A simulation approach for evaluating medication

International Journal of Systems Science: Operations & Logistics

ISSN: 2330-2674 (Print) 2330-2682 (Online) Journal homepage: http://www.tandfonline.com/loi/tsyb20

A simulation approach for evaluating medication supply chain structures Kathryn N. Smith, Anita R. Vila-Parrish, Julie S. Ivy & Steven R. Abel To cite this article: Kathryn N. Smith, Anita R. Vila-Parrish, Julie S. Ivy & Steven R. Abel (2016): A simulation approach for evaluating medication supply chain structures, International Journal of Systems Science: Operations & Logistics, DOI: 10.1080/23302674.2015.1135355 To link to this article: http://dx.doi.org/10.1080/23302674.2015.1135355

Published online: 22 Jan 2016.

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A simulation approach for evaluating medication supply chain structures Kathryn N. Smitha , Anita R. Vila-Parrisha , Julie S. Ivya and Steven R. Abelb Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA; b Department of Pharmacy Practice, Purdue University, West Lafayette, IN, USA

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a

ABSTRACT

ARTICLE HISTORY

Healthcare costs per capita in the United States are one of the most expensive in the world. It may be surprising to note that the second largest expense in a hospital is in inventories. In this paper, we address the need for developing better quantitative models of the hospital medication supply chain system. We develop two simulation models which represent commonly used supply chains: centralised and stockless. We present a case study using meropenem, an antibiotic, to explore the impact of product and demand characteristics on the cost effectiveness of each approach. The results show that while the stockless system is almost always higher performing in terms of cost, it may be at the expense of patient safety. The results of the simulation models suggest developing a strategy using classifications to aid strategic supply chain decisions related to the hospital environment could improve inventory management.

Received  May  Accepted  December 

1. Introduction Healthcare costs per capita in the United States are one of the most expensive in the world, as shown by Schoen et al. (2010). It may be surprising to note that the second largest expense in a hospital is in supply chains (Moon, 2004). Supply chains encompass the entire system of organisations, people, costs, and activities that are involved in ordering products from suppliers, storing the inventory at a facility, and distributing them to a customer, in the case of this paper, the patient. Despite the fact that these expenditures are so large, inventory management of pharmaceuticals and medical supplies have received relatively little attention. This is in part due to the clinical nature of pharmacists who are tasked with inventory management in addition to patient care (Alverson, 2003). Alverson (2003) describes the impacts of this mismanagement, which include delays in patient care, medication waste, and decreased patient time. In traditional industrial settings, the main objective of inventory and supply chain optimisation is often cost reduction. However, in a hospital environment the primary objective is the service level to patients and cost reduction may be a secondary objective. In the context of healthcare, service level implies the proper, timely care of the patients while avoiding rework (meaning readmission or any error that affects the patient in this context). The American Hospital Association (AHA) reported that CONTACT Anita R. Vila-Parrish ©  Taylor & Francis

[email protected]

KEYWORDS

Simulation; supply chain management; inventory

99.5% of hospitals have reported at least one medication shortage on the last six months, and 82% reported that the treatment was delayed due to this shortage (AHA, 2011). These shortages impact the hospital and healthcare delivery in two ways. First, when a shortage occurs the hospital may need to order off contract at a more expensive price. Second, there may be consequences for the patient’s health as a result of a delayed procedure or substitution of the preferred medication (Gebicki, Mooney, Chen, & Mazur, 2013). Balancing the service level required to provide high quality medical care with inventory costs in a complex, variable, and uncertain environment where the study of inventory optimisation is not a core competency can be a challenging task that commonly leads to suboptimal inventory control. In this paper, we have developed medication inventory models to study different supply chain structures commonly found in hospitals today using Monte Carlo simulation. Healthcare inventory modelling is used to evaluate the performance of two common supply chain strategies: centralised and stockless as a function of different demand and medication attributes. The paper is organised as follows: in Section 2, the current literature is analysed and presented; Section 3 describes the simulation models; Section 4 summarises the case study and model results; and section 5 discusses the conclusions and future research directions.

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2. Literature review

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2.1. Inventory management in healthcare Although there is a wealth of research focused on optimising supply chain and inventory management in traditional industries (such as retail), there are few studies that focus on the hospital environment due to its unique characteristics (Bijavank & Vis, 2012). In most hospitals, pharmacists and technicians decide when to order from the supplier, how much to order and whether to store the inventory in the clinic or the pharmacy. In order to maximise patient safety and service level, they tend to overstock, leading to high inventory costs and waste which occurs when the medicine exceeds the expiration date (Gebicki et al., 2013; Uthayakumar & Priyan 2013). Due to the fact that demand is linked to patient condition and census, it is difficult to accurately forecast pharmaceutical demand in a hospital environment (Danas, Roudsari, & Ketikidis, 2006). A commonly encouraged inventory management system for hospitals is the stockless inventory system. According to Wilson, Cunningham, and Westbrook (1992), the purpose of the stockless system is to completely eliminate the inventory in the storeroom. The goals are to reduce the amount of inventory, the cost of running a storeroom, and hospital assumed costs of obsolescence (Rivard-Royer, Landry, & Beaulieu, 2002; Wilson et al., 1992). While the stockless inventory system may not be the most efficient for all hospitals or all drugs (Colletti, 1994; Wilson et al., 1992), it is not clear what characteristics determine whether the stockless system is suitable.

2.2. Classification systems The ABC classification is an easy to apply method of categorising products by specific attributes such as cost, in order to focus improvement efforts on the most impactful products. This classification system, based on annual dollar usage, has been used in some medication inventory studies including a study in an Indian hospital by Ramanathan (2006). A limitation of the ABC approach is that it is based on a one-dimensional criteria and ignores other potentially relevant product characteristics. For this reason, many authors have developed multi-attribute classification models such as the multiattribute spare tree analysis (MASTA) approach used in the spare parts inventory management. MASTA considers four criticality categories and a resulting inventory policy is determined (Braglia, Grassi, & Montanari, 2004). Danas et al. (2006) adapted the MASTA classification system of spare parts to the hospital scenario, and called it Med-MASTA.

The four major categories analysed were patient treatment (danger of loss life, quality of treatment, replacement with other treatment), supply characteristics (lead time, number of potential suppliers, replacement), inventory problems (price, space required, special condition, expiry date), and usage rate (over stocking, frequency of use). After the items were classified, an inventory system was proposed for each class: A – was stocked in each clinic that uses them and the safety stock at the central pharmacy, B – was stocked in each clinic that uses them, but the safety stock distributed in the virtual pharmacy, C – was stocked only in the clinics that uses them, and D – was supplied by the Just in Time system (Danas et al., 2006). Another classification system that has been studied for pharmaceuticals is the VED classification system. The VED system: ‘V’ is for vital items without which a hospital cannot function, ‘E’ for essential items without which an institution can function but may affect the quality of the services, and ‘D’ stands for desirable items, unavailability of which will not interfere with functioning (Gupta, Gupta, Jain, and Garg (2007). This classification system determines the criticality of supplies in a different way. These classification systems are important because they represent the main drug attributes that influence inventory management and patient outcomes: demand level, criticality, cost, etc.

2.3. Healthcare supply chain modelling While many of the aforementioned papers are conceptual, there has also been work in simulation and operations research modelling. The work most closely related to our research by Gebicki et al. (2013) developed a simulation of a hospital medication supply chain system and evaluated four different policies, each policy considering different medication characteristics, costs, and structures. All four policies involved systems with a central pharmacy but one of the policies tested tried to minimise the amount of inventory in the central pharmacy. The closest policy to a decentralised structure had the highest number of global stockouts (i.e. complete system stockout) but also had the lowest average cost. Other work focusing on optimal ordering policies is summarised in Table 1. While most of the research presented has focused on the optimisation of inventory ordering, the objective of this work is to develop simulation models: (1) to evaluate two supply chain structures under different demand and medication characteristics, (2) to quantify the impact of the supply chain structure, and (3) to identify the best inventory policy and supply chain structure as a function of hospital characteristics.

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Table . Pharmaceutical inventory modelling literature review summary of recent experimental work.

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Author

Method

Objective

Attanayake, Kashef, and Andrea ()

Discrete-event system simulation

Inventory policy to minimise cost (borrowing, holding, ordering, and stockout)

Gebicki et al. ()

Event-driven simulation

Little and Coughlan ()

Constraint programming optimisation model (unbounded knapsack)

Rosales, Magazine, and Rao ()

Simulation-based optimisation heuristic and search engine

Shukla, Sudi, and Darek ()

Pathway variation analysis (PVA): modelling and simulations

Swaminathan ()

Simulation: multi-objective optimisation model heuristic Operations research and constrained inventory models

Optimal inventory management policy based to minimise total cost and stockouts based on varying levels of information Optimal stock levels of overall products to achieve high service levels at least cost Optimise long-run average cost and provide insights on benefits of hybrid ordering system Improve patient care pathways to reduce pathway diversions using pathway variation analysis and Monte Carlo simulation Drug allocation taking into account efficiency, effectiveness, and equity Optimal inventory lot size, lead time, and number of deliveries to achieve customer service level target with minimum total cost Optimising drug inventory (minimising waste and maximising access)

Uthakakumar and Priyan ()

Vila-Parrish, Ivy, and King ()

Simulation: Markov decision process for demand as a function of patient condition which decides level of inventory and order policy

3. Simulation models 3.1. Medication supply chain preliminaries We developed simulation models that represent two common hospital supply chain systems which we define as: (1) stockless and (2) centralised. Monte Carlo simulation was used in Matlab in order to instantaneously and randomly generate demand at the beginning of every day and then observe how the given attributes affect system cost and stockouts. The objective was to develop representative systems where performance, defined as total system cost and number of stockouts, could be tested under a variety of scenarios. Similar to the stockless system described by Rivard-Royer et al. (2002), medications are stored at the unit (hospital) level and the inventory is managed directly between the clinic and the supplier. In the centralised system, there is a central pharmacy in addition to clinic level inventory locations. Suppli-

Assumptions

Results

Poisson demand, supply unlimited, all stockouts are filled from sister hospitals Fixed review period, holding costs, ordering costs, stockout costs, and expiration costs

Optimal inventory policies under stochastic demand and continuous review

Product demand is normally distributed

Optimal ordering policy based on space, delivery, and criticality

Poisson demand, stationary inventory policy

Initial periodic inventory and out-of-cycle par levels

Capacity completely determined by number of beds

Decision support system for improved patient care pathways using PVA

Basing analysis on demand, cost of drugs, availability, criticality, and expiration window improves savings and patient safety

Decision support system Finite production rate of drugs, perishability, continuous review, payment delay due to trade-credit system

Optimal lot sizes, lead time, and number of deliveries based on desired, customer service level, floor space

Demand fulfilled by somewhere immediately, lead time of a day for raw materials

Optimal base-stock policy

ers replenish the inventory at the central pharmacy and the central pharmacy replenishes the inventory levels at the patient unit level. In this supply chain structure, there tends to be more inventory throughout the system since there is inventory held at the centralised pharmacy and the clinics, each having different associated holding costs. Although the costs and the waste could be higher, the chance of stocking out at the hospital level may be lower in the centralised system than the stockless system. The centralised system allows for an additional risk pooling opportunity by having a pool of inventory stored centrally. We consider three types of stockouts as defined by Gebicki et al. (2013) as: local stockout, main stockout, and global stockout (described in Table 2). As the level of stockout moves from local to global, the cost associated with a stockout increases due to the time associated with the disruption in activities and potential cost of obtaining the medication outside of the hospital.

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Table . Description of stockout types and their associated costs. Stockout type

Definition

Local

For the centralised system: the medication is stocked out at the clinic level but not the central pharmacy. For the stockless system: this stockout type does not occur.

Main

For the centralised system: the medication is stocked out at the clinic and pharmacy. For the stockless system: the medication is stocked out at the clinic level. For the centralised system: medication is stocked out at the central pharmacy and all of the clinics For the stockless system: medication is stocked out in all clinics.

Global

Response to stockout For the centralised system: the central pharmacy is searched to see if it is capable of filling any, or all, of the shortage. For the stockless system: this stockout type does not occur. For the centralised and stockless systems: the other clinics are searched to see if they are capable of filling any, or all, of the shortage. For the Centralised and Stockless Systems: the medication is obtained from outside the hospital.

Cost impact Associated costs are due to the additional work required to locate doses at the central pharmacy.

Associated costs are due to the resource requirements to search for the drug in the other clinics in the hospital and getting it for the clinic that needs it. Associated costs include the resources involved in procuring the same drug in other hospitals, buying it from them (often at a premium) and transporting it.

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Figure 1(A) shows a stockout in Clinic A. In the centralised system, Clinic A will seek to fill demand from the central pharmacy first. If the central pharmacy cannot satisfy demand, the stockout is a main level stockout. Next Clinic A will seek to fill demand from the other clinics. If the other clinics cannot completely fill demand, a global stockout exists and the demand will be filled outside the hospital. As can be seen in Figure 1(B), there is no central pharmacy in the stockless system. Therefore, the first stockout in that system is a main stockout since the next step is to search the other clinics. Similar to the centralised system, if the other clinics cannot completely fill demand, a global stockout exists and the demand will be filled outside the hospital. 3.2. Model overview and notation

Figure . Centralised and stockless systems diagrams with the circles representing stockouts and the arrows representing where the clinic tries to fill the stockout from for each stockout type.

A visual representation of each type of stockout and the replenishment source for the centralised systems is shown in Figure 1(A) and the stockless system in Figure 1(B). The circles indicate a stockout, where each type is represented by a different type of line. The arrows connecting different entities match the designated stockout types to indicate where the clinic searches to fill the shortage.

The Matlab simulation models were developed to represent the two supply chain systems. A detailed description of each supply chain system modelled is presented in Sections 3.4 and 3.5. Each simulation model has three clinics (j = a, b, c). The inventory characteristics were analysed for one month (i.e. 30 days) (i = 1, 2, …, 30). The following cost variables are associated with the system: r h: annual holding cost per unit; r c: product cost per unit; r gs: global stockout cost per unit; r ms: main stockout cost per unit; and r ls: main stockout cost per unit. These costs are assumed to have the following relationship: gs > ms > ls. The following inventory-related decision variables and parameters are defined for the system: r Mc,S : clinic par level for stockless system; r Mc,E : clinic par level for centralised system;

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Table . Performance measure and variable equations for simulation model. Parameter Stockout indicator variable Total par level for stockless system Total par level for centralised system Initial cost for stockless system Initial cost for centralised system Total global stockout cost per clinic per day Total main stockout cost per clinic per day Total local stockout cost per clinic per day Clinic cost per day per clinic for stockless system Clinic and pharmacy cost per day per clinic for centralised system

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Total monthly cost for stockless system Total monthly cost for centralised system

r r r r r r

Mp : pharmacy par level; MT,S : total par level for stockless system; MT,E : total par level for centralised system; I: total inventory; ic j (t): inventory on-hand in clinic j at time t; ip (t): inventory on-hand in the pharmacy at time t; and r dj : realised demand in clinic j. The following performance measures are evaluated for the system under each supply chain structure: r C− c,S (t): total clinic cost per day for stockless system; r C− c,E (t): total clinic cost per day for centralised system; r CI,S : initial cost for stockless system; r CI,E : initial cost for centralised system; r Cj G (t): total global stockout cost per day; r Cj L (t): total local stockout cost per day; r Cj M (t): total main stockout cost per day; r SG (t): total number of items globally stocked out per day; r SL (t): total number of items locally stocked out per day; and r SM : total number of items mainly stocked out per day. Table 3 defines the equations that are used to calculate the cost performance measures for both a stockless and centralised system. The equations are used throughout the simulation to calculate the total monthly cost of the system for each scenario tested. The total monthly cost includes the initial cost required to bring the clinics and pharmacy (for the centralised system) up to the designated par levels and the daily operating costs.

Equation 

0, no stockouts occured 1, at least one stockout occured MT,S = 3Mc,S MT,E = 3Mc,E + M p CI,S = 3cMc,S CI,E = 3cMc,E + (cM p ) CGj (t ) = (gs)(SG ) j CM (t ) = (ms)(SM ) j CL (t ) = (ls)(SL ) j Cc,E (t ) = [c(Mc− (icj (t ) − d j (t )))

X =



+ hcicj (t )](1 − x)+[c(Mc ) + CGj (t ) + CMj (t )]X j Cc,S (t ) = [c(Mc − (icj (t ) − d j (t ))) + hcicj (t ) + hci p (t )](1 − X )+[c(Mc ) + CGj (t ) + CMj (t ) + CLj (t )]X 3 30   Ccj (t ) TCS = CI,S + TCE = CI,E +

i=1 j=1 30  3 

i=1 j=1

j

Cc (t )

3.3. Model description For both supply chain systems, the clinics are assumed to be independent; therefore, each clinic determines its own inventory policy. At the beginning of the horizon under each supply chain system, each clinic (j) begins with an initial inventory on hand, ic j (0). The demand is simulated using a negative binomial (NB) distribution for each clinic separately at the beginning of the day. At the start of each day, each clinic receives a replenishment that brings its current inventory back to the par level. A variety of par levels were tested in order to determine the maximum inventory that produces the lowest costs for the system. The simulation models were run for a 30-day period with 30 replications. Figure 2 shows the cumulative mean of the expected cost, as a function of the number of replications, for a representative par level for the centralised model. The graph was created based on the replication size determination methods described in Robinson (2014). This figure demonstrates that 30 replications are sufficient to provide an estimate with acceptable variability. As can be seen in Figure 3, the cumulative mean becomes fairly linear; we chose 30 replications in order to be more confident in the results. 3.4. Stockless system Recall that within the stockless supply chain environment the clinics each stock inventory close to the point of use. Their replenishments come directly from the supplier and stockouts occur at two levels (main and global). The stockless system simulation model operates as follows.

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Figure . Cumulative mean per number of replications for determination of number of replications with the middle line representing the cumulative mean and the top and bottom lines representing the upper and lower intervals, respectively.

(1) Each clinic is initiated with inventory up to the scenario’s maximum clinic inventory level, also known as the clinic par level (Mc,S ). The scenario starts with an inventory level of one half of the clinic’s mean demand and the inventory level is increased to 3∗ clinic’s mean demand. These ranges were chosen based on guidance from hospital pharmacists. (2) Next, dj is generated from a demand distribution for each clinic. (3) Each clinic’s demand that can be filled by the current inventory is filled. (4) If a shortage at one location occurs: (a) First, the neighbouring clinics are checked for excess inventory. If there is available inventory it is diverted to the clinic in need and the inventory at all affected locations is updated. This case is defined as a ‘main stockout’. (b) Second, if the neighbouring clinics cannot completely satisfy the shortage the hospital must issue an emergency order to the supplier and/or neighbouring hospitals. This case is defined as a ‘global stockout’. (5) At the beginning of every day, each clinic’s onhand inventory is raised to the par level. The total cost of the replenishment is c(Mc− (icj (t ) − d j (t ))) + hcicj (t ) (the product cost multiplied by the number of units ordered at each clinic). (6) Finally, the total cost for the month (30 days), TCS , is calculated by adding the daily replenishment, stockout (at each level), and holding costs. 3.5. Centralised system The centralised system simulation model is based in a hospital with three independent clinics and a central

pharmacy. Each clinic has its own demand, inventory, and par level. The pharmacy serves as an inventory reserve for the clinics. The simulation model operates similarly to the process described for the stockless system with a few key differences. (1) Each clinic is initiated with inventory up to Mc,E and the pharmacy is initiated with inventory up to MP . When a stockout at a clinic occurs, the system will first try to satisfy that stockout using available inventory at the pharmacy before it checks the clinics. If the pharmacy cannot fulfil the entire stockout quantity, the system will check the other clinics as defined in the stockless system. (2) At the end of each day, the pharmacy’s inventory is replenished by the external supplier to MP . (3) Finally, the total cost for the month, TCE , is calculated by adding the daily replenishment (at the clinic and pharmacy levels), stockout (at each level), and holding costs (at each location). Figure 3 summarises the process flow of the simulation model using the same notation as previously defined. The flow chart shows an iteration of the process for one clinic for one day. The process for one clinic occurs simultaneously for the other two clinics, and the total cost of the system for that day is calculated. Each 30-day run is repeated for 30 replications, which is outlined in the flow diagram. The shaded portion of Figure 3 refers to the part of the process that is unique to the centralised system.

4. Case study In order to get an accurate understanding and comparison of the two systems, we conducted a case study focused on the demand for one drug, meropenem, in a hospital care unit.

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Figure . Simulation model summary flow chart with the shaded portions representing the steps that happen in the centralised system but not the stockless system.

4.1. Introduction to meropenem

4.2. Experimentation

Meropenem is an antibiotic that is given intravenously in hospitals to treat a variety of bacterial infections. Because it is used throughout the hospital for a variety of infections, it provides a reasonable representation of pharmaceutical demand from multiple independent units. Meropenem is usually prescribed in 1 or 0.5 gm doses multiple times a day (every 8, 12, or 24 hours) over a period of time. The retail price of meropenem is around $77 a gram (Meropenem, 2015). Analysing drug pull data from one unit, it was determined that the demand for meropenem is not constant throughout the year. However, the monthly, unit demand follows a gamma Poisson mixture distribution. The gamma Poisson mixture is a type of NB distribution. Table 4 shows the p-values, means, and variances calculated for daily unit demand distribution.

The objective of this research was to develop a stockless and centralised pharmacy supply chain simulation model to compare the performance of these systems as a function of product and demand characteristics. The experimental design shown in Table 5 was used to capture the effect of varying the mean daily demand, variation of daily demand, stockout costs, holding cost, and product cost. The demand and cost data were extrapolated from our analysis of meropenem. Three levels of mean demand were tested with a NB distribution to capture different demand levels (the daily demand for meropenem from the case study hospital was typically fairly low, e.g. 4 units per day). The holding costs and stockout costs were estimated based on assumptions about the types of costs associated with the stockout types that were described earlier in Table 2. The local and main

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Table . Meropenem monthly demand data distribution. Month

p-value

Mean (λ)

Variance

Coefficient of variation

Sample size

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

           

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January February March April May June July August September October November December

stockout costs were estimated to be fairly small, since they are the costs associated with the disruption of work due to the stockout. The global stockout cost was estimated to be much larger since that would involve a disruption and obtaining the medication via a rush order. All of the scenarios tested were meant to capture realistic combinations of product and demand characteristics. For each of the scenarios in Table 5, we determined the clinic par level and total par level that corresponds to the lowest total cost. The clinic par levels for the stockless and centralised system are not the same when the total par levels are the same since the total par level is an order up to level for the entire system. For example, a total par level of 15 would be clinic level of 5 in the stockless system and clinic level of 3 and pharmacy level of 6 in the centralised system. In order to focus our results further, in the case of the centralised supply chain, we set the pharmacy’s par level equal to three times the scenario’s standard deviation of daily demand. This can be thought of as the clinics’ safety stock as it is the inventory that is held in the system in order to deal with variation in demand.

Table . Experimental design. Characteristic

Levels

Daily demand

Low Demand (C), Low Variability: NB(,.) Low Demand (C), High Variability: NB(,.) Medium Demand (C), Low Variability: NB(, .) Medium Demand (B), High Variability: NB(, .) High Demand (B), Low Variability: NB(.,.) High Demand (B), High Variability: NB(.,.) Low criticality (D): • Local Stockout: $ (centralised only) • Main Stockout: $ • Global Stockout: $ High criticality (V): • Local Stockout: $ (centralised only) • Main Stockout: $ • Global Stockout:$ Low: $ per unit High: $ per unit Low: % of the per unit cost per year High: % of the per unit cost per year

Stockout cost

Product cost Holding cost

4.3. Results and discussion The results of the simulation suggest some fairly consistent behaviours across the different scenarios that we considered. Evaluated from a cost performance standpoint, the stockless system always has a lower overall cost in all of the low and medium demand at every par level. The two systems have the same total system inventory, but the centralised system allocates some of that inventory to the central pharmacy. Therefore, there is less inventory in each clinic in the centralised system than there is in the stockless system for the same total par level scenario. This means that there are local stockouts occurring in the centralised system which are incurring a cost that the stockless system does not have. For the high demand cases, the lowest overall costs always occur in the stockless system, however this is not the case in the low variance scenarios. In the high demand, low variance cases, the centralised system is better at low par levels for some of the scenarios and the stockless system becomes better in terms of cost as the par levels increase. However, the lowest cost total par level for each scenario is for the stockless system. In general, the lowest cost total par level for each scenario is for the stockless system. Table 6 shows the lowest total cost per total par level for each scenario tested. The scenarios are organised by the ABC and VED classification systems. For example, C,D corresponds to low demand and low criticality. The scenario labels are in the format of variance first (HV or LV), holding cost (HH or LH) second, and product cost third (HC or LC). Therefore, for example, LVHHHC is the low variance, high holding cost, high product cost scenario. In Table 7, the scenarios presented in increasing order in terms of cost within the demand and criticality groups. As can be seen in the table, there are certain scenarios that are always in the same order for all demand and criticality groups. In order to more clearly represent the effects of different drug aspects on the total system cost,

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Table . Total par level corresponding to lowest average total system cost per scenario. a. C,D

b. C,V

Scenario

Min. cost

Clinic par

Total par

Scenario

Min. cost

Clinic par

Total par

LVLHLC LVHHLC HVLHLC HVHHLC LVLHHC HVLHHC LVHHHC HVHHHC

$, $, $, $, $, $, $, $,

       

       

LVLHLC HVLHLC LVHHLC HVHHLC LVLHHC HVLHHC LVHHHC HVHHHC

$, $, $, $, $, $, $, $,

       

       

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c. B,D

d. B,V

Scenario

Min. cost

Clinic par

Total par

Scenario

Min. cost

Clinic par

Total par

LVLHLC LVHHLC HVLHLC HVHHLC LVLHHC LVHHHC HVLHHC HVHHHC

$, $, $, $, $, $, $, $,

       

       

LVLHLC LVHHLC HVLHLC HVHHLC LVLHHC LVHHHC HVLHHC HVHHHC

$, $, $, $, $, $, $, $,

       

       

e. A,D

f. A,V

Scenario

Min. cost

Clinic par

Total par

Scenario

Min. cost

Clinic par

Total par

LVLHLC HVLHLC LVHHLC HVHHLC LVLHHC HVLHHC LVHHHC HVHHHC

$, $, $, $, $, $, $, $,

       

       

LVLHLC HVLHLC LVHHLC HVHHLC LVLHHC HVLHHC LVHHHC HVHHHC

$, $, $, $, $, $, $, $,

       

       

Table . Ranking of scenarios based on total cost within drug demand and criticality groups. Ranking Scenario

C,D

C,V

B,D

B,V

A,D

A,V

LVLHLC LVHHLC HVLHLC HVHHLC LVLHHC HVLHHC LVHHHC HVHHHC

       

       

       

       

       

       

Table 7 shows which scenario tested corresponded to the lowest cost. Table 7 shows that product cost is the most important factor, which is to be expected since the product cost is based on demand, not on the number of stockouts. It also appears that criticality does have much effect on the total system cost since there is only one case in which the ranking is different between high criticality and low criticality scenarios: LVHHLC and HVLHLC. As can be seen in the shaded cells of Table 6, the total system costs

between those scenarios are very similar. In contrast, variance in demand appears to have a large effect because the low variance scenarios are always higher ranked than their high variance counterparts. Figure 4 highlights the relationship between variance and the total system cost. Figure 4 shows the system cost per total par level graphs for the high holding cost and high product cost scenarios. As can be seen in the graphs, variance has an impact on the gap between the total system cost of the centralised and stockless system. The gaps in the high variance scenarios are wider in every case than their low variance counterparts. Most of the graphs for the scenarios, look very similar to those shown in Figure 4. This can be explained by the fact that the model allocates more inventory to the centralised pharmacy in high variance cases, since the centralised pharmacy is similar to safety stock and a function of the demand variance. For each of the high variance cases, the number of local stockouts is higher than in the low variance case because less inventory is held at the clinic level for the centralised system. The demand allocation for the stockless system is not related to variance and the system does not have local stockouts so the performance does not differ based on low and high variance.

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Figure . Average system cost by total par level for centralised and stockless systems in high holding cost and high product cost scenarios with the grey lines with diamonds representing the centralised system and the black lines with circles representing the stockless system.

The high demand and low variance scenarios are a little more interesting since stockless does not consistently outperform the centralised. Table 8 identifies the system with the lowest cost per par level for each scenario tested. If the box only has an S, this means that the stockless system always has the lowest cost. C-S means that the centralised system originally has the lower cost and at some point, the stockless system becomes cheaper. Table 8 demonstrates, for the scenarios tested, that the stockless system is cheaper in the low and medium demand cases. This is also true for the high demand, high variance scenarios. However, this trend does not consistently hold for the high demand, low variance cases. There are cases where the centralised system is lower cost Table . Lowest cost system for each scenario by par levels. Lower costing system Scenario

C,D

C,V

B,D

B,V

A,D

A,V

LVLHLC LVHHLC HVLHLC HVHHLC LVLHHC HVLHHC LVHHHC HVHHHC

S S S S S S S S

S S S S S S S S

S S S S S S S S

S S S S S S S S

C–S S S S S–C–S S C–S S

S S–C–S S S C–S S S–C–S S

for the smaller par levels and as the par level increases, the stockless system becomes the lower cost strategy (C–S). There are also cases where the lower cost strategy changes from stockless to centralised back to stockless as par levels increase (S–C–S). Figure 5 shows the average system cost by total par level for each case where the stockless system does not always have a lower cost than the centralised system. Figure 5 shows the six high demand and low variance scenarios where the stockless system is not always cheaper than the centralised system. However, the stockless system does become less costly before the minimum cost par level is reached in all scenarios. This could be because when there is a high demand, there are too many main stockouts at lower par levels to make up for the cost associated with local stockouts in the centralised system. In order to get a better idea of the behaviour of the total system cost, Table 9 shows the breaking points at which the stockless system becomes less expensive than the centralised system for each high demand, low variance case. As can be seen in Table 9, the point at which the stockless system becomes less costly is always multiple par levels before the par level associated with the minimum cost. In a case where the clinics can have as much inventory as needed, the stockless system will always be the better option in terms of total system cost. If there is a constraint

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Figure . Average system cost by total par level for centralised and stockless systems for select high demand and low variance cases.

and the drug has high demand and low variance, the centralised system could work better if the amount held on site is around or less than the average demand. In terms of sensitivity analysis for total cost, some extreme condition scenarios were tested to identify

the conditions under which the centralised system outperformed the stockless system in terms of total cost. We hypothesised such cases would be characterised by higher holding costs and higher stockout costs (worst case scenario) under different levels of variability. Even in

Table . Lowest total cost breaking points between stockless and centralised systems. A,D (high demand, low criticality)

LVLHLC LVLHHC LVHHHC

Central becomes better: total par

Stockless becomes better: total par

Minimum cost: total par level

– – 

  

  

A,V (high demand, high criticality) LVHHLC LVLHHC LVHHHC

 – 

  

  

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Figure . Total expected stockouts per total par level for centralised and stockless system in the high demand, low criticality, low variability, high holding cost, and high product cost scenario.

the conditions tested, the stockless system still yields the lowest total cost. The stockless system could be higher performing due to the fact that perishability or waste cost is only captured through the holding cost in our model.

In addition to the total cost, we explored how and where stockouts occur along the supply chain in the two different systems. As mentioned before, when the total par levels are equal, the centralised system had more total stockouts since there were fewer units at the clinic level. This can be seen in Figure 6, which is for the high demand, low criticality, low variability, high holding cost, and high product cost scenario. Figure 6 shows that as par levels increase, the number of total stockouts for both systems go to zero because the systems are holding more inventory than is needed to satisfy daily demand. As a result the two systems operate equally well in terms of stockouts at high total par levels. The total number of stockouts reflects only one aspect of the performance of the two systems. Another measure is the expected number of global stockouts, which are the most costly and would have the largest impact on patient safety. The expected number of global stockouts is similar between the two systems at the total par

Figure . Expected quantity of main stockouts per total par level for stockless and centralised systems for all demand and variability levels.

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level because they have the same number of units in the hospital. However analysis of the number of main stockouts (i.e. stockouts that are occurring when one clinic has to try to fill demand from one or more other clinics) showed the expected number of main stockouts actually differs significantly between the centralised and stockless systems. Figure 7 shows the difference in quantity of main stockouts by total par level. As can be seen in Figure 7, the centralised system performs significantly better in terms of main stockouts. This can be explained by the fact that the central pharmacy takes advantage of risk pooling due to the variability of demand. The larger difference in the number of main stockouts may not be captured in the expected system cost because there is not an increase in cost if the clinic that has a stockout has to try to fill demand from more than one clinic. This assumes there is a centralised information system where it does not take extra time and resources to look for excess inventory in more than one clinic. Just as in the case of the total stockouts, the centralised system and stockless system start performing equally well as the total par level increases because the number of stockouts go to zero. Stockouts not only increase the cost of the system, but they also have potential patient safety implications since a delay in obtaining the drug can result in a delay in the patient receiving the drug. Therefore, the fact the one system is better in terms of costs most of the times and the other is better in terms of main stockout shows the trade-off between the cost saving stockless system and patient safety favouring centralised system. At very high par levels, relative to mean demand, the two systems perform almost equally well if patient safety is relative to the total stockouts and the stockless system performs better in terms of cost. However, at lower par levels, the centralised system performs significantly better if the patient safety metric is the number of clinic stockouts although it operates at a higher cost.

5. Conclusion In this paper, we developed two simulation models that represent common hospital supply chain structures: centralised and stockless. We developed an experimental design that varied the cost of various types of stockouts, product cost, holding cost, and demand characteristics to characterise the performance of the two systems under varying hospital conditions. By doing so, we captured the behaviour in terms of both the cost performance and stockouts as a function of the total par level for a case study using the antibiotic meropenem.

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This case study lays the initial framework for additional analytical work in modelling the medication supply chain at the hospital level. The models were tested using specific but representative attributes associated with meropenem demand and pricing which could be expanded to get a better idea of which system is better under all (or most) scenarios. The results show that while the stockless system was almost always higher performing in terms of total system cost, the centralised system was higher performing in terms of patient safety at lower inventory levels. Additional work could be done in determining a specific classification system for which system to use under certain drug attributes. There are also opportunities to develop a more holistic approach that could incorporate other medication supply chain characteristics such as perishability, clinic capacity, and the resource impact of operationalising each structure. There is also opportunity for more work to be done to accurately assess costs, specifically costs for the various stockout types, in order to better predict which system will perform better. The model could also be expanded to consider varying demand types for the same product at the various locations. We can envision a roadmap which could integrate a classification scheme such as Med-MASTA with the results of this type of work which could inform medication supply chain strategies based on the product and patient characteristics.

Disclosure statement No potential conflict of interest was reported by the authors.

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