Computers ind. En~n@ Vol. 13, Nos I-4, pp.73-77, 1987 0360-8352/87 $3.00+0.00 Printed in Great Britain. All rights reserved Copyright c 1987 Pergamon Journals Ltd

EVALUATING INVENTORY TURNS FOR A HOSPITAL ENVIRONMENT

Rajiv Kapur, Ph.D and Chris Moberg

Georgetown University Hospital Washington, DC 20007

Abstract: This paper presents a unique approach, using a modified traditional EOQ model, to manipulate yearly inventory turns and generate optimal space requirements for the Stores operations at Georgetown University Hospital (GUH). The analysis used six months of material dispensed transaction data along with item cost and item size; it generated by item the economic order quantity, order point, safety stock, volume requirement and yearly turns. The advantage of this methodology is that a materiel management system can be configured for acceptable yearly turns such that space requirement can be reduced, avoiding the need for an external warehouse or internal facility construction. The modeling was developed on an IBM 4381 using SAS with transactional data transferred from a Data General (DG) mini computer.

Introduction: At GUH we were faced with the problem of space shortage for storing supplies in our warehouse. Since additional space internal to GUH was unavailable for warehousing activity the only viable option seemed to be leasing an external warehouse. While leasing costs for remote warehousing are not excessive, the high cost of transportation, additional staff requirements and coordination necessitated that we explore other avenues prior to leasing an external warehousing facility. Upon analyzing the operations in GUH stores we found that overall yearly inventory was turning at 5.8. It was apparent that increasing overall inventory turns would decrease space requirements, smooth workload in the receiving and stocking areas, minimize item spoilage and reduce carrying costs.

The following paper discusses the use of micro- and mainframe environments to evaluate inventory turns at GUH. The paper also illustrates a methodology for optimizing space utilization as a direct result of manipulating inventory turns in a stores operation.

Historical Perspective: At the onset of this analysis the traditional EOQ model was considered inadequate for generating order quantities that would be congruent with space constraints prevalent at GUH stores. In light of this a "space constraining" model was developed which considered, along with order cost, yearly demand, item cost, opportunity cost, maximum allowable storage height in the Stores and the item volume. The space constraining model ensured that high volume items would be ordered in lower quantities resulting in increased yearly turns and decreasing space requirements for GUH Stores. This model can be represented as:

EOQ = (3456 x yearly demand x order cost x max-allowable ht) I/2

[(1728 x opportunity costs x items costs x max-allowable ht)+

(2 x item volume x space costs)] I/2

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74 Proceedings of the 9th Annual Conference on Computers & Industrial Engineering

The above model was developed by differentiating with respect to order size with an objective of optimizing total costs. The model was programmed on an IBM PC-XT using an APL interpreter; all databases were developed through manual keyboard entry.

The limitations of the program were the lack of reliable data for item demand and the inability to perform simulations of 744 items for various scenarios. Since item demand has cyclical and seasonal variations, it is inappropriate to project item demand based on limited item usage data. Most item usage transactional data at GUH resides on the DG Eclipse System and could not be processed on the IBM PC due to lack of computing power.

Hence it was decided that a new set of programs be written on the IBM 4381 using SAS, with item usage data transferred from the DG System via magnetic tape and item cost & volume data transferred via floppy disk from the PC to the IBM 4381 environment. Upon simulation on the IBM 4381 it was found that the space constraining model did not adequately address the space issue and thus the traditional EOQ model was used with the introduction of a Turns Factor (TF). The following section discusses the rationale behind the Turns Factor along with modeling techniques and results.

METHODOLOGY & RESEARCH: Our approach in designing a workable EOQ expression was to create a formula roughly meeting our needs and then subjecting it to a series of "what if" evaluations (modeling). By analyzing two derivatives of the EOQ, Total Storage and Overall Inventory Turns, it was possible to determine the warehousing (space) and handling (labor) demands resulting from the expression. These data could then be compared with the known capacities of the Hospital's existing Stores warehouse and Receiving Department.

C~itical to the evaluation process was the establishment of quantitative measures of the Hospital's current storage and receiving capacity. The floor space (area) in the warehouse was determined from blueprints while a physical inspection revealed the actual overhead clearance in various locations. From this information, the hypothetical size and placement of shelving was optimized to yield the maximum storage capacity of the facility. This maximum (15,220 cu. ft.) was used as the in-house limit on Total Storage. Similarly, the receiving department was analyzed to determine its capacity to receive shipments. The receiving function was seen to have both a fixed and a variable component. The fixed component was primarily due to truck docking and manifest processing time and was independent of shipment size. The variable portion, shipment in-processing, was a function of shipment size. It was further observed, that the fixed component was, quite often, the significant portion of total receipt time. Taking these observations, the fact that the current inventory was turning at 5.8/year and accepted industry norms for turns fall between 12 and 18, we determined our inventory could turn at a rate of 12/year. This figure then gave us the yardstick by which to gauge Overall Inventory Turns.

The rough EOQ expression was built from the ground up using a traditional framework. Our expression contains standard variables representing demand and material cost. The expression deviates from the norm in that it omits parameters for ordering and carrying costs and includes a constant known as the Turns Factor (TF). The purpose of the TF is to provide a means for controlling inventory turns and ultimately receiving activity.

Kapur and Moberg: Evaluating inventory turns 75

To perform realistic modeling required further definition of system behavior. Namely, the calculations for Safety Stock and Reorder Points needed to be defined. It was felt that existing formulations for these variables in our new inventory system were adequate and were used as is. However, based on early experiences with the model, a refinement of the Turns equation was instituted. Namely, to ensure that all items in the inventory turned at some minimal rate, the value of Turns was not allowed to fall below two.

The complete set of expressions used in the modeling exercise are presented on the next page.

EOQ i = ~(2 * D i * TF)/C i

S i = (D i * Li)/365

I)

2)

O i = 2 * S i 3)

T = D i /EOQ i (4)

ISV i = (s i + EOQ i) + v i (5)

n OT = ~ Di/ EOQi

r-~---l= i=l

(6)

n TISV =i__~ ISV i (7)

Whe re,

EOQ = D =

TF = C = S = L = O = T =

ISV = V =

OT = TISV =

inventory item (from 1 to 750 at GUH) Economic Order Quantity Yearly Demand Turns Factor Item Cost Safety Stock Lead Time (Days) Order point Turns Item Shelf Volume (Cu. Ft. Item Volume Overall Turns Total Item Shelf Volume

The modeling was performed on the Hospitals current inventory of 744 widely varying items (both in size and demand). Item cost, Volume and Lead Time information on each item were up-loaded from an APL workspace on an IBM PC (the APL workspace had been manually loaded as part of a prior study). Real demand history was culled from the existing on-line order system. To minimize the effect of transient or seasonal demand, six months of order history (76,212 transactions) was collected. These data elements were amassed on an IBM 4381 mainframe and subsequently input two-phased to a SAS program. In the first phase the actual usage history was extrapolated to yield realistic annual demand estimates. The second phase modeled the overall yearly turns and space requirements (in conjunction with other parameters); the essence of the second phase can be found on the following page:

76 Proceedings of the 9th Annual Conference on Computers & Industrial Engineering

DATA EOQ; MERGE EOQ.DEMOG EOQ.DISPENSD; BY CATNUM;

TF=x; EOQ=ROUND(((2*DISPENSD*TF)/COST)**0.5); SAFETY=ROUND((DISPENSD*LEAD)/365); ORDERPT=ROUND(((DISPENSD*LEAD)/365)+SAFETY); VOLUME=(HEIGHT*WIDTH*LENGTH*(EOQ+SAFETY))/1728;

TURNS=DISPENSD/EOQ;

IF TURNS < 2 AND TURNS <> 0 THEN DO; TURNS=2; EOQ=DISPENSD/2; VOLUME=(HEIGHT*WIDTH*LENGTH*(EOQ+SAFETY))/1728;

END;

PROC MEANS MAXDEC=I N MEAN SUM; VAR TF VOLUME DISPENSED EOQ; TITLE3 GUH CENTRAL STORES; TITLE4 INVENTORY TURNS AND VOLUME STATISTICS; TITLE5 (ANNUALIZED FROM 6 MONTHS DATA);

The SAS program was used to iterate the value of TF from a low of 1 to a high of 25 and for each value compute Total Storage and Overall Turns. Space does not permit a comprehensive presentation of all of the data input to the program, but the table below does show actual results for a variety of TF values.

TABLE i

TF Overall Yearly Total Storage Turns (cu.ft)

1 28.4 5703 2 19.8 6681 3 16.2 7413 4 14.1 8022 5 2.5 8557 6 11.4 9061 7 10.7 9490 8 i0.0 9906 9 9.5 10311 i0 9.0 10670 15 7.4 12274 20 6.5 13542 25 5.8 14640

Conclusion: Table 1 illustrates that for overall yearly turns of 5.8, 14,640 cu.ft, is needed as compared to 8557 cu ft. for 12.5 yearly turns. These results indicate why GUH Stores felt the need for additional warehousing space. At 5.8 turns storage needs were around 14,640 cu.ft, and available storage was only 11,031 cu.ft.

With the help of a floor plan realignment the original 11,031 cu.ft, of space expanded to an optimal available 15,226 cu.ft. Thus, not only did this analysis eliminate any need for external warehousing, it showed an excess of 6669 cu. ft. (15,226 cu.ft. - 8557 cu. ft.) of space (given overall turns of 12.5). This meant that part of this excess of 44% could accommodate "porosities" created within the shelves due to different item package dimensions.

This study saved GUH a huge sum of potential expenditures. In addition, the modular program design facilitates analysis with updated item and usage data to project multiple parameters for inventory management.

Kapur and Moberg: Evaluating inventory turns 77

BIBLIOGRAPHY

APL, An Interactive

SAS Institute Inc.,

Analysis of Inventory

Gilman, L, and A.J. Rose (1976). Approach. John Wiley & Sons, N.Y.

SAS User's Guide: Statistics (1982). Cory, NC.

Hadley, G. and T.M. Whiten (1963). Systems. Prentice-Hall, Inc., N.J.

Housley, C.E. (1978). Hospital Materiel Management. Aspen Systems Corporation, MD.

Housley, C.E. (1983). Strategies in Hospital Materiel Management: Case Analysis and Masterplanning. Aspen Systems Corporation, MD.