inventorycontrolforautomateddrugdispensingmachines-informs2007-100411232231-phpapp01

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Inventory Control for

Automated DrugDispensing Machines:A Service Level PolicyINFORMS Annual Meeting 2007John KobzaTexas Tech University Department of Industrial Engineering

Steven MylesHewlett-Packard Company

Sean DunaganSandia National Laboratories

Garrett Heath & Surya LimanTexas Tech University Department of Industrial Engineering


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copyright 2007 Myles, et al. 207 November 2007

Notes

Corresponding author Steven Myles

[email protected] http://steve.mylesandmyles.info/

The views expressed are those of the authors and do not

necessarily reflect the policy or practice of Hewlett-PackardCompany nor are they intended to be an official statementby Hewlett-Packard Company.

The views and opinions expressed in this presentation are

those of the authors and do not reflect the official policy orposition of Sandia Corporation, Lockheed MartinCorporation, the Department of Energy, the U.S.Government, or any agency thereof. Any errors oromissions are the responsibility of the authors.


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Overview

Background local hospital Service level policy

Simulation Pilot study Conclusion

References Questions

An automated drug dispensing machine


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Local hospitals goals Reduce pharmacy inventory and transportation costs Reduce the number of medication delivery errors Increase nurses and pharmacists time for other activities

Attempted solutions Implemented automated drug-dispensing machines (ADDMs)

Lower costs Supply-chain costs equal approx. 40% of healthcare costs (Haavik, 2000) Management of demand, inventory, and ordering could save up to 4.5% of

overall supply chain costs (Brennan, 1998) Reduction of medication errors

Shown to reduce medication errors by > 5% (Borel and Rascati, 1995)

Redistribution of nurses and pharmacists time Reduction in medication-related activities Increase in patient interaction (Lee et al., 1992)

Led to Increase in drug shortages

Formulated a policy to optimize the drug-dispensing machines

(Dunagan, 2002)

Background local hospital


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Background local hospital (cont.)

Current inventory policy Modified (s, S) inventory policy

Set max (order up to) and min (reorder point) levels for all drugs in allmachines

Run different reports five times daily to determine which drugs need

to be refilled Refill each drugs inventory level to max if level falls below the drugsmin level between reporting cycles

Refill drug inventories that are close to their respective min levels

Current policys flaws Policy is arbitrary

Relies on pharmacy technicians feelings rather than empirical data

Policy is manually intensive Setting inventory levels does not take into account how long

inventory will last


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Service level policy (Dunagan, 2002)

Service level Set inventory level to provide a given shortage probability during the

inventory review period

Cost increases exponentially as SL approaches 100%

Chose machine for simulation Based on a Pareto analysis of withdrawals from all machines during

a one month period Assumed stationary Poisson daily demand distribution based on

chosen machines data Used Poisson probability mass function to set max levels based on

desired service level

( ) , 0, 1, 2, ...!

D de D f d d

d

= =

{ }shortage 1 P SL=


7/19copyright 2007 Myles, et al. 707 November 2007

Service level policy (cont.)

Simulated with three demand arrival distributions Poisson Uniform Lognormal

Determined optimal review period length using EOI

C = cost of placing an order (estimated by pharmacy at $1.04 forlabor)

R = annualized demand H = holding cost per item per year (based on drugs value) T* = 4 days (hospital prefers one week (7 day) review period)

* 2CT

RH=



Service level policy (cont.) Computed max levels based on average weekly demand

using a cumulative Poisson distribution table For example, if average weekly demand = 5 and desired SL =

95%, max level =9 (actual service level = 96.4%)



Service level policy simulation

Simulated demand on chosen machine using four andseven day review periods Ten randomly chosen locations in the simulated machine Current operation simulated for twenty runs of 360 day years SL policy simulated for 1,800 thirty-one day months to obtain a

confidence interval of 5% Tested Poisson, uniform, and lognormal demand arrival distributions

Predicted 33.2% reduction in refills with 97.5% servicelevel and 33.4% reduction in refills with 99% service level

Projected cost savings of $5,450/year on the simulated ADDM ifimplemented (based on estimated order cost alone) Could mean $100,000+ annual savings hospital-wide assuming the

chosenmachine is typical



Service level policy pilot study

Pilot study of ADDM service level inventory policy Gathered and evaluated historic data

Seven quarters worth of withdrawal data Chose machine for pilot study

Performed a Pareto analysis of top 20% of machines based on

withdrawals Four machines accounted for 43.9% of withdrawals

Chose machine #4 (previously simulated machine) In top 20% of machines Smaller number of drugs

Performed a Pareto analysis of chosen machine Total number of withdrawals = 177,476 Total number of drugs = 296 59 drugs account for 81.5% of withdrawals



Service level policy pilot study (cont.) Estimated restocks per drug

and per day n = number of drugs

withdrawn during a givenquarter

Ni = minimum number ofrestocks required per drug

N= total number of restocksper quarter

N= average number ofrestocks per quarter

=

mincurrent-maxcurrent

lswithdrawaofnumberiN

=

=n

i

iNN

1

n

NN =

_

34.980.173200.8315.45Mean

41.150.213378619.62Q303

34.220.180316616.40Q203

34.790.178308016.04Q103

28.260.146260013.47Q40239.830.172366415.86Q302

31.620.123290911.32Q202

Est. TotalRestocks/ Day

Est. MeanRestocks /Drug / Day

Est. TotalRestocks

Est. MeanRestocks /

DrugQuarter

Summary of quarterly

estimates for currentoperation



Service level policy pilot study (cont.) Determined drugs for testing

Based on number of withdrawals and drug type as defined bypharmacists (e.g., no life or death drugs, no controlled substances)

Chose ten of the top 20% of drugs in terms of withdrawals from theADDM (which accounted for 82% of total withdrawals)

Performed a chi-square goodness-of-fit test to determine if demand

for the chosen drugs was Poisson distributed Drugs A, C, E, and I had test statistics of 1.28, 1.71, 1.60, and 0.16

respectively, indicating that the Poisson distribution is appropriate for thedemand of these drugs with = 0.10

Drugs H and J had test statistics of 3.67 and 4.18 respectively,indicating that demand arrivals for these drugs is very close to having a

Poisson distribution Drugs B and D failed the chi-square test for Poisson arrivals Insufficient data to perform the test for drugs F and G

Set review period (7 days) Determined by hospital



Service level policy pilot study (cont.) Set initial levels for all test drugs

Set max levels using cumulativePoisson table Verified applicability of max levels

with pharmacy Set all min levels at zero

SL policy includes safety stock inmax level

Ran policy for nine reviewperiods Time for study limited by hospital

Monitored policys performance at end of each period Shortages per drug per period Restocks per drug per period Withdrawals per drug per period Shortages per number of withdrawals per drug per period

38Vecuronium 20 mg injG

40Phenylephrine HCl 10 mg injF

J

I

H

E

D

C

B

A

Drug Id.

26Furosemide 20 mg inj

31Potassium Cl 20 mEq IVPB

31Acetamin-Hydorcod 500-7.5mg 0tab

42Magnesium Sulfate 50% 1G inj

47Calcium Gluconate 1 G inj

50Albumin 5% 12.5 G inj

57Propofol IV 1000 mg inj

71Heparin 5000 unit inj

MaxDescription



Service level policy pilot study (cont.) Results

The mean probability of a shortage of a given drug during a givenperiod was 0.0045

The mean probability of a shortage of any drug during a givenperiod was 0.9559

SL comparison Average SL for all drugs during seven reviewed quarters prior to the

pilot study was 86.67% SL of the ten test drugs during pilot study was 95.55%

This discrepancy is likely related to the different number of reviewperiods (approximately 160 review periods for the seven quarters ofpre-pilot demand data vs. nine for the pilot study)

( ) ( )( ) 0.9559studypilotindrugs10|druganyofshortage

druggivenaofshortageno1studypilotindrugs10|druganyofshortage 10

==

P

PP



Restocks per period Estimated restocks prior to pilot study for each drug was 0.17 per

day (or 0.68 per four-day review period) Mean restocks per period over the pilot study was 10.22 (average

restocks per drug per seven-day period was 1.02)

Again likely due to the long period of analyzed data pre-pilot studycompared to the short pilot study Estimated restocks per period was derived from aggregate demand data

for all drugs in the machine

In the SL policy, expected restocks per drug per period was 1.5

Service level policy pilot study (cont.)



Service level policy pilot study (cont.) Actual shortage probability

Analyzed the four drugs (A, C, E, and I) in which the assumedPoisson arrival process of demand was verified Max inventory level to ensure a SL 97.5%, corresponding to the mean

withdrawal data stated

Upper and lower bounds of the confidence intervals forshortage probabilities

With the exception of drug E, the value of 0.025 is not included in any of the rangesfor shortage probabilities Inventory levels could be lowered to achieve that probability

I

EC

A

Drug Id.

1912

29214233

4738

SL = 97.5%4-Day Demand

I

E

C

A

Drug Id.

0.0000.000

0.0250.000

0.0240.000

0.0140.000

P(shortage) upper endP(shortage) lower end



SL policy performed well in simulation and reasonably wellduring pilot study

The proposed SL policy could help reduce healthcare costs Supply chain labor costs

Reduce time spent by pharmacy personnel restocking ADDMs

Reduce time spent by nurses on drug-related activities The SL policys performance could be improved by

Further testing Implementing the model for a larger number of drugs

Implementing the model for a longer period of time Incorporating drug mix into the analysis

Assigning drugs to the appropriate machine for the patients in that ward

Service level policy conclusion



References Borel, J.M. and K.L. Rascati (1995). Effect of an automated, nursing unit-based

drug-dispensing device on medication errors. American Journal of Health-SystemPharmacy, 52, September, 1875-1879. Brennan, C.D. (1998). Integrating the Healthcare Supply Chain. Healthcare Financial

Management, 52(1), 31-34. Dunagan, S. (2002), Inventory Model for Drug Dispensing Machines, Master of Science

Thesis, Texas Tech University, Lubbock, TX. Haavik, S. (2000). Building a Demand-Driven, Vendor-Managed Supply Chain.

Healthcare Financial Management, 54(2), 56-61. Lee, L.W., et al. (1992). Use of an automated medication storage and distribution system.

American Journal of Hospital Pharmacy, 49(4), 851-855. Pyxis: High tech, big profits, fewer jobs. California Nurse, 90, 10, (June 1994). Quick, J.D. (1982). Applying Management Science in Developing Countries: ABC

Analysis to Plan Public Drug Procurement. Socio-Economic Planning Science,16(1), 39-50.

Ray, M.D., L.T. Aldrich, and P.J. Lew (1995). Experience with an Automated Point-Of-UseUnit-Dose Drug Distribution System. Hospital Pharmacy, 30(1), 18, 20-23, 27-30.

atir, A. and Cengiz, D. (1987). Medicinal Inventory Control in a University HealthCentre.Journal of the Operational Research Society, 38(5), 387-395.

Tersine, R.J. (1994). Principles of Inventory and Materials Management, 4th ed.,Englewood Cliffs, NJ: PTR Prentice-Hall.


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