Inventory Control For Automated Drug Dispensing Machines

Inventory Control for
Automated Drug
Dispensing Machines:
A Service Level Policy
INFORMS Annual Meeting 2007
John Kobza
Texas Tech University Department of Industrial Engineering

Steven Myles
Hewlett-Packard Company

Sean Dunagan
Sandia National Laboratories

Garrett Heath & Surya Liman
Texas Tech University Department of Industrial Engineering

Notes
 Corresponding author
 Steven Myles
 steve@mylesandmyles.info
 http://steve.mylesandmyles.info/
 The views expressed are those of the authors and do not
necessarily reflect the policy or practice of Hewlett-Packard
Company nor are they intended to be an official statement
by Hewlett-Packard Company.
 The views and opinions expressed in this presentation are
those of the authors and do not reflect the official policy or
position of Sandia Corporation, Lockheed Martin
Corporation, the Department of Energy, the U.S.
Government, or any agency thereof. Any errors or
omissions are the responsibility of the authors.
07 November 2007 copyright © 2007 Myles, et al. 2

Overview
 Background – local hospital
 Service level policy
 Simulation
 Pilot study
 Conclusion
 References
 Questions

An automated drug dispensing machine


Background – local hospital
 Local hospital’s 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 (cont.)
 Current inventory policy
 Modified (s, S) inventory policy
 Set max (order up to) and min (reorder point) levels for all drugs in all
machines
 Run different reports five times daily to determine which drugs need
to be refilled
 Refill each drug’s inventory level to max if level falls below the drug’s
min level between reporting cycles
 Refill drug inventories that are “close to” their respective min levels
 Current policy’s flaws
 Policy is arbitrary
 Relies on pharmacy technician’s feelings rather than empirical data
 Policy is manually intensive
 Setting inventory levels does not take into account how long
inventory will last

Service level policy (Dunagan, 2002)
 Service level
 Set inventory level to provide a given shortage probability during the
inventory review period
P { shortage} = 1 − SL
 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 machine’s data
 Used Poisson probability mass function to set max levels based on
desired service level
e− D D d
f (d ) = , d = 0, 1, 2, ...
d!

Service level policy (cont.)
 Simulated with three demand arrival distributions
 Poisson
 Uniform
 Lognormal
 Determined optimal review period length using EOI
2C
T* =
RH
 C = cost of placing an order (estimated by pharmacy at $1.04 for
labor)
 R = annualized demand
 H = holding cost per item per year (based on drug’s value)
 T* = 4 days (hospital prefers one week (7 day) review period)


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 and
seven 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% service
level and 33.4% reduction in refills with 99% service level
 Projected cost savings of $5,450/year on the simulated ADDM if
implemented (based on estimated order cost alone)
 Could mean $100,000+ annual savings hospital-wide assuming the
chosen machine 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  Summary of quarterly
and per day estimates for current
 n = number of drugs operation
withdrawn during a given
quarter Quarter
Est. Mean
Restocks /
Est. Total
Est. Mean
Restocks /
Est. Total
Restocks
Restocks
Drug Drug / Day / Day
 number of withdrawals 
Ni =   Q202 11.32 2909 0.123 31.62
 current max - current min  Q302 15.86 3664 0.172 39.83

 Ni = minimum number of Q402 13.47 2600 0.146 28.26

restocks required per drug Q103 16.04 3080 0.178 34.79

n Q203 16.40 3166 0.180 34.22
N= ∑
i= 1
Ni Q303 19.62 3786 0.213 41.15
Mean 15.45 3200.83 0.17 34.98

 N = total number of restocks
per quarter
N
N =
n
_
 N = average number of
restocks per quarter

 Determined drugs for testing
 Based on number of withdrawals and drug type as defined by
pharmacists (e.g., no “life or death” drugs, no controlled substances)
 Chose ten of the top 20% of drugs in terms of withdrawals from the
ADDM (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 the
demand of these drugs with α = 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


 Set initial levels for all test drugs Drug Id. Description Max
 Set max levels using cumulative A Heparin 5000 unit inj 71

Poisson table B Propofol IV 1000 mg inj 57

 Verified applicability of max levels C Albumin 5% 12.5 G inj 50
D 47
with pharmacy Calcium Gluconate 1 G inj
E Magnesium Sulfate 50% 1G inj 42
 Set all min levels at zero
F Phenylephrine HCl 10 mg inj 40
 SL policy includes safety stock in
G Vecuronium 20 mg inj 38
max level
H Acetamin-Hydorcod 500-7.5mg 0 31
 Ran policy for nine review tab
I Potassium Cl 20 mEq IVPB 31
periods J Furosemide 20 mg inj 26
 Time for study limited by hospital
 Monitored policy’s 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

 Results
 The mean probability of a shortage of a given drug during a given
period was 0.0045
 The mean probability of a shortage of any drug during a given
period was 0.9559
P ( shortage of any drug | 10 drugs in pilot study ) = 1 − P ( no shortage of a given drug )
10

P ( shortage of any drug | 10 drugs in pilot study ) = 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 review
periods (approximately 160 review periods for the seven quarters of
pre-pilot demand data vs. nine for the pilot study)


 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 study
compared 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


 Actual shortage probability
 Analyzed the four drugs (A, C, E, and I) in which the assumed
Poisson arrival process of demand was verified
 Max inventory level to ensure a SL ≥ 97.5%, corresponding to the mean
withdrawal data stated
Drug Id. 4-Day Demand SL = 97.5%
A 38 47
C 33 42
E 21 29
I 12 19

 Upper and lower bounds of the confidence intervals for
shortage probabilities
 With the exception of drug E, the value of 0.025 is not included in any of the ranges
for shortage probabilities
 Inventory levels could be lowered to achieve that probability
Drug Id. P(shortage) lower end P(shortage) upper end
A 0.000 0.014
C 0.000 0.024
E 0.000 0.025
I 0.000 0.000

Service level policy – conclusion
 SL policy performed well in simulation and reasonably well
during 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 policy’s 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


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-System
Pharmacy, 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-Use
Unit-Dose Drug Distribution System. Hospital Pharmacy, 30(1), 18, 20-23, 27-30.
 Şatir, A. and Cengiz, D. (1987). Medicinal Inventory Control in a University Health
Centre. 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.


Questions


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