Hospital Inventory Management New Trends in Healthcare
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1 Hospital Inventory Management New Trends in Healthcare Claudia Rosales Michigan State University Michael Magazine and Uday Rao University of Cincinnati In collaboration with Sylvain Laundry HEC Montreal Richard Philippe Logi-D
2 Problem Motivation Supplies management significant costs involved 30-40% of the average hospital s budget (Neil, 2005) Many different supplies Many different locations Little or no visibility of inventory at point-of-use Stock rotation is critical Focus on patient care 2
3 Traditional Hospital Inventory Practices Service Centers Nurse Servers 3 Central Warehouse
4 Literature Review Inventory management at hospitals Bijvank and Vis (2012) Little and Coughlan (2008) Lapierre and Ruiz (2007) Opolon, et al. (2009) Landry and Beaulieu (2009) Impact of technology adoption Delen (2007) Lee and Ozer (2007) Gaukler et al. (2008) Cakici et al. (2010) 4
5 Dealing with inventory complexities Automated Dispensing Machines (ADMs) Computerized cabinet allows inventory visibility at point-ofuse 90% of large hospitals (> 300 beds) have ADMs (*) Hospital Substituted nurse servers for Pyxis Supply Stations (*)Pedersen et al.,
6 Benefits of ADMs New Technology Improve the dispensing and control of medical supplies Allows continuous time tracking of inventory Improve billing accuracy Enabled the use of new/improved inventory replenishment practices 6 Hospital management unsure how to take advantage of new technology
7 New Inventory Practices Using ADMs Inventory is tracked continuously A par value Refill level Critical level Stockout level Replenish at start of every shift - (S,s) Replenish between shifts (Q,R) Between shifts if inventory hits critical level - item is replenished Should we replenish if close to periodic replenishment? What are the benefits of allowing the replenishment of a critical item? How much improvement do we get versus traditional periodic replenishment? 7
8 What Makes this Problem Challenging? Hybrid Inventory Policy Periodic (s,s) replenishment Beginning of shift Continuous (Q,R) replenishment out of cycle whenever needed Optimal policy likely non-stationary Behavior of non-stationary R 8
9 What Makes this Problem Challenging? There is a fixed cost of performing a replenishment - the out-of-cycle replenishment is considered more costly out of cycle fixed cost (k o ) > periodic fixed cost (k p ) There is no restriction to the number of out-of-cycle replenishments Holding costs associated with limited space available Penalty cost when stock-outs occur wasting valuable nurse time Many items (> 100) 9
10 Single Item Hybrid Policy Solution Approach No simple closed form expression for average cost given s,s,r,q Cost function not convex 1. Develop a stochastic optimization heuristic using simulation 2. Obtain approximate parameter expressions using the optimal solution to deterministic Hybrid policy 10
11 Optimization Heuristic Search heuristic Coded in C++ Iteratively searches for (R,Q) and (s,s) values until convergence is reached Heuristic is re-started with different starting points looking for better local optima Simulation is used to evaluate long run average cost Cost within 1% of optimal vs. exhaustive grid search Heuristic used to test different scenarios 11
12 Hybrid Cost Function 12
13 Single Item - Insights Obtained High economic benefits possible for hybrid - up to 18% improvement Significant differences observed in parameter values S << S periodic Hybrid flexible, can behave as periodic policy, or approach continuous policy Hybrid provides maximum benefit when cost of periodic and continuous policy is equal 13
14 Approximate Solution From Deterministic Hybrid Estimates for the stochastic hybrid policy parameters * * ( S s) ( Sd sd) * Q Q d * s s d safety stock (periodic replenishment interval + order lead time) * R R d safety stock (order lead time) Estimated parameters performed well for hospital conditions tested Parsimonious solution for large number of items still needed 14
15 Dealing with Multiple Items The Two-Bin System Motivated by lean principles Each item s inventory stored in two bins primary and secondary Stock from primary bin is consumed first - secondary bin becomes the new primary No manual counting necessary / No need to track individual item consumption Number of items per bin usually selected to provide a pre-specified number of inventory turns. 15
16 Two Bin System - Advantages No need to track individual item inventory continuously Fewer parameters to be defined for inventory control Replenishment can be triggered periodically or by accumulation of empty bins Can be used for all types of products (drugs, supplies, office, etc) 16
17 Two-Bin Replenishment System with RFID Each bin carries one RFID tag When a bin is emptied, the RFID tag is placed on the board and read Information is downloaded to MM information system Depending on system conditions, a replenishment is triggered If order triggered stock delivered after some time While replenishment is processed more bins may become empty 17
18 Two Bin-RFID System in Hospitals Hospitals used to periodic replenishment With RFID hospitals don t always take advantage of additional information system conditions that should trigger replenishment are not defined Several factors may trigger an order When a predetermined number of tags appear on the board When a tag of a primary bin has been on the board for a predetermined period of time When the tag of a secondary bin appears on the board 18
19 Hospital Data Access to over one year of data Data for two different hospitals 19 P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 1/3/11 11:23 AM 1/4/11 7:33 AM 1/4/11 10:29 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 1/21/11 10:31 AM 1/22/11 8:03 AM 1/22/11 11:08 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 1/26/11 3:20 PM 1/27/11 7:37 AM 1/27/11 10:31 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 2/6/11 1:22 PM 2/7/11 7:34 AM 2/7/11 10:37 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 2/9/11 1:55 PM 2/10/11 7:32 AM 2/10/11 10:24 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 4/4/11 4:03 PM 4/5/11 7:31 AM 4/5/11 10:29 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 4/20/11 10:10 AM 4/21/11 7:29 AM 4/21/11 10:26 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 5/9/11 8:50 AM 5/10/11 7:30 AM 5/10/11 10:36 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 6/5/11 3:54 PM 6/6/11 7:30 AM 6/6/11 10:24 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 6/16/11 9:23 AM 6/17/11 7:28 AM 6/17/11 10:40 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 6/24/11 3:55 PM 6/25/11 7:50 AM 6/25/11 11:10 AM P2124C P2124C Bandage rayonne extensibln 9 5 P 1 PQT (12/UN 7/10/11 8:21 AM 7/11/11 7:36 AM 7/11/11 10:28 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 6/30/10 10:42 AM 7/1/10 7:39 AM 7/1/10 9:38 AM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI 7/12/10 11:39 AM 7/13/10 7:37 AM 7/13/10 10:41 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 7/12/10 11:39 AM 7/13/10 7:37 AM 7/13/10 10:41 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 7/24/10 11:55 AM 7/26/10 7:36 AM 7/26/10 11:23 AM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI 7/29/10 1:41 PM 7/30/10 7:32 AM 7/30/10 10:56 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 7/29/10 1:41 PM 7/30/10 7:32 AM 7/30/10 10:54 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 8/6/10 9:28 AM 8/7/10 8:07 AM 8/10/10 9:26 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 8/6/10 9:28 AM 8/7/10 8:07 AM 8/10/10 9:26 AM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI 8/6/10 9:29 AM 8/7/10 8:07 AM 8/7/10 1:27 PM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI 8/6/10 9:29 AM 8/7/10 8:07 AM 8/7/10 1:27 PM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI 8/10/10 9:12 AM 8/11/10 7:31 AM 8/11/10 9:25 AM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI 8/10/10 9:12 AM 8/11/10 7:31 AM 8/11/10 9:25 AM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI 8/29/10 10:22 AM 8/30/10 7:36 AM 8/30/10 9:40 AM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI 8/29/10 10:22 AM 8/30/10 7:36 AM 8/30/10 9:40 AM P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI :28: :36: :28: P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI :41: :36: :24: P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI :47: :34: :33: P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI :47: :37: :23: P2124C P2124C Bandage rayonne extensibln 9 6 S 1 PQT (6/UNI :39: :58: :40: P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI :01: :56: :27: P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 10/2/10 8:15 PM 10/3/10 8:05 AM 10/3/10 11:46 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 10/11/10 4:00 PM 10/12/10 7:42 AM 10/12/10 10:47 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 10/21/10 4:04 PM 10/22/10 7:37 AM 10/22/10 9:06 AM P2124C P2124C Bandage rayonne extensibln 9 6 P 1 PQT (6/UNI 10/23/10 4:04 PM 10/24/10 7:58 AM 10/24/10 10:20 AM
20 Hospital Data Hospital Data using a Two-Bin RFID System under periodic review Several departments within the hospital Data for one year / hundreds of different items Hospital Department Item Code Item Description units/bin Bin type Bin on Board Replenishment Ordered Replenishment Completed E Intravascular Adult Incontinence catheter 1 pads 36 P 6/27/11 8:02 PM 6/28/11 7:20 AM 6/28/11 11:24 AM We were able to obtain from the data: Average demand rates for each item Number of item s per department Average replenishment lead time Hospital provided information for fixed order cost and stockout costs 20
21 Two Bin System - Options for Improvement Traditionally bins replenished daily (periodically) - filling up all empty bins Bin replenishment involves time/effort fixed replenishment cost In case of stockouts nurse procures item stockout cost Too many items to replenish Cost-efficient & practical 21
22 Two Bin System - Options for Improvement 1) Improvement: Parameter Improvement Optimize periodic review parameters to minimize cost Find right replenishment cycle (daily, weekly, etc.) Assuming bin demand follows a Poisson Process Average cost per unit time J P (T) ; T = periodic replenishment cycle (decision variable) Model parameters: L =delivery lead time; N= number of items; r stockout costs per unit ; r= stockout cost per unit time; l bin consumption rate; K = fixed order cost 22
23 1) Parameter Improvement. We show quasi-convexity of J P (T) with respect to T (under conditions we specify). We can find the optimal average cost for the periodic review model J P (T) and the optimal review interval T using a search procedure that finds: We use C++ and a Golden Section search approach to find the optimal average cost J P (T) and the optimal review interval T* 23
24 Two Bin System - Options for Improvement 2) Improvement: Policy Improvement Use of technology to improve inventory visibility continuous review inventory model We formulate a Semi-Markov Decision model Estimate the average cost per unit time J C under continuous review Similar parameters as in periodic review Orders triggered when: a) secondary bin empty b) when n* primary bins are empty (decision variable) 24
25 2) Policy Improvement Bellman optimality equations Using Linear Programming this model can be solved to obtain the optimal cost J C and the optimal number of bins that should trigger a replenishment n* 25
26 Parameter vs. Policy Improvement From hospital data we obtained a base scenario (median values) T = 24 hrs; N = 200; l = bins/hr; r = 55 $/ bin; K = 100 $/replenishment; (Damodaran, 2012) We obtained the optimal average cost per unit time under periodic, J P (T*), and continuous review, J C*, as well as the current hospital periodic average cost per unit time J P (T). Optimal Continuous Review 26 Optimal Periodic Review Hospital Baseline
27 Parameter vs. Policy Improvement Lower values of l (more items per bin) favor the use of periodic review with parameter optimization Factor such as expiration dates and inventory rotation should be taken into consideration 27
28 Parameter vs. Policy Improvement Costs increase more dramatically under periodic review as N increases Less expensive to have a smaller number of large storage rooms than a large number of small storage units. Need to balance with the need to supply stock close to the point-of-use 28
29 Parameter vs. Policy Improvement Storage areas where most items are noncritical could be replenished using periodic review Storage areas where most items are fairly critical and/or expensive (cath lab) can see great benefits from policy improvement 29
30 Future Work - Impact of Different Demand Processes Exponential inter-arrival times good fit for several items, but not all Other distributions (Weibull, Beta, Erlang) provided good fit for several items Test robustness of results under different distributions Simulation model test results under real hospital data 30
31 Conclusion Expensive items can be closely monitored with ADM machines using simple expressions to compute inventory policy parameters. For inexpensive, yet critical items, the two-bin system provides a more parsimonious inventory management system. Under the two-bin system, policy improvement (with the use of RFID or barcodes) provides greatest benefits. 31
32 Conclusion The benefits of policy improvement should be compared to the cost of investing in new technology such as RFID or barcodes. We provide a tool that can estimate the economic benefits of technology investment, and can provide hospital management guidelines to improve the use of available resources. 32
33 Questions? 33
34 Thank you! 34
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