Cost performance of traditional and vendor managed inventory approaches in hospital pharmaceutical supply chains

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1 Cost performance of traditional and vendor managed inventory approaches in hospital pharmaceutical supply chains Sineenart Krichanchai* and Bart L. MacCarthy Operations Management and Information Systems Division Nottingham University Business School, United Kingdom. Abstract With the increasing pressures to reduce costs and enhance service levels, hospitals are considering Vendor Managed Inventory (VMI) approaches. VMI transfers responsibility for ensuring supply from the hospital to the supplier with the hospital sharing information on demand and inventory levels. A simulation model is employed to investigate cost performance in supply between a hospital and distributor under traditional, basic VMI and dynamic VMI approaches. The study examines factors including different demand patterns, ordering policies and information inaccuracy. It finds that in most cases VMI does not reduce total costs and is more beneficial for the hospital than the distributor. Keywords: Vendor Managed Inventory, Simulation, Pharmaceuticals Introduction The concept of VMI has radical implications for supply chain participants. It transfers responsibility for managing a customer's inventory to the supplier (Disney and Towill, 2003). It eliminates one echelon of decision-making as the customer no longer places an order with the supplier. The role of the customer changes from managing its own stock to sharing information related to demand and inventory status with the supplier (Classen et al., 2008, Yao and Dresner, 2008). Access to customer information can be a manual or electronic process via electronic data interchange and/or the internet (Elvander et al., 2007, Yao and Dresner, 2008). Various potential benefits arising from increased demand visibility and greater supply chain integration are expected from VMI adoption. Kaipia et al., (2002) suggest that demand visibility in VMI gives the supplier time benefits in replenishment planning. VMI may allow better delivery planning with reductions in transportation costs (Lee, 2004, Waller et al., 1999). As the customer no longer orders from the supplier, the customer s administration cost should reduce (Kumar and Kumar, 2003). However, Dong and Xu (2002) point out that although benefits to the customer are apparent, benefits to the supplier are still controversial. In this study, we investigate cost performance in operating VMI in hospital pharmaceutical supply chains through simulation. The paper is structured as follows. Literature related to VMI implementation and

2 characteristics of hospital pharmaceutical supply chain are then considered. In the following section, the conceptual framework for the research is discussed. Methodology, assumptions, experimental factors and parameters, and cost performance outcomes are then discussed and the experiments conducted are noted. Subsequently, the results and analysis are presented, followed finally by conclusions from the study. Model and simulation literatures Both simulation and analytical models have been employed to study factors affecting VMI performance (e.g, Angulo et al, 2004, Waller et al., 1999, Yao and Dresner, 2008). Waller et al., (1999) explore how VMI performs under a particular constraint including different levels of demand variability, limited manufacturing capacity and partial channel adoption. Using a simulation model, the results show that VMI brings benefits to the manufacturer and distributor, even trickling down benefits to non-vmi customers. Angulo et al., (2004) evaluate the information sharing effects of variation in demand and lead time on VMI. The results show that information delay impacts on performance measures significantly, while information inaccuracy does not. Disney and Towill (2003) develop a simulation model to compare performance of the VMI approach with a traditional serially linked supply chain. The results show that the VMI approach outperforms the traditional approach in response to demand volatility. Sari (2007) developed a simulation study to compare the effect of information inaccuracy, demand uncertainty and lead time on two performance metrics in traditional approaches, VMI and CPFR. The study shows that even though CPFR provides better performance improvement than VMI, it is sensitive to operating conditions and shows a significant drop in performance improvement in terms of total cost reduction and fill rate. However, the effect of these factors on VMI are negligible. Yao et al., (2007) develop models to study the effect of ordering costs and carrying charges on cost saving obtained from a VMI approach. The results show that VMI does not distribute the benefit equally to both trading partners as one may gain all benefits while another has to bear addition costs. According to previous studies, it suggests that several factors, including demand variability, lead time, information inaccuracy, influence performance outcomes under VMI adoption. Characteristics of Hospital pharmaceutical supply chain Distributors and wholesalers play an important role in hospital pharmaceutical supply chains. Many manufacturers tend to outsource distribution to a third party distributors and wholesalers, allowing the manufacturer to concentrate on their core business while the third party can leverage its warehouse and distribution infrastructure to provide benefits through economies of scale (Rossetti, 2012; Whewell, 2010). Various factors affect the demand characteristics of pharmaceutical products including a hospital's size, its geographic location, specializations and government regulations. In addition, demand from each ward or department in the hospital may differ depending on their specialization. Thus, a hospital s pharmaceutical demand comprises a wide variety of high and low volume items, perishable and durable items, critical and non-critical items, and high and low value items (DeScioli, 2001). It also has to cope with unpredictable demand patterns. Maintaining high inventory levels is the simplest way to ensure product availability in the hospital (Li, 2010). Hospital stocks can be managed by either continuous or periodic review

3 policies, depending on the type of products. The report of Management for Health (2012b) suggests two common reorder formulas are used to control hospital stocks - a minimum and maximum formula, and a consumption-based reordering formula. However, Gebicki et al.,(2013) suggests the classical (R,S) policy to control the medication inventory in the hospital. The conceptual framework The objective of this study is to investigate how the inventory management approach affects cost performance under VMI operating conditions in hospital pharmaceutical supply chains. The conceptual framework is presented in the Figure1. The study has a particular focus on the hospital-distributor relationship. An empirical study has also been conducted to understand inventory management and VMI implementations in hospital pharmaceutical supply chains. Empirical data is used to inform the simulation study and to develop appropriate assumptions for the model. The effects of three inventory management approaches are studied a traditional approach, a basic VMI and a dynamic VMI approach. The study considers demand profiles, demand volumes, lead times and information inaccuracy. Cost performance is considered with respect to the distributor, the hospital and total supply chain cost. Supply chain integration characteristics TRAD, Basic VMI, Dynamic VMI Physical lead time Information inaccuracy Product characteristics Demand profiles Demand volumes Cost performance Distributor cost, Hospital cost and Total supply chain cost Methodology and assumptions Figure 1- The conceptual framework A simulation study is selected as a research methodology for this study (using the ARENA simulation software). A number of simulation studies of VMI have been conducted previoulsy in different supply chain contexts (e.g., Angulo et al., 2004, Kaipia et al., 2002, Sari, 2007). A simulation model allows a researcher to explore a phenomenon further than can be explored by conducting case studies alone. Using a simulation model enables the researcher to mimic the behavior of a real system and conduct experiments. It can provide transparency and demonstrate the interaction between different factors, which may not be observed in case studies. The researcher can design the model to either test the effect of input parameters or predict possible outcomes from combining input parameters and operating policies, potentially enhancing the validity of research (Kelton et al., 2012) The supply chain is composed of a supplier, a distributor and a hospital. End customer (patient) demand is fulfilled by the hospital while demands at the hospital and at the distributor are fulfilled by the distributor and the supplier, respectively. However, this study focuses particularly on the relationship between the hospital and the distributor. Information flows from

4 downstream echelon to upstream echelon. Once upstream members receive information, which can be either orders from downstream members (in the case of a traditional inventory management approach) or actual information and inventory position (in the case of vendor managed inventory), the quantity of products is then decided based on this information and products flow in the opposite way to downstream members. Demand management process Customer demand is the total amount of product required daily by the end customer. A beta distribution is used to represent different demand profiles (DF) as it is very flexible in terms of shape and prevents the assignment of negative values (Fente et al., 1999; Law, 2007). In this study, we investigate whether different demand profiles can affect the cost performance outcomes. The level of demand variability is measured by the coefficient of variation (CV). Kaipia et al. (2002) note three typical levels of demand variability - Low (CV= 0.1), Medium (CV= 0.5) and High (CV=1.0), which we use in this study. The study uses the beta (1,1) distribution, which generates a steady demand pattern, as a base case. The parameters used to generate seven further different demand profiles are given in Table 1. Table 1- Different demand patterns Type DF ADI C.V. Std. dev. Mean Demand pattern 1 Beta (1,1) Smooth 2 Beta(24,24) Smooth 3 Beta (9,2) Smooth 4 Beta(0.5,2) Erratic 5 Beta (1,1) Intermittent 6 Beta(24,24) Intermittent 7 Beta (9,2) Intermittent 8 Beta(0.5,2) Lumpy Three levels of demand volume have been considered - Low, Medium and High - generated by multiplying the beta distribution by a constant value (Law, 2007), as shown in Table 2. Table 2 - Different level of demand volume Demand volume Range Parameter Low 0-10 Beta*10 Medium Beta*100 High Beta*1000 At the beginning of the day the hospital calculates the inventory (both recorded and physical inventory). Then, it decides whether to replenish the requested demand based on the physical stock. If the physical stock is equal to or greater than demand, demand is fulfilled. If it is less, demand is satisfied with the available inventory. At the hospital, excess demand is not backlogged as it is assumed that the patient will be partially fulfilled and leaves after receiving the medicines. After fulfilling demand, the physical inventory is reduced appropriately. At the

5 end of the day, the stock is recorded in the system in order to proceed to the inventory management process. Three inventory management approaches Three inventory management approaches are considered to compare cost performance- a Traditional approach, a Basic VMI approach, and a Dynamic VMI approach. In the first approach the hospital and the distributor operate the replenishment process in a traditional manner where the hospital sends an order to the distributor and then the distributor makes a replenishment based on the hospital's order. For the two VMI approaches the distributor assumes the responsibility for inventory management at the hospital. The difference between the two approaches is that basic VMI uses a periodic replenishment (R,S) policy, while dynamic VMI uses a continuous replenishment policy (s,s). Under the traditional approach, the hospital is responsible for monitoring its own stock and making replenishment decisions. No information is shared between the hospital and the distributor except for the orders sent from the hospital. To control a hospital's inventory, the (R,S) policy is employed. A pharmacist or medicine manager is responsible for reviewing the stock daily and creating a purchase order. The stock is checked at the end of the day to determine if it is below the calculated S level. If it is then an order quantity equal to the difference between the current inventory position and S level is calculated.. It is assumed there is no delay for order transmission. Once the distributor receives the hospital's order, it checks its stock in order to make a replenishment. If the stock at the distributor is greater than the hospital's order, it means that the hospital will receive the product in full amount. If not, partial stock is delivered and a backlog is recorded in the system. Thereafter, the unsatisfied demand from the previous order is added to the next review. To control the hospital's inventory, the (R,S) policy is employed (Silver et al., 1998), as shown in equation (1). To calculate the order-up-to level (S) at the hospital, average demand (D) and standard deviation (σ D ) is calculated from customer demand (depending on the demand profile from the seven demand profiles in Table 1-1 above). Z is set to 1.65 in order to achieve a 95 percent service level. S level = D R + (Z σ D R (1) This policy is also used to monitor the stock in the hospital's warehouse for a particular item, where R is the review interval and S is the order-up-to level. It is assumed the distributor is responsible for managing only its own inventory. The distributor also employs the (R,S) as an inventory policy to monitor the stock in its warehouse and under a traditional inventory management approach, the formula in Eq.(1) is also applied at the distributor. However, average demand experienced by the distributor (D) is estimated from the actual orders received from the hospital. When a replenishment quantity is assigned to the upstream supplier by the distributor, it is assumed the supplier has unlimited production capacity and the supplier is able to fulfill the quantity in full. There is no backlogging at this stage. Zero lead time is assumed for information transmission and physical lead time between the distributor and its upstream supplier. Under the VMI approaches, it is assumed that the distributor takes responsibility for monitoring the hospital's inventory. The distributor has authorization to access real-time inventory status and customer demand, which allows it to review the hospital's stock daily. The hospital no longer creates purchase orders. Instead, inventory management is operated

6 electronically by the distributor. The distributor calculates the safety stock for the hospital based on actual customer demand information. So, when the stock is lower than the safety stock, the distributor makes a replenishment simultaneously. The distributor implements an (R,S) policy to control and decide when and how much to replenish its own stock. It is assumed that the S level at the distributor is 1.5 times greater than the S level at the hospital. Dynamic VMI shares similarities with basic VMI. The distributor has access to real-time inventory and customer demand, the hospital no longer creates purchase orders and the distributor calculates safety stock for the hospital based on actual customer demand information. Unlike basic VMI, the distributor responds to demand by implementing a continuous review policy (s,s) and reviews the stock daily. So, when the stock drops to or below the reorder point (s level), the distributor makes a replenishment simultaneously. To calculate the S level at the hospital, average demand and standard deviation is calculated from the customer demand (depending on the demand profile from the seven demand profiles in Table 1 above). It is assumed that the reorder point (s level) at the hospital is typically sets to 70 % of S level. For dynamic VMI, the distributor still implements (R,S) policy to decide when and by how much to replenish its own stock. The S level at the distributor is 1.5 times the S level at the hospital. Physical lead time and information inaccuracy Two levels of physical lead time are considered, 0 days and 3 days (Sari, 2007). Inaccuracy of inventory records is simulated by multiplying recorded inventory at the hospital at the end of the day by a random number generated from a uniform distribution in the range from 1-IAC to 1+IAC, where IAC is the percentage information inaccuracy occurring in the supply chain. Two levels of information inaccuracy are considered in this study, which are 0 % and ±15 % (Angulo et al., 2004, Sari, 2008, Waller et al., 2006) Cost performance measurement Three cost performance measures are considered the hospital's cost, the distributor's cost and the total cost in the supply chain. Total cost analysis is used for two reasons (1) analyzing cost in the current system to find out the opportunity to optimize the cost and (2) modeling the cost of potential changes in the supply system (Management Science for Health, 2012b). Below we first explain the details of the costs considered in the study and then explain how cost performance is measured under different inventory management approaches. Data validation has used both the literature and the empirical study. Five cost elements are considered - purchasing cost, inventory holding cost, ordering cost, shortage cost and transportation cost. The purchasing cost is the cost of purchasing a product, which is equal to product value per unit multiplied by the quantity in the inventory (Junita and Sari, 2012; Kelton et al., 2010). The purchasing cost is set based on the actual price of medicines from WHO report, International drug price indicator guide, which is published by Management Sciences for Health (2012a). This study compares three levels of product value. Purchasing cost at the distributor are set at 0.77, and 45 whereas purchasing cost at the hospital are set at 0.92, and 54. Inventory holding cost is the cost incurred when holding stock in the inventory. It is typically considered as a percentage of value per unit time (Junita and Sari 2012). For the hospital supply chain, it is approximately 10 % of annual inventory expense. In this study, the holding cost is estimated per day. Therefore, it is equal to 0.03 % of product

7 value per day (Gebicki et al., 2013). Ordering cost is the cost associated with placing an order to the upstream supply. It is assumed that it costs 5 money units per order (Junita and Sari, 2012; Kelton et al., 2010). Shortage cost is the cost incurred when there is a shortage of stock. It is assumed that shortage cost is equal to 20% of the purchasing cost of the product (Angulo et al., 2004). Transportation cost is the cost incurred when the distributor delivers products to the hospital, which is assumed to be approximately 10% of product prices (Pharmaceutical Health Information System, 2010). The differences in cost allocation under the traditional and VMI approach is that under a VMI approach the hospital no longer bears the ordering costs or shortage costs. Ordering cost is eliminated while the shortage cost is transferred to the distributor. Table 3 shows how cost performance metrics are calculated at each echelon. Table 3 - Cost performance measurement Echelon Traditional approach Basic and Dynamic VMI approach Hospital cost Distributor cost Purchasing cost, Holding cost, Ordering cost and shortage cost Purchasing cost, Holding cost, Transportation cost Purchasing cost, Holding cost Purchasing cost, Holding cost, Transportation cost and Shortage cost Total supply chain cost Hospital cost+ Distributor cost Hospital cost+ Distributor cost Experimental descriptions The traditional approach is designed to replicate the existing system in the hospital while the VMI approach is designed based on proposed VMI plans from the empirical case study. Under the traditional and VMI approaches, 6 factors are considered (See in Table 4): Supply chain type (SCTYPE), which is the inventory management approach; Physical lead time (LT); Information inaccuracy (INACC); Demand profile (DF); Demand volume (DV); and Product value (PV). The total number of simulation factor combinations for this study is Table 4 - Simulation parameters Factor SCTYPE TRAD Basic Dynamic VMI LT 0 day 3 days INACC 0 ±15% DF 8 Demand profiles 8 Demand profiles 8 Demand profiles DV Low Medium High PV Low Medium High To enhance experimental validation, issues related to the run- length, warm-up period and the number of replications have been considered to ensure accuracy in simulation results. Each set of experiments runs for 3650 days (ten years). To validate information output, a warm up period is set to eliminate initial bias. Time-series inspection is used to analyze the length of the warm up

8 period of a base case (Robinson et al., 2004). From inspection, 1800 days are set as a warm-up period. 50 replications are performed to obtain more accurate estimates of mean performance. Analysis and results Space limitations preclude showing detailed simulation results. Only the overall results are presented from a statistical analysis used to compare performance outcomes under the three inventory management approaches. One-way repeated ANOVA is selected to study the effect of inventory management approaches (SCTYPE), physical lead time (LT) and information inaccuracy (INACC). The results are presented in Table 5. Two-way repeated ANOVA is employed to investigate the effect of demand profiles (DP), demand volume (DV), and product value (PV). The results from the two-way repeated ANOVA are presented in Table 6. Table 5 - One way ANOVA analysis results Experimental factor Dependent variables F-value (p-value) Hospital cost Distributor cost Total cost SCTYPE (0.000) (0.000) (0.000) SCTYPE*LT (0.000) (0.000) (0.000) SCTYPE*INACC 14.7(0.000) (0.000) (0.000) The one-way repeated ANOVA results in Table 6 reveal that there are significant differences between three approaches with respect to cost performance at the hospital, distributor and for the total supply chain cost. Under the VMI approach, the ordering cost at the hospital is eliminated and the shortage cost is transferred to the distributor. Therefore, the hospital gains an obvious benefit in terms of cost reduction while the distributor bears a greater cost. From the simulation output, the hospital can reduce stock by nearly 40 % for low value products and approximately 10 % for medium and high value products. For the distributor, the cost increases by nearly 50 %. The total supply chain experiences a cost reduction of % for low value products value but costs increase by 20 % for medium and high value products. With a 3 day physical lead time, there is a significant differences among the three inventory management approaches on cost performance. The simulation output shows that VMI can reduce costs at the hospital by approximately 10% while the distributor experiences significantly greater cost than under a traditional approach (more than 200%). The total supply chain costs increase as well. Comparing both VMI approaches, the dynamic VMI performs better than the basic one in all performance outcomes. For example, with low product value, the hospital experiences a stock reduction of approximately 20% and 40% under basic and dynamic VMI, respectively. Even though the distributor s cost and total supply chain costs increase, the magnitude of increase in basic VMI is greater than twice that of dynamic VMI. When information is recorded inaccurately at the hospital, the statistical output shows significant differences between the three inventory management approaches. The VMI approaches are able to cope better with inaccuracy as they still enable cost reduction at the hospital. However, the distributor has to bear greater costs under VMI than traditional approaches. Surprisingly, under low demand volumes for low product value, VMI is able to reduce the total supply chain cost as well. In addition, when performance outcomes are observed for both VMI approaches, dynamic VMI can result in better outcomes.

9 Two-repeated ANOVA results in Table 6 reveals that there is no significant differences among the eight demand profiles on cost performance outcomes for the three inventory management approaches (p>0.05). The statistical results are similar for the interaction effects of demand profiles and supply chain approaches with no significant differences found. Table 6 - Two way ANOVA analysis test results Experimental factor Dependent variables F-value (p-value) Hospital cost Distributor cost Total cost Demand profile (DF) 2.820(0.132) (0.132) (0.132) Demand volume (DV) (0.000) (0.000) (0.000) Product value (PV) (0.001) (0.001) (0.001) SCTYPE*DF (0.132) (0.131) (0.131) SCTYPE*DV (0.000) (0.000) (0.000) SCTYPE*PV (0.005) (0.001) (0.001) The statistical results do show significant differences across the three demand volumes on cost performance. Higher demand volume leads to greater costs incurred at the hospital and the distributor. When assessing the results from the interaction of variables, it shows that VMI provides more benefits than traditional approach for low demand volumes and especially for low product values with a significant reduction in hospital and total supply chain costs. Regarding product value, the two-way repeated ANOVA results in Table 6 indicate that the effect of product value affects the three performance outcomes significantly. It is unsurprising that product value affects cost performance outcomes. When assessing the interaction of product value and inventory management approach, it shows that low product value cost performance gains under a VMI approach in terms of cost saving at the hospital and total supply chain more than medium and high product values. Conclusions The objective of this study was to compare cost performance outcomes under three inventory management approaches, examining the impact of factors including different demand patterns, ordering policies and information inaccuracy. Through a comprehensive set of simulation experiments and statistical analysis, a number of observations are made from this study. In most cases VMI does not reduce total costs and is more beneficial for the hospital than the distributor, irrespective of whether information inaccuracy or physical lead times are considered in the replenishment process. When VMI is implemented the hospital is able to eliminate the ordering cost and the shortage cost is transferred to the distributor. As a result, it contributes to higher distributor costs. However, VMI may either increase or decrease the total cost, depending on product value and demand volumes. Product value and demand volumes affect all cost performance metrics. The simulation results suggest that under VMI approach low product value and low product volumes can gain more benefits than other types of demand. In comparing VMI approaches, it is suggested that the continuous review policy under dynamic VMI outperforms the basic VMI approach as it enables more cost savings at the hospital with less stock increases at the distributor and may reduce the total supply chain cost.

10 References Angulo, A., H. Nachtmann, M. A. Waller, Supply chain information sharing in a vendor managed inventory partnership. Journal of Business Logistics, 25(1): Classen, M. J., A. J. van Weele, E. M. van Raaij, Performance outcomes and success factors of vendor managed inventory (VMI), Supply Chain Management: An International Journal, 13(6): DeScioli, D.T Differentiating the hospital supply chain for enhanced performance. Master thesis. Massachusetts Institute of Technology. Available at (accessed Jan12, 2014) Disney and Towill The effect of vendor managed inventory (VMI) dynamics on the Bullwhip Effect in supply chains. Int. Journal of Productions Economics, 85(2): Dong, Y., Xu, K A supply chain model of vendor managed inventory, Transportation Research Part E, 38 (2): Elvander, M. S., S. Sarpola, S. Mattsson, Framework for characterizing the design of VMI Systems, Int. Journal of Physical Distribution & Logistics Management, 37(10): Fente, J., K. Knutson, C. Schexnayder, Defining a beta distribution function for construction simulation model. In WSM. Proceeding of the 1999 Winter Simulation Conference: Gebicki M., E. Mooney, S. J. Chen, L. M. Mazur Evaluation of hospital medication inventory policies. Health Care Management Science: 1-15 Junita, I., R. K. Sari, ABC-VED Analysis and Economic Order Interval (EOI)- multiple items for medicines inventory control in hospital. In ICBM. The 2012 International Conference on Business and Management: Kaipia, R., J. Holmström, K. Tanskanen, VMI: What are you losing if you let your customer place orders, Production Planning & Control: The Management Operations, 13(1): Kumar, P., M. Kumar, Vendor managed inventory in retail industry, White Paper, Tata Consultancy Services. Available at (accessed Jan12, 2014) Kelton, W. D., R. P. Sadowski, N. B. Zupick, Simulation with Arena. 5th Edition. McGraw-Hill Irwin, Singapore Law, A. M Simulation modelling and analysis. 4th ed. McGraw-Hill Irwin, New York Lee, H. L The triple-a supply chain, Harvard Business Review, 82(10): Li, Z Evaluating inventory collaboration in healthcare industry: A system dynamic study. Master thesis. Tilburg University. Management Sciences for Health (2012a). International Drug Price Indicator Guide: Management Sciences for Health, Arlington. Management Sciences for Health (2012b). MDS-3: Managing Access to Medicines and Health Technologies. Management Sciences for Health, Arlington. Pharmaceutical Health Information System, PHIS Hospital Pharma Report. Pharmaceutical Health Information System, London. Rossetti, M. D., N. Buyurgan, E. Phol, Medical Supply Logistics. Hillier, F. S., eds. Handbook of Healthcare System Scheduling. Springer, New York, Sari, K Exploring the benefits of vendor managed inventory. Int. Journal of Physical Distribution & Logistics Management, 37(7): Sari, K Inventory inaccuracy and performance of collaborative supply chain practice, Industrial Management & Data Systems, 108(4): Silver, E. A., D. F. Pyke, R. Peterson, Inventory management and production planning and scheduling, 3rd ed. Wiley, New York. Waller, M., M. E. Johnson, T. Davis, Vendor-managed inventory in the retail supply chain. Journal of Business Logistics, 20(1): Whewell, R Supply Chain in the pharmaceutical industry. Surrey, Gower Publishing Limited. Yao, Y., P. T. Evers, M. E. Dresner Supply chain integration in vendor-managed inventory. Decision Support Systems, 43(2): Yao, Y., M. Dresner, The inventory value of information sharing, continuous replenishment and vendor managed inventory. Transport Research Part E: Logistics and Transportation Review, 44(3):