DYNAMIC BUY QUANTITY: A WORKABLE ALTERNATIVE TRADITIONAL ECONOMIC ORDER QUANTITY METHODS JAMES H. PERRY ASSOCIATE PROFESSOR OF BUSINESS ADMINISTRATION

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1 535 DYNAMIC BUY QUANTITY: A WORKABLE ALTERNATIVE TO TRADITIONAL ECONOMIC ORDER QUANTITY METHODS BY JAMES H. PERRY ASSOCIATE PROFESSOR OF BUSINESS ADMINISTRATION THE GEORGE WASHINGTON UNIVERSITY APRIL 1989

2 5 O *"* 3o INTRODUCTION Many firms, both distributors and manufacturers, utilize a continuous review, reorder point system to manage material inventories. The reorder point, composed of leadtime and safety level, is used to alert the inventory manager when a replenishment order is required. The order quantity, in turn, indicates how much should be reordered. Order quantities (often called operating levels or cycle requirements) provide material to satisfy normal usage between replenishment actions. This order quantity has been traditionally based on the economic tradeoffs which exist between procurement workload (represented by the cost per order) and inventory investment (represented by the cost to hold the inventory). Established order-cost and holding-cost parameters, and an estimate of steady-state demand for the item in question, are used to compute an Economic Order Quantity (EOQ) - the quantity of material for which item annual order costs and annual holding costs are balanced to minimize total variable costs. This EOQ is then typically passed, via the procurement process, to the vendor as an order requirement. This paper examines the process used to determine these so-called "economic order quantity" requirements and evaluates the effectiveness of current EOQ techniques in an operating

3 environment where some, if not most, of the critical underlying assumptions do not hold. CONCEPTUAL FOUNDATIONS The theoretical purpose of the order quantity is to provide a level of material to cover normal operating requirements between replenishment actions. The quantity of material to be ordered conceptually balances the firm's procurement workload (and cost) and inventory investment. In customer environments where demand is random, this EOQ methodology is extremely common. It should be noted, however, that this general approach involves several critical assumptions: o Order cost and holding cost parameters used to determine the EOQ are accurate and consistent, o Material ordered is received in one delivery or is phased at a constant rate over the full procurement leadtime. o The administrative processing time (or administrative leadtime) which derives from the system is reasonable in terms of processing capabilities and does not unduly impact other investment costs (such as investment in safety level). o The price paid is not a function of the quantity ordered.

4 o Demand is reasonably accurate and is "steady-state" over the period in question. The so-called Economic Order Quantity concept was first introduced by Harris 1 in This basic lot-sizing approach to balancing operations and costs was later updated by Wagner and Whitin2 to reflect the dynamics of the reorder process and has been further refined by many authors over the years. 3 Based on order cost and holding cost parameters (which are typically specific to the item in question) the EOQ approach computes an economic order quantity to serve as the buy quantity over time. Fordyce and Webster, 4 Tersine and Toelle5 and LaForge and Patterson6 have specifically examined the impact of unit cost or price variation on the traditional Wagner-Whitin formulation while Ritchie and Tsado, 7 ' 8 Donaldson, 9 Silver, 10 Ritchie 11 ' and Woolsey and Lienert 12 have addressed the conceptual issue of demand variation and have proposed alternative approaches to deal with the existence of known demand variation. While all the assumptions on which the EOQ concept is founded may be inappropriate for some items, three assumptions are particularly suspect in many operating environments and require further examination. First, based on the typical operating environment of the firm, order costs reflect a valid

5 approximation of the cost to order only at a stated or given administrative leadtime level. Indeed, to estimate these costs most firms use historical procurement workload and cost data. No explicit consideration is generally given to the associated administrative processing times related to these order costs. However, these administrative leadtimes are one major factor which influences the determination of safety level in reorderpoint systems. As a result, it is possible that understated order costs (by not incorporating administrative leadtime impacts) may not fully reflect the real cost to order to the firm. Second, price and quantity relationships may be quite strong for certain items and should be recognized in the material management and purchasing process. Unfortunately, these specific price-quantity tradeoffs do not typically surface until after order quantity is determined and the information on pricequantity options may not be available until the time that the buy is awarded. Finally, demand variation over the procurement cycle is often significant and can substantively impact the real requirement. Failure to appropriately recognize and incorporate demand variance in the actual buy decision introduces the possibility of two alternatives, namely long-supply/excess assets or material shortages.

6 540' -5- METHODOLOGY This study addresses the potential impacts of these separate assumptions in a typical operating environment where the administrative leadtime, price, and demand assumptions normally invoked in EOQ-systems may not hold. In order to assess the potential impact of market dynamics in an EOQ-based replenishment environment, the material management and procurement processes of a large, multi-national wholesaler were examined. Using a statistical data sample of approximately 800 stocked items, the study analyzed the three primary factors which tend to weaken EOQ-based models, namely the impact of administrative leadtimes, the relevance and impact of quantity discounts on the least-cost buy quantity, and the dynamics of customer demand over the procurement cycle. The original data sample was drawn in March In July 1987, this sample information was updated, thus providing the status of those same items approximately 15 months later. The two criteria for selecting sample items were that their EOQ order quantities would normally compute to a quantity of less than one (1) year and that overall demand stability was considered sufficient by the firm to allow the item to be managed under EOQ methods. Table I below provides a profile of the item sample at the two points in time.

7 54i -6- TABLE I Item Sample Profile Months status Dollars status Months Dollars 3 Average inventory Order quantity Safety level Administrative leadtime(alt) Production leadtime (PLT) Annual demand value a) 1987 dollars in millions. RESULTS Based on this item sample, the impact of order quantities on procurement workload over the period analyzed was unclear. Today's material management and purchasing environment is highly volatile and policy and procedural changes in many diverse functional areas generate additional workload, which affects the ability of the organization to manage the resulting throughout. Thus, purchasing workload is often particularly difficult to forecast.

8 -7- As shown in Table II, an overall 20 percent decrease in the volume of purchase requests processed was experienced by the organization, however, this decline could not be quantitatively linked to the size of the order quantities used. This is because many other factor also changed during the fifteenmonth period including processing requirements, buying methods, and the mix of total workload flowing through procurement. For example, some of the procurement workload reduction resulted from innovative multiple-year procurement methods. However, at the same time additional processing requirements were added which increased administrative leadtimes. While procurement workload declined by about 20% over the period, staffing remained relatively constant, and administrative leadtimes increased by 30%. Table II PROCUREMENT WORKLOAD VOLUME (Thousands of Purchase Requests) Buying Office Purchase Request Change Percentage change A BC D Total - 1,

9 Second, the analysis clearly indicates that, for this data sample, significantly opportunities exist to exploit vendor production or distribution economies. Thus, price-quantity alternatives are available and can be readily identified. By far the most successful technique being used by the organization was the solicitation of multiple quantities (ranges) based on the order quantity requested in the purchase request. In some cases, these were specified percentages (50 percent, 75 percent, 150 percent, etc.) of the purchase request quantity, while.in other cases alternative quantity ranges were used. Through this method, the organization was able to elicit quantity discount alternatives specific to the line item in question and was able to exploit these quantity discount alternatives where appropriate to minimize total cost to the organization. Moreover, we found that valid PC-based evaluation models had been developed and had been implemented to mechanize and standardize the process of evaluating alternative price-quantity combinations. Finally, the data sample examined strongly suggests that demand volatility represents a major issue in the application of. traditional EOQ methods. Since these items had been identified as stable-demand items, demand was expected to be reasonably constant over the period encompassed by the two samples. The results, however,

10 A \ -9- indicate a striking variability in demand. As seen in Table III, of the 789 items in the sample, demand increased for 255 item (32.3 percent), declined for 512 items (64.9 percent), and remained the same for 22 items (2.8 percent). Almost two-thirds of the sample experienced demand changes greater than 20 percent, either up or down. Of the 512 items with demand decline, twofifths had demand drop off greater than 40 percent. The demand data used were forecast demand, which is smoothed; actual demand variation was even greater. TABLE III DEMAND CHANGE IN ITEM SAMPLE Percent decrease Percent increase Number of items Total -512(64.9%)22(2.8%)255 (32.3%) A DYNAMIC BUY QUANTITY CONCEPT Based on our analysis, we believe that strict application of EOQ principles in determining the order quantity fails to properly compensate for existing purchasing workload constraints,

11 does not adequately recognize the possibility of quantity discounts on selected items, and ignores the potential for substantial demand variance. Balancing order costs and holding costs through the use of traditional EOQ methods may be a valid approach for determining general inventory requirements, for basic budget development, and for generating an initial target stock replenishment order quantity. This so-called EOQ should not be accepted as the ultimate buy quantity, however, without adjustment as necessary for changes in demand, asset position, and available price-quantity discounts at the time the purchase is actually made. Thus, traditional EOQ should be viewed as an economic order quantity, not necessarily an economic buy quantity, and indeed, the information necessary to determine an economic buy quantity is generally available only at the time of award. In recognition of the potential deficiencies of the EOQ approach, a basic strategic change in purchasing and materials management policy is necessary, a change that will exploit existing market opportunities on a selective basis while integrating the efforts and objectives of the inventory management and procurement functions. This Dynamic Buy Quantity concept has the following characteristics or elements: o Use of EOQ methods only for generating a target order quantity for solicitation purposes. This EOQ approach

12 -11- should be designed to recognize the economic tradeoffs between order cost and holding cost. Routine solicitation of quantity ranges (as multiples of the EOQ quantity). Given the proven success of this approach in creating opportunities to make costeffective buy decisions, this technique should be a standard part of most purchasing actions to provide the flexibility to adjust to demand and asset changes during the administrative leadtime and at the same time effectively generate price-quantity options where they exist. These options can in turn, typically be employed directly in purchase decision without further interaction with vendors. Moreover, the method also gives the supplier incentives to provide price breaks where production and distribution cost economies will allow. Determination of the Dynamic Buy Quantity at the time purchase is actually made using the quantity discount information (and other relevant data such as current demand/asset position by adjusting the initial EOQ target quantity. This approach will allow the buyer to be selective in that the recommended EOQ-based quantity would be adjusted in the buying process only in those specific instances in which the price-quantity data

13 indicate a lower total cost to the firm that can be defended based on known line item data. The actual buy quantity, determined by the buyer in consultation with the inventory manager when necessary would be dynamic and could be determined by the input of price-quantity options into a structured evaluation process which would determine total cost to the firm for each option and recommend the optimal buy quantity to the buyer for the final purchase decision. Total cost to the firm would include not only the actual material costs associated with each option, but would also consider transportation, inventory investment, and relevant administrative costs in making a recommendation. Such evaluation techniques and models exist, are computationally sound, and provide creditable and defensible logic to support dynamic buy quantity decisions. POLICY IMPLICATIONS The management policy implications of this shift are dramatic. The approach essentially recognizes that for inventory management purposes, the basic traditional cost tradeoffs between order cost and holding cost remain valid and appropriate in development general inventory requirements and in providing a target range for solicitation. At the same time, the strategy

14 -13- provides an effective vehicle for dealing with real price differentials associated with the buy quantity by acquiring and using the specific vendor data necessary to effectively evaluate and exploit purchases opportunities and allows the buyer to adjust to market dynamics and demand changes. It represents a reconciliation of two diverse, but equally valid, views of the stock replenishment process. Finally, while today's distributed information processing systems have many of the capabilities necessary to implement the strategic policy thrust noted above, these capabilities are often not fully-integrated into main, online processing systems, do not currently provide mechanized feedback to inventory management files, and may not have not been utilized with the purchasing volumes anticipated under this concept. Accordingly, the move to Dynamic Buy Quantity policy, where the actual buy quantity is routinely determined at point of purchase, may also require associated changes in information processing resources. Several specific systems capabilities are necessary. First, many off-line evaluation models now in use must be integrated to the extent feasible into the firm's normal on-line processing flow. Second, when the buyer purchases a quantity larger than the EOQ quantity the firm's inventory management structure and processes must recognize that decision

15 -14- as a valid inventory requirement. Third, an appropriate financial management process must be developed to effectively accommodate purchase quantities larger than the initial EOQ-based order quantity. In summary, the continued application of strict EOQ-based quantities in the purchasing process does not adequately address the dynamics of the interaction of customer demand, time, and market conditions which must be incorporated at the line item level to make a reasoned buy quantity decision at the time purchase. These shortcomings argue for a major strategic change to current EOQ based material management. This strategic shift, which may require information systems changes and revised processing rule in many companies is essential to effective materials management in the future.

16 Endnotes 1. Harris, F.W., "Operations and Cost, Factory Management Series, A.W. Show Company, Chicago, (1915), pps Wagner, H.M. and Whitin, T.M. "Dynamic Version of the Economic Lot Size Model," Management Science. Volume 5, No. 1 (October 1958), pp See Aucamp, D.C., "A Variable Demand Lot-Sizing Procedure and a Comparison with Various Well Known Strategies," Production and Inventory Management, Vol, 26, #2, pps. I Fordyce, J.M. and Webster, F.M., "Nonconstant Unit Cost/Price with the Wagner-Whitin Algorithm," Production and Inventory Management. Vol. 26. #3. DPS. II-80. Inventory Management, 5. Tersine, R.J. and Toelle, R.A., "Lot Size Determination with Quantity Discounts," Production and Inventory Management. Vol. 26, #3, pps La Forge, R.L. and Patterson, J.W., "Adjusting the Partperiod Algorithm for purchase Quantity Discounts," Production and Inventory Management, Vol. 26, #1, pps Ritchie, E. and Tsado, A., "The Penalties of Using the EOQ: A Comparison of Lot Sizing Rules for Linear Increasing Demand," Production and Inventory Management. Vol. 27, #1, pps Ritchie, E. and Tsado, A., "A Review of Lot Sizing Techniques for Deterministic Time-Varying Demand," Production and Inventory Management, Vol 27, #3, pps Donaldson, W.A., "Inventory Replenishment Policy for a Linear Trend in Demand - An Optimal Solution," Journal of the Operational Research Society. Vol. 28 (1977), pps

17 rr Silver, E.A., "A Simple Inventory Replenishment Decision Rule for a Linear Trend in Demand" Journal of the Operational. Research Society, Volume 30 (1979), pps Ritchie, E. "Practical Inventory Replenishment Policy for a Linear Trend in Demand followed by Steady Demand," Journal of the Operational Research Society. Volume 31 (1980), pps Woolsey, R.E.D. and Lienert, C.E., "Ordering Inventory When The Forecast Is Ridiculous," Production and Inventory Management. Vol. 27, #1 (1986), p. 144.

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