROP/ EOQ technique. Finally, cost advantages were noted for safety stock quantities that were equal to the lead time period. A change in the current system of inventory management used in the clinical chemistry laboratory appears warranted. The most cost-effective method can be implemented using a computer program to facilitate the process. Additional savings could be realized if more items are applied to this inventory management system •
