Inventory Control For Automated Drug Dispensing Machines

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Inventory Control For Automated Drug Dispensing Machines

  1. 1. 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
  2. 2. 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
  3. 3. Overview  Background – local hospital  Service level policy  Simulation  Pilot study  Conclusion  References  Questions An automated drug dispensing machine 07 November 2007 copyright © 2007 Myles, et al. 3
  4. 4. 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) 07 November 2007 copyright © 2007 Myles, et al. 4
  5. 5. 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 07 November 2007 copyright © 2007 Myles, et al. 5
  6. 6. 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! 07 November 2007 copyright © 2007 Myles, et al. 6
  7. 7. 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) 07 November 2007 copyright © 2007 Myles, et al. 7
  8. 8. 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%) 07 November 2007 copyright © 2007 Myles, et al. 8
  9. 9. 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 07 November 2007 copyright © 2007 Myles, et al. 9
  10. 10. 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 07 November 2007 copyright © 2007 Myles, et al. 10
  11. 11. 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 07 November 2007 copyright © 2007 Myles, et al. 11
  12. 12. Service level policy – pilot study (cont.)  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 07 November 2007 copyright © 2007 Myles, et al. 12
  13. 13. Service level policy – pilot study (cont.)  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 07 November 2007 copyright © 2007 Myles, et al. 13
  14. 14. Service level policy – pilot study (cont.)  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) 07 November 2007 copyright © 2007 Myles, et al. 14
  15. 15. Service level policy – pilot study (cont.)  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 07 November 2007 copyright © 2007 Myles, et al. 15
  16. 16. Service level policy – pilot study (cont.)  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 07 November 2007 copyright © 2007 Myles, et al. 16
  17. 17. 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 07 November 2007 copyright © 2007 Myles, et al. 17
  18. 18. 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. 07 November 2007 copyright © 2007 Myles, et al. 18
  19. 19. Questions 07 November 2007 copyright © 2007 Myles, et al. 19

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