- Email: [email protected]
Reducing Inventory Cost
REDUCING
INVENTORY COST
By Peter (halos
R
ising medical costs continue to outpace price increases in other sectors ofthe economy. Fixed reimbursement plans are but one example of recent innovative efforts to contain costs. Grappling with productivity issues, hospital administrators are looking at optimal personnel policies, standard costing, and capital budgeting. 40
Complicating their efforts is awareness that improved productivity must be carefully balanced against the quality of health care delivered. One administrative area where better management techniques will not adversely affect health care quality is improved inventory management. Typically, a large hospital has an inventory of phar-
maceuticals and medical supplies worth many millions of dollars. The cost of maintaining such an inventory runs into the hundreds of thousands of dollars per year. Contrary to the manufacturing sector, where management is acutely aware of inventory costs, many hospital administrators do not appear to understand the
American Pharmacy, Vol. NS27, No.7, July 1987/488 1
potential cost savings to be realized by better inventory management. Rarely is any effort made to implement quantitative lot sizing in determining optimal reorder points and quantities. A look at the inventorying of one often-used drug product suggests that substantial cost savings can be realized by implementing fairly straightforward inventory management techniques. To examine inventory management in the pharmacy of a large urban hospital with an aggregate inventory worth more than $7 million and including hundreds of pharmaceutical lines, we studied only one item - the antibiotic vancomycin. Its annual sales represented approximately 2% of the pharmacy's total inventory. Because the pharmacy manager was essentially ordering inventory on an ad hoc basis, optimal reorder points and quantities for the antibiotic had not been determined. The goal ofthe study was to introduce techniques to the pharmacy for improved inventory management that would significantly reduce cost in the process. We began by establishing the cost parameters of the inventory model. These costs were then determined, and a simple method of estimating demand for the drug in question was developed. Actual cost and demand data were then applied to determine optimal order size for vancomycin, the product under study. The effect of possible cost and demand misestimates upon the model was measured. Finally, given demand uncertainty, an optimal reorder point for the product was determined.
the model holds up well given the possible effects of incorrect estimates.
Vancomycin Carrying and Ordering Costs
costs are simply the costs of placing the order and the related shipping costs. Both carrying and ordering costs are incremental costs associated with the particular order. (Fixed costs that do not vary with any particular order should not affect the decision at hand.) Mathematically, the point at which the total cost of both ordering and carrying an item is minimized yields the Economic Order Quantity. Formally, this may be defined as:
Q* = Y2AP/S where S = annual carrying cost per unit; A = annual demand; and P = order cost per unit. Estimating annual demand for a pharmaceutical product is relatively straightforward. The estimation technique used in this study is simply to regress past demand for the product through time. This regression can then be used to estimate future demand. Some margin of error may exist in both the cost and demand estimates, but
i&iji'
Inventory Costs
Purchase Price per Unit Transportation-In
Cost and Demand Parameters of the Model Effective inventory cost control minimizes total cost while maintaining an adequate supply of inventory. Inventory cost components can be divided into two areas - carrying and ordering costs. Carrying costs include taxes, insurance, and spoilage related to inventory. The largest component of carrying costs, however, is the cost of capital related to the amount of investment in inventory. Ordering
The various carrying and ordering cost components for vancomycin, obtained from hospital accounting records, are shown in Table 1. As can be seen, there are several components of the carrying cost category that are not relevant. For example, the hospital is self-insured, eliminating insurance cost. Nor are there any inventory taxes. The allocation of depreciable items to the pharmacy amounted to some $11,000; but since these costs would be incurred regardless of the level of inventory held, they were not included in the determination of the Economic Order Quantity. In other words, they were completely fixed. Another carrying cost that typically is included in the valuation of inventory is transportation-in. In this case, as shown in Table 1, freight charges were included in the price of the drug, so no additional charge needed to be included. Finally, the administrative fee levied on the pharmacy amounted to $62,000, which could have been spread pro rata over the sales value of the pharmaceutical product lines. But given that this was an arbitrary overhead allocation indi-
Cost per Order
$19.88 Included in purchase price $70.00
Receiving and Inspection Personnel
$21,000.00
Administration Personnel
$62.000.00
Storage Cost per Square Foot Insurance Taxes Depreciation Cost of Capital
American Pharmacy, Vol. NS27, No. 7, July 1987/489
$7 .68 Self-insu red None $11,200.00
9%
41
rectly related to supporting the pharmaceutical operation as a whole, there seemed to be little point in doing this. Thus we were left with only storage and finance charges as relevant carrying costs. The former was considered variable and directly related to the square footage occupied by the product. In other words, the space would have been put to alternate economic use had it not been occupied by the drug in question. The 1,480-square-foot pharmacy was charged rent of $11,366, or $7.68 per square foot per year. A storage unit of vancomycin, which occupied 0.5 square feet, was charged $3.84 annually. A final charge to the inventory was financing the investment. A cost of capital of 9% was levied against the $19.88 unit cost of the inventory item, yielding a charge of $1. 79 per annum. The total annual carrying cost for vancomycin was thus $5.63, or (0.09 [$19.881 + 0.5 [$7.68]). The ordering costs could be from two categories - receiving and inspection charges, and manual placement and administrative charges. The former consisted of general hospital receiving and inspection, which amounted to $105,000, of which 20% or $21,000 was allocated to the pharmacy (see Table 1). In this case, no cost savings would be realized should the pharmacy discontinue its operations. Receiving and inspection overhead would continue unchanged. Thus, this charge was viewed as nonincremental relative to inventory ordering, and so not included in the model. The storage charges were salaries for three workers who were directly involved with placing orders, shelving drugs, keeping order records, and the like. Total salaries amounted to $56,000 and were viewed as traceable to and variable with the amount of time spent on ordering. The aggregate annual cost of vancomycin relative to total annual inventory costs of some $7 million, a ratio of approximately 2%, was determined. This resulted in a cost of$70 per order of van co mycin ($56,000 [0.02]116 orders per year). 42
Annual Demand for Vancomycin The final component of the model was annual demand for the antibiotic. Demand for most pharmaceutical products is not constant from year to year. Rather than simply use the prior year's demand, a more accurate and very straightforward
'MijiJ
method is to regress prior monthly demand through time. This regression line can then be extrapolated into the next year to estimate future monthly demand. This can be done very quickly on a personal computer with a regression package or in a more limited fashion by simply using a statistical calculator. From inventory records, the prior 48 months of consumption for vancomycin was tabulated. As shown in Table 2, the regression through time yielded a very good fit, R = 0.87 (maximum possible being 1.0), indicating strong explanatory power. Actual data points about the regression line were randomly distributed (ie, no
Regression Estimation of Inventory Demand
Variable
Regression Coefficient
Intercept
- 10.14 11.27
Time
Standard Error
Standard Coefficient
Statistic
1.170
0.82
9.63
0.817
Multiple Correlation
112.320
Standard Error of Estimate Durbin Watson
1.848
Autocorrelation
0.075
Period
T
Actual
Predicted
Residual
49
565
542
23
50
513
553
- 40
51
498
564
- 66
52
615
576
39
53
841
587
254
54
635
598
37
55
555
610
-55
56
401
621
-220
57
571
632
- 61
58
694
644
50
59
1,048
655
393
60
511
666
-155
7.447
7.248
Total
American Pharmacy, Vol. NS27, No.7, July 1987/490
autocorrelation). This suggests that seasonality was not significantly influencing the distribution of the demand. When the regression line was extended into the most recent time period, August 1985--July 1986, this yielded an estimate of demand for this period. As can be seen in Table 2, when actual demand for August 1985--July 1986 (shown as Periods 49-60), is compared to that predicted by the regression, the prediction is quite accurate. Total actual demand for the 12 months was 7,447 units vs predicted demand of 7,248 units, a 2.6% error. It should be noted that for a few of the months, there was fairly high residual error. The effect of this variance on monthly demand will be discussed later in conjunction with reorder points.
Implementation The reason for determining the Economic Order Quantity was to minimize total inventory cost, ie, carrying and ordering costs. Formally, letting
Q* = Y 2AP/S then 8 = carrying cost per unit, or $5.63; A = annual demand, or 7,447 units; and P = ordering cost per unit, or $70. By substitution,
Q* = Y2(7,447){$70)/$5.63 = 430 units. The average carrying cost was Q* 8 /2 = 430($5.63)/2 = $1,210. The ordering cost was AP/Q* = $70(7,447)/430 = $1,212. This yielded a minimum total cost of $2,422 for the drug in question. To determine the effects of parameter misestimates in cost and demand on the minimal total cost, we reran the model with different terms. As shown in Table 3, the model worked well with respect to changes in estimates. For example, if the demand predicted by the regression model is used at the beginning of the period in place of actual demand, only a very small Economic Order Quantity differ-
summary, because the Economic Order Quantity is derived from a square root formulation, any errors in the cost and demand estimates are dampened by this function. This suggests that the model may prove quite useful, even where cost and demand estimates are difficult to obtain, or are viewed as somewhat suspect. ence arises. This scenario is more realistic, as actual demand is only known at the end of the period. Using the predicted demand of 7,248 units rather than actual post hoc demand, the Economic Order Quantity becomes 424 units rather than the previously derived 430 units. As indicated in Table 3, total cost with this quantity was $2,389 rather than the actual $2,422, an insignificant increase because of the demand misestimate. Likewise, assuming cost misestimates, if the carrying costs are assumed, arbitrarily, to be actually 15% greater than estimated and the ordering costs 10% larger, then the Economic Order Quantity becomes 421 units, yielding a total minimum cost of $2,724, an 11% total cost error. In
Reorder Point Once the optimal quantity to be ordered is determined, all that remains is to determine exactly when to reorder the drug in question. If the order is placed earlier than necessary, needless carrying costs are incurred due to inventory supply exceeding demand. If placed too late, stockouts will occur as demand exceeds available supply. A simple method of determining a reorder point is to balance the daily distribution of demand with the lead time required between placement and receipt of the order in question. For example, the predicted annual demand for vancomycin was 7,248 units. Given 250
Optimal Inventory Under Demand and Cost Uncertainty
_
Predicted Demand (units)
7,248
Actual Carrying Cost
$5.63
Actual Ordering Cost
$70.00
Y 2(7,248) ($70)/$5 .63 (units)
Q*
=
c.c.
= 424($5 .63)/2
O.c. =
424 1,193
$70(7,248)/424
1,196 $2,389
Total Cost Actual Demand (units)
7,447
Revised Carrying Cost (Ll15%)
$6.47
Revised Ordering Cost (Ll10%)
$77.00
Q*
=
Y2(7,447) ($77)/$6.47 (units)
c.c.
=
421 ($6.47)/2
$1,362
O.c.
=
$77(7,447)/421
$1,362
421
$2,724
Total Cost * Q = Economic Order Quantity;
American Pharmacy, Vol. NS27, No.7, July 1987/491
c.c. = Carrying Cost;
O.c. = Ordering Cost.
43
working days in a year, this yields an average estimated daily demand for the product of about 29 units. Because the lead time required between the placement of the order and its delivery to the pharmacy rarely exceeded 2 working days, a plausible reorder point would be at 58 units of remaining inventory (2 days x 29 units). However, it should be noted that daily demand fluctuates around this average figure. Therefore, a safer procedure is to anticipate this variance about the mean demand. This is typically given in the regression output, performed earlier, for estimating demand. The standard error of the estimate associated with the monthly demand for vancomycin was 112 units (see Table 2). Given 20 working days in a month, this translates into a standard error of daily demand of about six units. Thus, the reorder point becomes:
R = DL + ZUL = (29 x 2) 1.64(6) = 68
+
where DL = demand during lead time; Z = confidence level (95%; 1 tailed); and
Implementation The present study examined only one product, albeit one of high value, in the pharmacy of a large urban hospital. Both the historical demand for the product and the costs related to carrying and ordering it were examined in detail. 44
clearly is worthwhile for selected large-value items. Typically, 10% of inventory product lines may account for a significant portion of total inventory values. Product demand data can be rolled over or updated routinely by dropping the earliest 12-month period and adding the most recent 12-month data over a cumulative 4- or 5-year period. Economic Order Quantity and reorder points can then be readily obtained for the most important pharmaceutical lines. These data can be neatly summarized in spreadsheet format (see Table 4). The product number, type, and cost are entered in each cell for each pharmaceutical line. The estimated monthly demand and its standard error are also entered for each product. The spreadsheet package is then preprogrammed to automatically perform the arithmetic operations necessary in determining the Economic Order Quantity and the reorder point for each pharmaceutical line. In this manner, the pharmacy has a very efficient tabulation of inventory order points and quantities for its products. Given a typical multimillion dollar investment in hospital pharmacy inventory, substantial cost savings can be realized. Recent
These costs included all variable and traceable accounting costs related to both carrying and holding the inventory item in question. Fixed costs were excluded in the analysis. When the currently existing inventory policies at the pharmacy were examined with respect to vancomycin and compared to those derived in the study, it became apparent that the pharmacy was reordering in inefficient quantities. It was also ordering much too soon, thus carrying needlessly high safety stock for the product. In other words, it was incurring sizable inventory costs that could have been avoided. Needless staff-hours of ordering costs as well as carrying costs were being incurred. When total actual inventory costs were compared to those derived in this study, they were approximately 20% higher. These potential cost savings can readily be generalized
Inventory Spreadsheet Lead Reorder Time Point
Item No.
Product
Unit Cost
Est. MthlyDem.
Std. Error
E.D.Q.
150
22
Vancomycin
$19.90
220
25
180
2
22
151
23
Tobramycin
24.20
330
35
270
4
66
152
24
Cefazolin
16.50
180
15
150
3
27
to other inventory pharmaceutical lines. All that is needed to implement this inventory management technique is a one-time, thorough study of pharmacy costs related to carrying and reordering inventory. Once done, the demand pattern for each pharmaceutical line can be input into a regression, or equivalent, package. Although this may not be worthwhile for hundreds of inventory items of small value, it
manufacturing evidence suggests that industry has made a frontal assault on reducing inventory costs. It behooves the health care sector not to ignore these trends, and to make a sustained effort to improve the efficiency of its inventory management. ®
Peter Chatas, PhD, is professor, department of accounting, University of Illinois at Chicago, 60680.
American Pharmacy, Vol. NS27, No.7, July 1987/492
INVENTORY COST
By Peter (halos
R
ising medical costs continue to outpace price increases in other sectors ofthe economy. Fixed reimbursement plans are but one example of recent innovative efforts to contain costs. Grappling with productivity issues, hospital administrators are looking at optimal personnel policies, standard costing, and capital budgeting. 40
Complicating their efforts is awareness that improved productivity must be carefully balanced against the quality of health care delivered. One administrative area where better management techniques will not adversely affect health care quality is improved inventory management. Typically, a large hospital has an inventory of phar-
maceuticals and medical supplies worth many millions of dollars. The cost of maintaining such an inventory runs into the hundreds of thousands of dollars per year. Contrary to the manufacturing sector, where management is acutely aware of inventory costs, many hospital administrators do not appear to understand the
American Pharmacy, Vol. NS27, No.7, July 1987/488 1
potential cost savings to be realized by better inventory management. Rarely is any effort made to implement quantitative lot sizing in determining optimal reorder points and quantities. A look at the inventorying of one often-used drug product suggests that substantial cost savings can be realized by implementing fairly straightforward inventory management techniques. To examine inventory management in the pharmacy of a large urban hospital with an aggregate inventory worth more than $7 million and including hundreds of pharmaceutical lines, we studied only one item - the antibiotic vancomycin. Its annual sales represented approximately 2% of the pharmacy's total inventory. Because the pharmacy manager was essentially ordering inventory on an ad hoc basis, optimal reorder points and quantities for the antibiotic had not been determined. The goal ofthe study was to introduce techniques to the pharmacy for improved inventory management that would significantly reduce cost in the process. We began by establishing the cost parameters of the inventory model. These costs were then determined, and a simple method of estimating demand for the drug in question was developed. Actual cost and demand data were then applied to determine optimal order size for vancomycin, the product under study. The effect of possible cost and demand misestimates upon the model was measured. Finally, given demand uncertainty, an optimal reorder point for the product was determined.
the model holds up well given the possible effects of incorrect estimates.
Vancomycin Carrying and Ordering Costs
costs are simply the costs of placing the order and the related shipping costs. Both carrying and ordering costs are incremental costs associated with the particular order. (Fixed costs that do not vary with any particular order should not affect the decision at hand.) Mathematically, the point at which the total cost of both ordering and carrying an item is minimized yields the Economic Order Quantity. Formally, this may be defined as:
Q* = Y2AP/S where S = annual carrying cost per unit; A = annual demand; and P = order cost per unit. Estimating annual demand for a pharmaceutical product is relatively straightforward. The estimation technique used in this study is simply to regress past demand for the product through time. This regression can then be used to estimate future demand. Some margin of error may exist in both the cost and demand estimates, but
i&iji'
Inventory Costs
Purchase Price per Unit Transportation-In
Cost and Demand Parameters of the Model Effective inventory cost control minimizes total cost while maintaining an adequate supply of inventory. Inventory cost components can be divided into two areas - carrying and ordering costs. Carrying costs include taxes, insurance, and spoilage related to inventory. The largest component of carrying costs, however, is the cost of capital related to the amount of investment in inventory. Ordering
The various carrying and ordering cost components for vancomycin, obtained from hospital accounting records, are shown in Table 1. As can be seen, there are several components of the carrying cost category that are not relevant. For example, the hospital is self-insured, eliminating insurance cost. Nor are there any inventory taxes. The allocation of depreciable items to the pharmacy amounted to some $11,000; but since these costs would be incurred regardless of the level of inventory held, they were not included in the determination of the Economic Order Quantity. In other words, they were completely fixed. Another carrying cost that typically is included in the valuation of inventory is transportation-in. In this case, as shown in Table 1, freight charges were included in the price of the drug, so no additional charge needed to be included. Finally, the administrative fee levied on the pharmacy amounted to $62,000, which could have been spread pro rata over the sales value of the pharmaceutical product lines. But given that this was an arbitrary overhead allocation indi-
Cost per Order
$19.88 Included in purchase price $70.00
Receiving and Inspection Personnel
$21,000.00
Administration Personnel
$62.000.00
Storage Cost per Square Foot Insurance Taxes Depreciation Cost of Capital
American Pharmacy, Vol. NS27, No. 7, July 1987/489
$7 .68 Self-insu red None $11,200.00
9%
41
rectly related to supporting the pharmaceutical operation as a whole, there seemed to be little point in doing this. Thus we were left with only storage and finance charges as relevant carrying costs. The former was considered variable and directly related to the square footage occupied by the product. In other words, the space would have been put to alternate economic use had it not been occupied by the drug in question. The 1,480-square-foot pharmacy was charged rent of $11,366, or $7.68 per square foot per year. A storage unit of vancomycin, which occupied 0.5 square feet, was charged $3.84 annually. A final charge to the inventory was financing the investment. A cost of capital of 9% was levied against the $19.88 unit cost of the inventory item, yielding a charge of $1. 79 per annum. The total annual carrying cost for vancomycin was thus $5.63, or (0.09 [$19.881 + 0.5 [$7.68]). The ordering costs could be from two categories - receiving and inspection charges, and manual placement and administrative charges. The former consisted of general hospital receiving and inspection, which amounted to $105,000, of which 20% or $21,000 was allocated to the pharmacy (see Table 1). In this case, no cost savings would be realized should the pharmacy discontinue its operations. Receiving and inspection overhead would continue unchanged. Thus, this charge was viewed as nonincremental relative to inventory ordering, and so not included in the model. The storage charges were salaries for three workers who were directly involved with placing orders, shelving drugs, keeping order records, and the like. Total salaries amounted to $56,000 and were viewed as traceable to and variable with the amount of time spent on ordering. The aggregate annual cost of vancomycin relative to total annual inventory costs of some $7 million, a ratio of approximately 2%, was determined. This resulted in a cost of$70 per order of van co mycin ($56,000 [0.02]116 orders per year). 42
Annual Demand for Vancomycin The final component of the model was annual demand for the antibiotic. Demand for most pharmaceutical products is not constant from year to year. Rather than simply use the prior year's demand, a more accurate and very straightforward
'MijiJ
method is to regress prior monthly demand through time. This regression line can then be extrapolated into the next year to estimate future monthly demand. This can be done very quickly on a personal computer with a regression package or in a more limited fashion by simply using a statistical calculator. From inventory records, the prior 48 months of consumption for vancomycin was tabulated. As shown in Table 2, the regression through time yielded a very good fit, R = 0.87 (maximum possible being 1.0), indicating strong explanatory power. Actual data points about the regression line were randomly distributed (ie, no
Regression Estimation of Inventory Demand
Variable
Regression Coefficient
Intercept
- 10.14 11.27
Time
Standard Error
Standard Coefficient
Statistic
1.170
0.82
9.63
0.817
Multiple Correlation
112.320
Standard Error of Estimate Durbin Watson
1.848
Autocorrelation
0.075
Period
T
Actual
Predicted
Residual
49
565
542
23
50
513
553
- 40
51
498
564
- 66
52
615
576
39
53
841
587
254
54
635
598
37
55
555
610
-55
56
401
621
-220
57
571
632
- 61
58
694
644
50
59
1,048
655
393
60
511
666
-155
7.447
7.248
Total
American Pharmacy, Vol. NS27, No.7, July 1987/490
autocorrelation). This suggests that seasonality was not significantly influencing the distribution of the demand. When the regression line was extended into the most recent time period, August 1985--July 1986, this yielded an estimate of demand for this period. As can be seen in Table 2, when actual demand for August 1985--July 1986 (shown as Periods 49-60), is compared to that predicted by the regression, the prediction is quite accurate. Total actual demand for the 12 months was 7,447 units vs predicted demand of 7,248 units, a 2.6% error. It should be noted that for a few of the months, there was fairly high residual error. The effect of this variance on monthly demand will be discussed later in conjunction with reorder points.
Implementation The reason for determining the Economic Order Quantity was to minimize total inventory cost, ie, carrying and ordering costs. Formally, letting
Q* = Y 2AP/S then 8 = carrying cost per unit, or $5.63; A = annual demand, or 7,447 units; and P = ordering cost per unit, or $70. By substitution,
Q* = Y2(7,447){$70)/$5.63 = 430 units. The average carrying cost was Q* 8 /2 = 430($5.63)/2 = $1,210. The ordering cost was AP/Q* = $70(7,447)/430 = $1,212. This yielded a minimum total cost of $2,422 for the drug in question. To determine the effects of parameter misestimates in cost and demand on the minimal total cost, we reran the model with different terms. As shown in Table 3, the model worked well with respect to changes in estimates. For example, if the demand predicted by the regression model is used at the beginning of the period in place of actual demand, only a very small Economic Order Quantity differ-
summary, because the Economic Order Quantity is derived from a square root formulation, any errors in the cost and demand estimates are dampened by this function. This suggests that the model may prove quite useful, even where cost and demand estimates are difficult to obtain, or are viewed as somewhat suspect. ence arises. This scenario is more realistic, as actual demand is only known at the end of the period. Using the predicted demand of 7,248 units rather than actual post hoc demand, the Economic Order Quantity becomes 424 units rather than the previously derived 430 units. As indicated in Table 3, total cost with this quantity was $2,389 rather than the actual $2,422, an insignificant increase because of the demand misestimate. Likewise, assuming cost misestimates, if the carrying costs are assumed, arbitrarily, to be actually 15% greater than estimated and the ordering costs 10% larger, then the Economic Order Quantity becomes 421 units, yielding a total minimum cost of $2,724, an 11% total cost error. In
Reorder Point Once the optimal quantity to be ordered is determined, all that remains is to determine exactly when to reorder the drug in question. If the order is placed earlier than necessary, needless carrying costs are incurred due to inventory supply exceeding demand. If placed too late, stockouts will occur as demand exceeds available supply. A simple method of determining a reorder point is to balance the daily distribution of demand with the lead time required between placement and receipt of the order in question. For example, the predicted annual demand for vancomycin was 7,248 units. Given 250
Optimal Inventory Under Demand and Cost Uncertainty
_
Predicted Demand (units)
7,248
Actual Carrying Cost
$5.63
Actual Ordering Cost
$70.00
Y 2(7,248) ($70)/$5 .63 (units)
Q*
=
c.c.
= 424($5 .63)/2
O.c. =
424 1,193
$70(7,248)/424
1,196 $2,389
Total Cost Actual Demand (units)
7,447
Revised Carrying Cost (Ll15%)
$6.47
Revised Ordering Cost (Ll10%)
$77.00
Q*
=
Y2(7,447) ($77)/$6.47 (units)
c.c.
=
421 ($6.47)/2
$1,362
O.c.
=
$77(7,447)/421
$1,362
421
$2,724
Total Cost * Q = Economic Order Quantity;
American Pharmacy, Vol. NS27, No.7, July 1987/491
c.c. = Carrying Cost;
O.c. = Ordering Cost.
43
working days in a year, this yields an average estimated daily demand for the product of about 29 units. Because the lead time required between the placement of the order and its delivery to the pharmacy rarely exceeded 2 working days, a plausible reorder point would be at 58 units of remaining inventory (2 days x 29 units). However, it should be noted that daily demand fluctuates around this average figure. Therefore, a safer procedure is to anticipate this variance about the mean demand. This is typically given in the regression output, performed earlier, for estimating demand. The standard error of the estimate associated with the monthly demand for vancomycin was 112 units (see Table 2). Given 20 working days in a month, this translates into a standard error of daily demand of about six units. Thus, the reorder point becomes:
R = DL + ZUL = (29 x 2) 1.64(6) = 68
+
where DL = demand during lead time; Z = confidence level (95%; 1 tailed); and
Implementation The present study examined only one product, albeit one of high value, in the pharmacy of a large urban hospital. Both the historical demand for the product and the costs related to carrying and ordering it were examined in detail. 44
clearly is worthwhile for selected large-value items. Typically, 10% of inventory product lines may account for a significant portion of total inventory values. Product demand data can be rolled over or updated routinely by dropping the earliest 12-month period and adding the most recent 12-month data over a cumulative 4- or 5-year period. Economic Order Quantity and reorder points can then be readily obtained for the most important pharmaceutical lines. These data can be neatly summarized in spreadsheet format (see Table 4). The product number, type, and cost are entered in each cell for each pharmaceutical line. The estimated monthly demand and its standard error are also entered for each product. The spreadsheet package is then preprogrammed to automatically perform the arithmetic operations necessary in determining the Economic Order Quantity and the reorder point for each pharmaceutical line. In this manner, the pharmacy has a very efficient tabulation of inventory order points and quantities for its products. Given a typical multimillion dollar investment in hospital pharmacy inventory, substantial cost savings can be realized. Recent
These costs included all variable and traceable accounting costs related to both carrying and holding the inventory item in question. Fixed costs were excluded in the analysis. When the currently existing inventory policies at the pharmacy were examined with respect to vancomycin and compared to those derived in the study, it became apparent that the pharmacy was reordering in inefficient quantities. It was also ordering much too soon, thus carrying needlessly high safety stock for the product. In other words, it was incurring sizable inventory costs that could have been avoided. Needless staff-hours of ordering costs as well as carrying costs were being incurred. When total actual inventory costs were compared to those derived in this study, they were approximately 20% higher. These potential cost savings can readily be generalized
Inventory Spreadsheet Lead Reorder Time Point
Item No.
Product
Unit Cost
Est. MthlyDem.
Std. Error
E.D.Q.
150
22
Vancomycin
$19.90
220
25
180
2
22
151
23
Tobramycin
24.20
330
35
270
4
66
152
24
Cefazolin
16.50
180
15
150
3
27
to other inventory pharmaceutical lines. All that is needed to implement this inventory management technique is a one-time, thorough study of pharmacy costs related to carrying and reordering inventory. Once done, the demand pattern for each pharmaceutical line can be input into a regression, or equivalent, package. Although this may not be worthwhile for hundreds of inventory items of small value, it
manufacturing evidence suggests that industry has made a frontal assault on reducing inventory costs. It behooves the health care sector not to ignore these trends, and to make a sustained effort to improve the efficiency of its inventory management. ®
Peter Chatas, PhD, is professor, department of accounting, University of Illinois at Chicago, 60680.
American Pharmacy, Vol. NS27, No.7, July 1987/492