eoq (economical order quantity) for management collage

Socio-&on Plan Sci Vol. 16, No. 1, pp. 3%50, 1982 Printed in Great Britain

~3~l21/82/010039-1wM.ool0 Pergamon Press Ltd.

APPLYING MANAGEMENT SCIENCE IN DEVELOPING COUNTRIES: ABC ANALYSIS TO

PLAN PUBLIC DRUG PROCUREMENT?

JONATHAN D. QUICK Management Sciences for Health, 141 Tremont St., Boston, MA 02111, U.S.A.

(Receiwd 10 June 1981)

Abstract-Despite the vital role of pharmaceuticals in the prevention and treatment of major causes of death and disability in the developing world, high costs and frequent shortages remain chronic problems for drug supply programs. Yet, management techniques developed to optimize the use of scarce resources have had limited application in the settings of greatest need.

An important determinant of the cost and supply of drugs is the procurement pattern. This study reviews procurement patterns in selected public supply programs and, using management science techniques, compares alternative procurement patterns in terms of inventory costs and shortages. Using drug cost and quantity estimates from two countries, a simulated ABC value analysis was performed. This analysis showed drug inventories to be typical of industrial inventories: Over 80% of the consumption in dollars was accounted for by less than 20% of the drugs. Procurement patterns with more frequent purchasing or delivery of high usage drugs could reduce average inventories 20-X% over the commonly observed annual purchasing pattern.

Sensitivity analysis of the results confirmed that variability in the delivery time and consumption pattern has a significant impact on the efficiency and economy of a procurement system. Closer supplier monitoring and better forecasting should reduce this variability.

We found that methods of management science-specifically, ABC value analysis and sensitivity analysis-are feasible means to evaluate procurement patterns in public drug supply programs and that the results of these analyses have a great deal of practical significance.

1. INTRODUCTION

In a 1975 policy paper, the World Bank concluded that the major causes of poor health in developing countries were demographic factors, malnutrition, sanitary conditions and poor housing[l]. Although the primacy of these factors is undeniable, it must also be recognized that many, if not most, of the diseases which account for death and disability in developing countries are prevent- able or treatable with pharmaceutical products.+ Pneu- monia, much of it bacterial, is among the top three killers in numerous developing countries, including Peru, black South Africa, Chile, Kenya and Papua New Guinea[2]; diarrhea1 disease, which kills millions of infants and children each year, is controlled and its mortality is significantly reduced with availability of simple glucose- electrolyte sachets [3]; despite the availability of vaccines, measles a major killer in many parts of the world and poliomyelitis continues to kill or cripple hundreds of thousands each year; tuberculosis, for which effective treatment has long been available, also remains a dominant cause of death in many countries; and so on[2].

tLJnless otherwise noted, references to specific developing countries are based on first-hand observations by the author or other Management Sciences for Health field staff: In 1978, under a Technical Services Ameement with the World Health Organization, the author visited seven countries to study pharmaceutical supply in public health programs. This study was supported ir@art by the World Health Organization, Manage- ment Scienc& for Health, and a Year-Out Fellowship from the University of Rochester School of Medicine, Rochester, New York, U.S.A.

$In this paper pharmaceutical products and drugs will be used interchangeably to refer to any drug product used in prevention or treatment, including vaccines, oral rehydration sachets, tablets, capsules, injectables and galenicals.

Despite the potential role of pharmaceuticals in preventing death and disability in the developing world, the annual per capita expenditure for pharmaceuticals is below one US dollar in many developing countries and it is estimated that 60-80% of the population of the developing world is without constant access to even the most essential drugs[4]. Where government funds are allocated for drug procurement, they may account for as much as 40% of the health care budget, making the efficient management of drug expenditures an important consideration of health officials [5].

In addition to the direct health impact of pharmaceutical products, their striking effectiveness against some of the common serious diseases such as malaria and pneumococcal pneumonia has impressed rural populations and often serves to establish credibility for new and often suspect community health workers. Such credibility is essential in achieving long term environmental and nutritional changes in the basic health determinants.

Despite the potential public health impact of pharmaceutical products, high costs and frequent shortages remain chronic problems for drug supply. The reasons for this are many-fold. The role of the commercial pharmaceutical companies in encouraging irrational and excessively costly drug utilization has been well-docu- mented and cannot be over-emphasized[6-91. At the other end of the spectrum, local health beliefs frequently push physicians and auxiliary medical workers into prescribing practices which deviate sharply from standard medical training and which ineffectively utilize limited drug resources. Another, almost ubiquitous, reason for drug shortages is the limited funds available to the public or the government with which to purchase or distribute drugs.

It is the underlying assertion of this study that, despite these barriers, substantially greater use could be made of

39

40 J, D. QUICK

available resources through improved management of the procuremem process. Unfortunately, sound planning and supplies management practices which have been developed by cost-conscious government and commercial enterprises in industrialized countries have only recently been applied to public management problems in developing countries. Ironically, analytic techniques designed to optimize the use of scarce resources have seen little application in the settings of greatest scarcity.

The purpose of this study is to demonstrate the potential value of specific management science techniques, classical inventory models and ABC value analysis, in scheduling drug procurement for a public health program. The analysis is based on a comparison of the expected inventory holding costs associated with six different procurement schedules. The costs were determined through simulation, using data from two national drug supply programs and assumptions based on the experiences of numerous developing countries visited or studied by the author.

Although the study focuses on drug procurement, the results are applicable to public procurement of dispos- able supplies of any type.

2. DRUGPROCURJMENTINPUBLICHEALTHPROGRAMS Multinational pharmaceutical corporations and a

growing number of local producers serve an increasing commercial drug market in developing countries. At the same time, more and more ministries of health are organizing centralized bulk purchasing and distribution of drugs essential to provide primary health care to rural and medically indigent populations.

To understand current procurement practices and to compare the effectiveness of various models, it is useful to first review basic inventory concepts[1&12].

(a) Classic inventory models The basis for understanding procurement practices is

the classic inventory problem: balancing the benefits of holding inventory against the costs of inventory. The benefits of keeping stock on hand are that it allows timely delivery to dispensing points, it protects against uncertainty in the delivery of new stock or in the demand for stock on hand, it increases transportation efficiency by allowing large volumes to be delivered periodically, and it facilitates bulk purchasing. From the viewpoint of a patient in a health system, drug inventories exist to assure that when he is sick, the correct medicine is in the country and available to him at the right time.

But inventories are costly to maintain. There is a capital cost, as if the drug inventory were a loan. The capital cost of inventory is generally valued at the prevailing bank interest rate, which ranges from 10 to 30%, depending upon the country and the prevailing financial cdnditions. Other inventory holding costs include storage expenses, losses due to expiration and spoilage of supplies, pilferage, and the change-of-preference cost which occurs when drugs in inventory fall from favor among prescribing physicians.

Inventory holding costs are determined by the average volume of the inventory, which is a function of order quantities and safety stocks. Safety stocks, also known as buffer stocks, are extra inventory kept on hand to protect patients from shortages caused by variation in demand, ordering time, and supplier lead time. By raising the inventory level, safety stocks decrease the likelihood of shortages, but they increase the holding costs.

In commercial enterprises, the optimal safety-stock level can be estimated using several bits of information, including the loss of income which occurs if there is a stockout. In pharmaceutical supply, as in other public service enterprises, there is no financial optimum, since there is no loss of income from a stockout. Instead, the cost of additional safety stock must be weighed against the potential health impact of shortages.

The term used to describe the stockout frequency is service level. Service levels can be defined by the number of stockouts per order cycle, the number of stockouts per year, the fraction of demand which can immediately be filled, or the fraction of operating days in which demand can be met [lo].

To measure the service level for a pharmaceutical supply system, the third method provides the most easily interpreted and intuitively attractive measure. For this method a service level of 99% means that for every 100 units of an item which are requested, on the average, 99 units will be immediately available.

On the basis of standard probability theory the safety stock required for different levels of service can be calculated from available information concerning the lead time, variability of the lead time, the demand, and the variability of the demand[lO]. Details of this calculation are presented below.

Although numerous variations exist, inventory models are classically divided into perpetual and periodic systems[lO-121. When demand is constant and lead time is constant, both systems can be represented by the ideal inventory model (Fig. 1). In this model drugs are issued in response to demand the quantity steadily declines until the point where an order must be placed. Following a lead time period, during which consumption continues at the same rate, drugs are received and the inventory is back to its starting point.

In the perpetual system the same number of units is always ordered, but the order interval varies with the demand rate. The perpetual inventory system naturally adjusts to changes in demand through the shortening or lengthening of the order interval. In this system, the crucial decision for the inventory manager is the est- ablishment of the order quantity. In public service purchasing, the desired level of service is weighed against the acquisition costs, holding costs, order costs and possible stockout costs to determine the order quantity.

In the periodic inventory system the order interval remains constant and the number of units ordered varies. Each time the order interval has passed, the inventory position of each item is reviewed and an order is placed for an amount which will return stock levels to a pre- established maximum. The periodic system has no in- herent mechanism for adjusting to transient changes in demand. Therefore, it must rely on having set tile maximum inventory level high enough to fulfill average supply needs during the order period and lead time as well as to provide a generous safety stock for variable demand and lead times.

The most critical decision for the manager of a periodic inventory system is the choice of the optimal order interval. As in the perpetual inventory system, standard formulae exist which allow the commercial manager to use available cost and demand information to calculate the economic order quantity, but which require the public service manager to make some more subjective choices regarding the trade-off between cost and service level.

Applying management science in developing countries

Ideal Inventory Model

41

cl+S

I i x f; E J 0

S

Order Placed

\

-----

Time *

Fig. 1. The ideal inventory model.

Although drug procurement systems have developed under a variety of political and economic circumstances, there is surprisingly little variation in the basic inventory system structure among countries known to the author. All of the systems studied fit into one of the two classic inventory models. One special type of periodic inventory system, annual purchasing, is common enough to deserve separate discussion. The following survey provides an overview of the models currently used by public health programs and a summary of the experiences which certain countries have had with these models.

(b) Annual purchasing Procuring drugs through a single major annual pur-

chase is a common, if not the most common, purchasing pattern used by government procurement officials. Under this system, drug requirements are determined once annually and contracts are awarded to suppliers for one years expected drug consumption. Countries using this system generally have mechanisms for placing sup- plementary orders throughout the remainder of the year, should the need develop.

The popularity of the single annual purchase is attri- butable to several factors. First, in some countries the accounting policies of the ministries of health or finance effectively require that funds be committed and expen- ded within the same fiscal year. To accomplish this, drug procurement agencies initiate purchases early in the year so that drugs will arrive before the end of the fiscal year.

Annual purchasing is also advantageous when purchasing is done on the basis of estimated requirements submitted by a large number of separate health facilities. By requiring estimates to be submitted once annually from each consuming health facility, the expected needs can more readily be collated to obtain the total purchase

tit also appears that single annual purchases may contribute to collusion among bidders. Suppliers may find bidding on all items at one time to be extremely risky. If a company bids low on too many items its capacity will be over-committed and it will either have to renig on some items, thereby jeopardizing its reputation with the government, or sub-contract certain items, which is likely to cost more than the bid price. If a company bids high on too many items, it may receive no government contracts and, as a result, it will have its capacity severely under-utilized. In at least one Central American country which purchases drugs by annual bidding, manufacturers allegedly met routinely before submission of annual bids and allocate items among each other.

requirements for the year. In Sri Lanka, e.g. the State Medical Stores requires each of the 15 health regions served by the Ministry of Health to prepare an estimate of annual drug needs each October. These estimates are then consolidated and reviewed by the State Medical Stores. By January the final list of drug requirements is prepared and presented to the procurement section.

The single annual purchase also facilitates the comparison of estimated drug needs with available funds. In Costa Rica, concern over Ministry of Health drug expenditures led in the mid-1970s to the formation of a special General Inventories Department responsible for coordinating the supply system. Among its other res- ponsibilities, the General Inventories Department must review the annual estimate of drug requirements, compare the estimated acquisition cost with available funds and make any adjustments necessary to reduce purchases to within the allowed budget.

Lastly, annual purchasing is a convenient way to stock a drug supply system at its inception and may remain the purchasing pattern simply because procurement officials do not look beyond the single annual purchase after having begun with it.

Despite the appealing aspects of the singie annual purchase, there are several recurrent problems which substantially limit the efficiency and economy of such a system. One major limitation is the uneven work load which results from a single annual purchase. The staff with purchasing expertise are overwhelmed during the first part of the !&al year by the need to initiate the orders and to negotiate purchase contracts. During the second part of the year, these individuals are less active, while the wharf-clearing, checking, and warehouse staff are seriously overburdened.

Another problem with this purchasing pattern is the very large sum of money and foreign exchange that is required within a very short period. This may create difficulties in completing payment and clearing the goods from the port.

The single annual purchase is also costly in terms of inventory balance and holding costs. When drugs are ordered once yearly, then the value of the average inventory will exceed 50% of the value of annual drug consumption, with corresponding holding costs in the hundreds of thousands of dollars or, for very large systems, in the millions of dol1ars.t

42 J. D. QUICK

Another difficulty with annual purchasing is that it does not adjust well for changes in consumption patterns. For highly variable items, it is difficult for such a system not to err, either by buying in excess and incur- ring additional holding costs or by buying quantities which prove to be inadequate.

(c) Periodic purchasing Periodic inventory systems with a standard order in-

terval of less than one year appear to be less common. Papua New Guinea (P.N.G.) operates a highly structured periodic system. Over 90% of the drugs consumed in that country are provided through the Pharmaceutical Ser- vices Section of the Ministry of Health. Because of major geographic barriers and the reliance on air and sea transportation, P.N.G. found it advantageous to establish six regional medical stores to which overseas suppliers make direct shipments and from which all drugs are dispatched to the six regions served by the stores. Since the requirements of all six stores must be collated to determine order quantities, a perpetual inventory system would not be feasible. Instead a periodic system was initiated.

P.N.G.s system divides items into three categories, depending on whether contracts are negotiated once, twice, or three times per year. Dividing shipment on annual purchases further reduces storage space, cuts holding costs and distributes the stock-handling workload more evenly throughout the year. Review of the purchasing and delivery schedules suggests that the average value of the inventory should be 20-30% of the annual consumption, rather than the 50-60% found in ,annual-purchase systems.

Periodic inventory control was also observed in a Southeast Asian country whose Government Medical Stores handled over US $20 m in medical supplies during 1977. This included a large volume of non-pharmaceutical supplies. The 7000 item inventory is divided into twelve major categories, one of which is reviewed each month. On the basis of this review, purchase quantities are determined and purchasing is initiated. The order quantity is, therefore, equal to one years consumption. Finished dose pharmaceuticals (injectables, tablets, capsules, etc.) are reviewed and ordered twice annually. For the most essential or highly used drugs, consumption information maintained at the main warehouse is sup- plemented by projections of future demand which are provided by the chief pharmacists in each of the health regions. With order quantities equivalent to six or twelve months worth of stock, it is not surprising to find that the average inventory in 1975 was about US $10 m with drug issues of $18 m.

(d) Perpetual purclshsing Variations of perpetual inventory systems are found in

Sri Lankas State Pharmaceuticals Corporation, Tan- zanias National PharmaceutiCalsCompany, and Costa Ricas prepaid health service foremployed persons. In at least two of these countries the perpetual inventory system was implemented after difficulties with shortages and/or high costs led to a review of inventory control policy. Since the operation of a perpetual inventory system requires frequent review of inventory records, it is not surprising that those programs using perpetual inventory control tend to have more complete drug utilization and consumption information.

The selection of the order quantity for each item is the

major determinant of the average inventory level and the average order interval. From item to item and country to country order quantities in the perpetual inventory systems varied between two weeks and one year worth of stock. Infrequently used items and items which were difficult to obtain tended to be ordered at yearly intervals. In each of the systems items were classified by their frequency of use, unit cost, shelf-life, utility value to patients and/or lead time. The classifications were used to determine order quantities. In Costa Rica and Sri Lanka, for example items were divided by the value of the total annual consumption into three categories. The items which accounted for the largest percent of the total value were purchased most frequently. In Sri Lanka order quantities were set at six or twelve months worth of stock, with the fast moving items having a six month order quantity.

Review of the inventory level can be daily, weekly, bi-monthly or monthly. Less frequent inventory review reduces clerical time needed to initiate orders. The perpetual inventory system offers at least three advantages over other systems. First, as noted above, perpetual inventory systems are inherently more responsive to changes in demand. Since items are reviewed and purchase orders are initiated on an item by item basis, it is possible to establish different order quantities for different types of items. By establishing order quantities which reflect the demand characteristics of the individual drug, the average inventory level and, therefore, the holding costs can be minimized with the least possible decrement in service level.

But there are two main disadvantages of the perpetual system. First, in countries such as Papua New Guinea and Peru, where contracting for drug supplies is done centrally, but no central warehouse exists and drugs instead are delivered directly to multiple health facilities or regional stores, use of the perpetual inventory system would seriously complicate the process of determining order quantities for individual items. Second, the perpetual inventory system makes it more difficult to plan and control the cost of drugs at the central level. If there are a limited number of purchases each year, then the estimated value of each set of purchases can be compared against the available funds and adjustments can made in the drug selections or order quantities. When there are twelve to fifty or more purchases per year, each for drugs in a variety of categories, it is more difficult to devise a system which assures that the total expenditures for the year will not exceed the budgeted amount. This problem has been minimized in Costa Rica by careful review of purchase quantities for each order and by careful monitoring of drug expenditures. In other drug programs which use perpetual inventory, the drug program often serves as an intermediary agent which sells the drugs to other health services. Under this system the drug procurement officers are concerned only with efficient inventory control. It is the responsibility of the individual health services to adjust their requisitioning to assume that funds are available throughout the year for the most needed drugs.

3. METHODOFANALYSIS

In the commercial sector, the optimum order quantity or order interval represents the economic balance of several cost factors. In drug procurement programs, the balance is between the acquisition, holding, order and stockout costs and the service level. Inventory formulas

Applying management science in developing countries 43

can be used to estimate the cost of achieving a specified service level, but they cannot estimate the health impact of a 1% stockout frequency vs a 20% stockout frequency. In practice, the manager of a drug procurement program is usually faced with a limited, pre-determined budget, within which he must provide the highest service level possible.

The analysis in this section will compare the costs and anticipated shortages associated with several alternative ordering patterns. The purpose is to illustrate the major impact which the procurement pattern can have on average inventory levels, the annual holding costs and the frequency of shortages. It is recognized that there are additional factors which are relevant in determining order intervals and order quantities: the availability of warehouse facilities, the shelf lives, the influence of seasonal changes on consumption and in-country transportation, and the number and type of overseas transportation routes must all be considered in the final decision. Therefore, this analysis should be viewed as demonstrating a methodology for developing a major portion-albeit not the only portion-of the information needed to establish the most economical procurement pattern.

(a) Country drug lists Complete consumption and cost data is difficult to

obtain for public drug programs, but approximate information was available for two countries. Since this information is used primarily as a tool for the analysis, rather than as the subject of the analysis, the countries are identified only as Country I and Country II. The two drug lists used for this simulation do not represent ideal lists, model lists or even suggested lists. They are merely the drug lists used by public heatlth programs in two countries studied by the author. Neither drug list includes narcotics or vaccines, since they are procured and/or regulated through separate channels. Otherwise, the lists include the entire spectrum of pharmaceutical products.? Country I is a very mountainous, primarily rural, agricultural Asian country with an estimated population of 20 m people (1977) and an estimated per capita gross national product of US $130 (1975). In the early 197Os, to improve the effectiveness and economy of pharmaceutical utilization, a senior committee appointed by the Minister of Health revised the national formulary and developed a list of about 400 drugs.

For the simulation, drug quantities were obtained as estimates from officials at the main medical depot and from epidemiological data concerning the population distribution and disease patterns. Prices (1974 F.O.B. country of origin bids or 1973 purchase price) and quantities were available for 344 drugs, the total value of which represents an estimated 80% of all drug requirements for the country. The total value of the 344 drugs purchased at the estimated quantities is US $14,787,144. The cost of 100% coverage would therefore be US $18,483,930, nearly US $1.10 per person for the 1974 population or slightly less than one percent of the per capita gross national product.

Country II, which includes desert, high sierra and jungle terrain, is dependent upon, in order of importance, manufacturing, agriculture and fishing, and mining. Fifty-

tComPlete listings, including ABC category, are available from the author [13].

five percent of its estimated 16.6 m inhabitants are urban dwellers (1977) and the estimated per capita gross national product is US $810 (1975). In 1978 the combined public and private expenditures on drugs were ap- proximately US $65 m. This represents about US $3.80 per person or less than one-half percent of the gross national product. In 1972, a program to provide basic drugs was established as a special government program to supplant a disjointed and unreliable drug supply system. The program now serves all Ministry of Health programs in urban and rural communities, a public health service which treats a large sub-segment of the working population, all armed forces and police health programs, local government programs, and numerous semi-public industries. The first drug list in 1972 contained 185 items in 265 dosage forms and the 1978 list contains 295 items in 428 dosage forms. However, only 291 of the 428 listed items were included on the list for bid solicitations in 1977-78. Quantities used for this study are the programs estimated 1977-78 requirements, which were based on the experience of the previous five years and projections of future usage. The prices represent the delivered to user cost as of February 1978. Of the 291 drugs for which quantity estimates were made, prices were available on 220. The total value of the 220 drugs purchased in the estimated quantities is US $9,218,322, which represents 70% of the programs total drug expenditures of approx. US $13,150,000.

(b) ABC analysis For illustrative purposes, we assume that a perpetuql

inventory system is in use and, therefore, it is the selection among different order quantities which is to be compared. If the average demand is assumed to be constant, then order quantities can be expressed in terms of the number of months of consumption fulfilled. If the order quantity is equivalent to four months of consumption, then three orders will be placed each year.

The work of the procurement section is minimized by establishing large order quantities which result in in- frequent orderings. Large order quantities often yield more favorable bulk rates. However, the larger the order quantity, the larger the average inventory and, therefore, the larger the inventory holding costs. Order quantities can vary from item to item. In establishing tlie. order quantities, the objective is to minimize the number of orders per year, obtain favorable bulk rates wherever possible, and at the same time minimize the average value of the inventory. These seemingly contradictory objectives can in part be realized through an ABC value analysis.

It is a well-known observation in inventory management that most of the value of annual consumption is accounted for by a relatively small number of items. It has been found useful to carry this observation further by categorizing items into three classes according to their annual dollar usage (unit cost times the number of units consumed annually)[l$14]. Class A items have the highest annual usage, with lO-20% of the items accounting for 7@-80% of the dollar usage. Conversely, class C items account for 60-80% of the items and only 5-25% of the dollar value of annual consumption. Becavse of their high dollar usage, it is advantageous to reduCe the inventory of class A items by purchasing smaller quantities more frequently. At the same time, the values of class A items are such that bulk discounts can still be anticipated and class A items are few enough in number so that more

44 J. D. QUICK

frequent ordering of these items has a limited impact on the work of the procurement section.

The cutoff point between class A, B and C items is flexible and varies with the type of items under consideration and their consumption pattern. To classify items, the annual dollar usage of each item is calculated and the items are arranged in descending order by the annual dollar usage. The cumulative dollar usage is then plotted against the cumulative number of items. Arrangement of the items in the Country I and Country II drug lists results in the usage curves presented in Fig. 2.

Based on changes in the contours of the curves, the Country I and Country II drug lists were divided into A, B and C categories. The characteristics of the drugs in each class are presented in Table 1.

It is interesting to note that the slope of ABC curve for Country I is rather steep, whereas that for Country II is more gradual. The Country II list is smaller and more selective, so it is not surprising to find that annual usages are more similar from item to item. For Country I, 75% of the annual usage is accounted for by less than 8% of the items. In contrast, for Country II, only 70% of the annual usage is accounted for by over 15% of the items.

In an operating procurement system, the dividing lines between the three classes would be adjusted on the basis of experience and the particular needs of the system.

ABC Value Analysis

DRUG LIST CHARACTERISTIC

Nunber of Items

Percent of All Item

Value of Annual Comurptlon (US $1

Percent of Total Annual Consunpt1on

Nunber of Units of Stock

Hean Nuuber of Units per Item

(c) Simulated procurement patterns In the survey of current practices among developing

countries it was noted that the most common order interval is one year and, therefore, the most common order quantity is roughly equal to one years consumption. Unreliable communication and transportation net- works and limitations in the number of staff available for order-processing make order intervals as short as one or two months impractical. Therefore, order intervals of four, six or twelve months with order quantities of four months stock, six months stock and twelve months stock are the most commonly observed and seemed the most reasonable for this analysis.

Based on these three alternate order quantities and the ABC classification, six different purchasing patterns were selected for analysis (Table 2).

(d) Calculation of average inventory, safety stock and holding costs [ 101

As illustrated in Fig. 1, when consumption is assumed to occur at a constant rate, (i.e. conditions are deter- ministic) the average inventory quantity is equal to the safety stock plus one-half of the order quantity:

I=Ss+;Q,

90 _....

_.:. _


where I= average quantity in inventory; SS = quantity of safety stock; and Q = order quantity.

When a system is under steady state conditions, the order quantity should be equal to the annual consumption divided by the number of purchases per year:

Q=$

where C = annual consumption, determined from inventory records and forecasting techniques; and N= number of purchases per year, determined by management.

The average inventory is also determined by the quantity of safety stock kept in storage. The quantity of safety stock needed for different levels of protection, or levels of service, depends upon the average consumption, the variation in this consumption, the average lead time, and the variation in this lead time.

As Fig. 1 indicates, the lead time begins when an order is initiated by an inventory clerk and ends when the goods are received by the medical stores. Lead times for public drug supply programs in developing countries range from four to over twelve months and are almost invariably under-estimated by procurement personnel. In addition to being rather long, the lead times are quite variable. The time required to complete all purchase order and contract procedures, variation in the prompt- ness of shipments by suppliers, and differences in transportation times all contribute to large variations in the lead time.

To perform necessary calculations in this study, it is necessary to estimate the standard deviation of the lead time demand. In the best available study of public procurement programs, the lead time was found to be 291 days, with a standard deviation of 50 days [IS]. In light of

this finding and in light of the common perception that supply is quite variable in developing countries, the standard deviation of the lead time consumption was estimated by be 25% of the lead time consumption. In other words, if the lead time demand was 100 units, the standard deviation was estimated to be 25 units.

As indicated earlier, the definition of service level to be used in this study is the fraction of demand which can immediately be filled. From the standard deviation of the lead time demand and the order quantity, the safety stock for any desired level of service can be calculated in two steps using formulae derived elsewhere [lo]. The first step determines the partial expectation, E,, a measure of the expected quantity short when there is a shortage:

E _FxQ = S4.D

where E, = partial expectation; F = stockout level fraction for units demanded, = number of units shortltotai number of units demanded; and Sd,, = standard deviation of lead time demand in units, = 0.25 x DL = 25% of lead time demand (based on above discussion about estimating the standard deviation of the lead time demand).

By consulting a standard normal table [lo], a statistic based on the normal distribution, the standard normal deviate 2, can be obtained for the partial expectation. The safety stock, SS, can then be determined from the following formula:

Ss=.ZxSd,,

The stockout fraction, F, is simply one minus the service level. If the desired service level is 99% or 0.99, then the stockout fraction is 0.01.

Table 2. Description af alternative procurement patterns

Order (Dellvery) Total Number of Indlvldual Orders Procurement ABC Quantity I" Months Orders (Oel~ver~es) (Dellverles) Per Year

pattern cateqory of Consumption Per Year Country I country II

Patter" A 334 220 A 12 1 B 12 1 C 12 1

Pattern El 369 254 A 6 2 B 12 1 C 12 1

pattern c 403 289 A 6 2 0 6 2 C 12 1

Patter" 0 668 440 A 6 2 B 6 2 C 6 2

Pattern E 428 323

A 4 B 6 : C 12 1

Pattern F 1032 660 A 4 3 R 4 3 C 4 3

46 I. D. QUICK

4. RESULTS

(a) Simulation results The values of the average inventories necessary to

provide alternative levels of service under each of the six purchasing patterns are given in Table 3. The safety stocks required to achieve different levels of service for each of three purchasing patterns are presented in Table 4.

Not .surprisingly, for all purchasing patterns and service levels, there is a substantial investment in inventory. For 95% service level using the commonly observed single annual purchase system (Pattern A), the value of the inventory is US $8.2 m for Country I and US $5.1 m for Country II-55% of the annual drug consumption in both cases. Assuming a rate of 25% for holding costs, the annual cost of maintaining these inventories is $2.0 m and $1.3 m for Countries I and II, respectively.

Although there is a considerable investment in inventory under any of the purchasing patterns, the individual patterns have a substantial impact on the average inventory. For a 95% service level in Country I, the average inventory represents 55% of the annual consumption with Pattern A, 43% with Pattern B, 40% with Pattern C, 38% with Pattern D, 37% with Pattern E and only 34% with Pattern F. The effect of this variation on holding costs is obvious.

Despite differences in the ABC curves for the two countries (Fig. 2) and the resulting ABC classifications, the relative impact on inventory levels of alternative purchasing patterns is virtually identical in the two countries.

As the size of the order quantity decreases, the order frequency increases and the total number of orders processed each year increases (Table 2). However, the in-

Table 3. Value of average inventory by level of service for alternative procurement patterns, County I and County II

?+oclJrement pattern Value of A veracje Inventory (UUO'S Of us lJ011arsi RBC Category -- Order ________________________________________________-______________________-___---________-_

(Delrvery) rJuant1ty Country I Countr II

Service Level: Service eveL: l! 99% 98% 95% 90% 85% 99% 98% 95% 908 85%

Pattern A 10, 801 9,730 8,204 7,394 7,394 6,733 6,066 5,114 4,609 4,609

A Drugs -- 12 months B Drugs -- 12 months C Drugs -- 12 months

Pattern B

A Drugs -- 6 months B Drugs -- 12 months C Orugs -- $2 months

6,766 7,750 6,302 5,217 4,606 5,565 4,929 4,022 3,360 3,009

Pattern C

'A Drugs -- 6 months B Drugs -- 6 months C Drugs -- 12 months

Pattern D

8*365 7,360 5,927 4,788 4,056 5,307 4,678 3,781 3,083 2,654

8,103 7,104 5,681 4,507 3,697 5,051 4,429 3,542 2,810 2,305

A Drugs -- 6 months B Drugs -- 6 months C Drugs.-- 6 months

Pattero,E

A Drugs ;- 4 months B Drugs --, 6 months C,Drugs -- 12 months

._ Pattern F

A Drugs -- 4 months B Drugs -- 4 months C Drugs -- 4 months

7,820 6,882 5,478 4,392 3,738 4,994 4,404 3,523 2,856 2,472

7,380 6,471 5,086 3,982 3,275 4,600 4,034 3,171 2,483 2,042

Table 4. Safety stock in months of consumption by service level for selected alternative procurement patterns

Purcha$ng Pattern Required Safety Stock (In Manths of Consumptxn)

Level of Service:

Pattern A

(All drugs purchased annually)

99% 98% 95% 90X 85%

2.7 1.9 0.7 0.0 0.0

Pattern D

(All drqs purchased twice yearly

3.6 2.8 1.6 0.7 0.0

Pattern'?

fAll.dtugs wrchased thrxze yearly)

4.0 3.2 2.1 1.2 0.7

Assumes lead time of nine months and standard devlatlon of lead time demand equal to twenty-five percent of lead time demand.

Applying management science in developi~ countries 47

48 J. D. QUICK

crease in number of orders varies according to the pattern of purchasing. For example, with Pattern D the number of individual orders is twice that of Pattern A, while with Pattern E the number of orders is increased by only 50%. At the same time, for 95% service the average inventory is lowered from the Pattern A inventory by slightly more than 30% with Pattern D and almost 40% with Pattern E. Thus, compared to Pattern D, Pattern E achieves a greater reduction in inventory with a substantially smaller increment in the number of orders which must be processed. In terms of achieving the greatest reduction in average inventory with the least increase in the work of ordering, Pattern E appears to be the most efficient.

The. most striking single difference is between Pattern A and Pattern B, where the average inventory is decreased over 20% and the number of orders increased by only one-tenth simply by purchasing class A items twice annually, rather than once annually.

A useful way to put the data in Table 3 in perspective is to compare the levels of service which would be obtained with the same amount of funds used under different procurement patterns. For example, if Country I has an annual drug budget of US$16.3 m, with Pattern A each product would be out of stock 15% of the time, whereas with Pattern F, the same funds would allow a 99% service level (each item out of stock an average of one percent of the time). As another example, if Country II was only able to allocate $10.1 m to drug procurement it could realize a -service level of almost 98% with Pattern F, a level of slightly better than 95% with Pat- terns D and E, a service level of 95% with Pattern C, and a level of somewhat:more than 90% with Pattern B. With Pattern A it is virtuaIly assured that many drugs will be out of stock by end of the year.

Table 4 demonstrates that smaller order quantities are associated with higher safety stocks. This situation fol- lows from the fact that smaller order quantities and more frequent ordering mean that stock balances are low more often. Whenever stock balances are low there is the possibility that demand will exceed the amount in inventory. To maintain a consistently high service level, greater buffer stock is required. To maintain 95% service, for example, once yearly purchasing requires less than one month of safety stock, whereas thrice yearly purchasing requires over two months of safety stock. It must be borne in mind that these safety stocks are based on a nine month lead time and a lead time standard deviation of 25% of the lead time. Should the procurement system become more efficient by reducing lead times and the variability of lead times, then the safety sto,ck could be reduced and the more frequent purchasing patterns would be even more advantageous.

It should be recognized that the service level represents the availability of stock for each individual item. With service levels for indtiidual items established at 85,90, or even 95%, and 200-30ditems in inventory, it is a virtual certainty that the system;irill be experiencing a shortage of numerousitems at any one time.

(b) Sensitivity analysis An important part of any quantitative analysis which

depends in part upon estimated parameters, rather than directly measured parameters, is the assessment of the extent to which errors in the parameter estimates could bias the conclusions. This assessment is termed sensitivity analysis, since it is an attempt to determine how

sensitive or responsive the conclusions are to errors in the parameter estimates. Major variation in the estimates alter the exact quantities in the results, but if these alterations do not change the basic relationships and the conclusions are the same, then the results of the study are credible. However, if small changes in parameter estimates reverse the observed relationships, then the results are probably not very generalizable.

The sensitivity analysis is performed by making all of the same calculations with alternative values for the estimated parameters. The results of these independent analyses are then compared to assess their consistency.

In performing the analysis for Table 3, assumptions were made about the lead time, lead time demand, and variation in lead time demand. The estimate of nine months for the lead time is well-justified on the basis on the experiences of developing countries on several con- tents. The parameter about which there is much less information and about which there should be greater concern, is the estimate of the standard deviation of the lead time demand. To evaluate the impact of the standard deviation of the lead time demand on the calculation of inventory levels, several different estimates of the standard deviation were tested. The estimate used for Table 3 was 25% of the lead time demand. In Fig. 3 the results based on using this estimate are compared with the results based on two other estimates, taken from the two extremes. The low variability estimate is based on a standard deviation of five times the square-root of the lead time demand and the high variability estimate is based on a standard deviation of 75% of the lead time demand.

Comparison of the three sets of curves indicates that when the variability of the lead time demand is very low, the average inventory required for a given service level is determined almost exclusively by the purchasing pattern; when the variability is high, the impact of the purchasing pattern is small compared to that of the service level.

Figure 3 highlights the major impact that uncertainty in the lead time and demand during lead time can have on the average inventory and/or service level. The relationships demonstrated in the figure suggest that countries which are experiencing extremely variable lead time demands should first analyze the causes of this variability and, then, systematically seek methods to reduce the lead time variability.

Although Fig. 3 shows marked differences in average inventories associated with various purchasing patterns and service levels, it indicates that the observations about the importance of purchasing patterns which were based on data in Table 3 are not qualitatively altered by wide ranges in the estimate of the variability of lead time demand: When the lead time demand has a moderate to low variability, the purchasing pattern has a major impact on the amount of inventory required to achieve a given level of service.

5. DISCUSSION The analysis has demonstrated several points of im-

portance for supplies management in developing countries. First, the application of a standard inventory management technique known as ABC analysis revealed that-at least for the two countries used for the simulation-the structure of public drug program inventory is typical of industrial inventories: Over 80% of the total


consumption in dollars is accounted for by less than 20% of the drugs. This observation has practical importance in that it allows the procurement officer to identify high usage drugs for which frequent purchasing and delivery of smaller quantities are most feasible. Because average inventories are dependent upon order quantities, smaller orders reduce average inventory. Procurement patterns based on more frequent purchasing or delivery of high usage drugs could reduce average inventories by 20-50% over single annual purchasing,

sometimes preferable for manufacturers also, since it gives them greater flexibility in planning their production runs and may allow more complete utilization of their capacity.

The ABC value analysis has several other important applications. Typically, professional purchasers use the ABC system to set priorities for cost reducing activities. Since the category A items are few in number, it is possible to devote special attention to locating the least expensive suppliers of acceptable quality. The value of the A items is such that a small price break by one supplier can have a noticeable impact on total drug expenditures. Category A and B items can also be reviewed to determine whether less expensive alternative drugs or dosage forms are available. Also, if drug quality becomes an issue in attempts to reduce expenditures for category A items, it may be worth the expense of having the suspect drugs analyzed. Routine analysis of all drugs may prove too costly, but for category A items and many category B items, such analyses may prove useful in convincing health officials that a less expensive product is acceptable. fn such an instance, the cost of the drug analysis would be more than offset by the savings in the purchase price. For some category B items and for many category C items, the cost of drug testing would exceed the possible savings from selecting a lower priced, but unknown bidder.

The second part of this study used sensitivity analysis to assess the impact of lead time variab~ity on the average inventory for the different procurement patterns. Sensitivity analysis-which simply requires repetition of the basic calculations using different parameters-is a powerful tool for understanding quantitative relationships without the use of sophisticated, computerized optimization routines. In this study the sensitivity analysis demonstrated that, when the lead times and drug consumption are highly variable, the amount of safety stock required to provide an adequate level of service is so great that the procurement pattern-reflected in the order quantities and order frequency-has only a small effect on the total inventory. Therefore, with high variability in lead time and consumption, management would do better to concentrate on reducing the lead time and improving the accuracy of consumption estimates than to change the procurement pattern.

Priorities for use of clerical time can also be established with the ABC categories. For example, punctual delivery is particularly important for class A items, since their bulk makes air-freighting emergency supplies costly. Application of close order-monitoring procedures and careful analysis of lead times [I51 is quite feasible for 25-30 class A items where it may not be feasible for all 2~3~ items. Use of clerical time for inventory control can also be made more efficient by devoting more time to class A items.

At first glance, the ABC and sensitivity -analyses presented here might appear to require complex com- puter calculations. In fact, once the basic formulae are chosen, all of the calculations necessary for these analyses can readily be performed by clerical staff working with pencil and paper or hand calculators. The calculations do depend upon inventory and consumption information which is fragmentary in some programs. However, when standard inventory practices are in use, the lack of electronic computers or other technical ap- paratus should not limit the application of modern management science methods.

As a final caveat, we must reiterate that this analysis has been in the form of a simulation, As in any simulation, numerous assumptions were made about the vari- ables and relationships involved. Some of these assumptions were tested through the sensitivity analysis, but others were not. Therefore, the data presented in Tables l-4 should be interpreted as represented q~litati~e differences only. Precise quantitative relationships must be determined individually for each supply system.

One caveat should be offered with regard to the ABC To our knowledge, management science/operations categories. The analysis has assumed that the unit cost of research techniques have seen little application in the drugs is not increased by buying smaller quantities more public health programs of developing countries. While frequently. For category A items, which are bought in such techniques are undoubtedly used in commercial and huge bulk, this assumption probably holds true, but as indus~ial endeavors, funds are generally the most limited the drugs in categories B and C are bought in smaller and in areas such as public health. A World Health smaller quantities, it is likely that some increase in unit Organization Expert Committee recently studied the ap- price will occur. Although common sense might dictate plication of systems analysis to. .health management, that any item bought in a smaller quantity will cost more, concentrating largely on the experiences of developing there is no available data to indicate that this is the case countries. The Committee concluded that such proce- with the size quantities which are required for national dures are suitable for widespread application and con- drug proc~ement. In fact, there are several reasons to tribute significantly to the effort to utilize scarce believe that prices may not rise with moderate decreases resources to achieve @maximum impact on the health in quantities. status of the populationll61.

Nevertheless, if unit costs are found to increase when the order interval decreases or if it does not appear feasible to increase the frequency with which new orders are placed, comparable or even more favorable reduc- tions in inventory can be achieved by using the ABC! categories to establish delivery schedules. By specifying that deliveries be divided, all of the inventory savings associated with more frequent purchasing could be realized, but without the increased workload of additional orders. An annual contract with divided deliveries is

It is our conclusion that techniques such as ABC value analysis, sensitivity analysis, and other management science/operations research methods are feasible for use in public procurement programs and offer the potential for substantially improving the use of scarce funds in primary health care.

Acknowledgements-The author gratefully acnkowledges the thorough, constructive critiques of Vimal Dias (National Institute of Management, Sri Lanka) and Margaret Hume (Management

50 J. D. QUICK

Sciences for Health), and the manuscript preparation by Pat McCarthy.

10. REFERENCES

1: World Bank, Health Sector Policy Paper. World Bank, 11. Washington, DC. (1975).

2. United Nations, Demographic Yearbood 1975. United Nations, New York (1976). 12.

3. World Health Organization, Treatment and Prevention of Dehydration in Diarrhoeal Diseases-A Guide for Use at the 13. Primary Level. World Health Organization, Geneva (1976).

4. World Health Organization, Background Documents. A31/Technical Discussions/l (1978).

5. World Health Organization, The Selection of Essentiul Drugs. World Health Organization, Technical Report Series, No. 14. 615,Geneva (1977).

6.. M. Silverman, The Drugging of the Americas. University of 15. CaliforniaPress, Berkeley (1976).

7. R. J. Ledogar, Hungary for Profits. International Documen- .tation/North America, New York (1975).

8. J. Yudkin, Provision of Medicines in a Developing Country, 16. (15 April 1978). pp. 810-812. The Lancet.

9. 0. Gish and L. L. Feller, Planning Pharmaceuticals for

Primary Health Care: The Supply and Utilization of Drugs in the Third World. American Public Health Association, Washington, D.C. (1979). R. J. Tersine, Materials Management and Inventory Systems. North Holland, New York (1976). D. S. Anmer, Purchasing and Materials Management in Health Care Institutions. D.C. Health and Company, Lex- ington, Mass. (1975). E. S. Buffa, Operations Management: Problems and Models. Wiley, New York (1972). J. D. Quick, Improving pharmaceutical supplies management in developing countries. Masters Thesis. University of Rochester School of Medicine and Dentristry, Department of Preventive Medicine and Community Health, New York (1979). J. H. Greene, Production and Inventory Control Handbook McGraw Hill, New York (1970). V. Dias, Introduction to Forecasting and Inventory Control Systems. State Pharmaceutical Corporation Report 1, National Institute of Management, Colombo, Sri Lanka (1975). World Health Organization, Application of Systems Analysis to Health Management. World Health Organization Tech- nical Report Series, No. 5%, Geneva (1976).

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