Information sharing in supply chains with heterogeneous retailers

Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 Information sharing in supply chains with heterogeneous retailers Roberto Domingueza,*, Salvatore Cannellab, Ana P. Barbosa-Póvoaa, Jose M. Framinanc aCentre for Management Studies, Instituto Superior Técnico (CEG-IST), Technical University of Lisbon, Portugal bDICAR, University of Catania, Catania, Italy cIndustrial Management & Business Administration Department, School of Engineering, University of Seville, Spain E-Mails: [email protected], [email protected], apo[email protected]a.pt, [email protected] *Corresponding author: Roberto Dominguez, Centre for Management Studies (CEG-IST), Instituto Superior Técnico, Technical University of Lisbon, Ave. Rovisco Pais 1, 1049-001, Lisbon, Portugal. Abstract This work analyses partial information sharing involving retailers with different operational configurations. Retailers are characterized by four operational factors, i.e., demand variance, lead time average, forecasting period and inventory policy. The findings show that the performance improvement based on information sharing depends on retailers’ operational factors. Consequently, partial information sharing structures need to be carefully designed in order to achieve a substantial performance improvement. The results also serve to provide innovative recommendations to supply chain managers in order to efficiently implement information sharing mechanisms at retailers. Keywords: Supply chain management; partial information sharing; heterogeneous retailers; bullwhip effect; multi-agent systems; dynamic performance. Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 2 1 INTRODUCTION 1.1 Context Globalization and a high volume of outsourcing has resulted in decentralized Supply Chains (SCs), shifting from a sequential linear SC to an increasingly complex global supply network (see e.g., Merzifonluoglu 2015, Annarelli and Nonino 2016, Li and Zhen 2016). SC partners have a higher autonomy, as they are part of many parallel chains at the same time (Zissis et al. 2015, Thomas et al. 2016). This fact reinforced the presence of conflicting objectives within the SC where competition exists for common resources and decisions are taken on individually based local incentives (Rached et al. 2016). The complexity of SCs has risen sharply in recent decades (Cardoso et al. 2015, Guertler and Spinler 2015), often leading to a lack of coordination among SC members. In this context, SCs from western economies to low-cost countries have been experiencing unpredictable and intensive deterioration of performance (Christopher and Holweg 2017). Additionally, the severe and synchronized trade collapse has amplified inefficiencies within the SCs, and subsequently led to detrimental phenomena such as the bullwhip effect (see e.g. Altomonte et al. 2012, Duan et al. 2015, Osadchiy et al. 2015). To overcome these inefficiencies, researchers and practitioners have been working on robust solutions. Among these, SC collaboration practices have been advocated as some of the most effective approaches (see e.g. Dejonckheere et al. 2004, Chen and Lee 2009, Trapero et al. 2012, Li and Zhang 2015, among others). At the core of collaboration practices lies information sharing (IS), a collaborative mechanism in which the supplier may obtain and utilize the demand and inventory status of the retailer (Huang et al. 2016). During the last decade, the benefits of IS in decentralized SCs have been deeply researched with empirical studies of real cases (see e.g. Huo et al. 2014, Bian et al. 2016, Ren 2017), analytical methods (Chen and Lee 2009, Trapero et al. 2012, Ali et al. 2017), and simulation (Datta and Christopher 2011, Ramanathan 2014, Dominguez et al. 2015b, Cannella et al. 2017). In general, regardless of the adopted methodologies and the explored aspects of IS (e.g. reasons for sharing, what information to share with whom, how to share, as well as pre-requisites, drivers and barriers to IS, see Kembro et al. 2014), the majority of the literature agrees on the pivotal role benefits of IS practices in SC performance (Maghsoudi and Pazirandeh 2016). The expected revenues (e.g. a Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 3 reduction in inventory holding cost, Hosoda et al. 2008) have been capturing the attention of SC practitioners (Kembro and Selviaridis 2015). As an example, a recent survey found that 61% of Chinese firms believe that IS is essential for business success (Bian et al. 2016). Basically, IS has been and continues to be a major topic in modern SC management and, contrary to popular belief, there is still significant need for more research regarding IS in SC (Kembro et al. 2014, Costantino et al. 2015). 1.2 Problem Statement Despite the potential benefits of IS in SC, its practical implementation presents relevant difficulties (Fawcett et al. 2011, Spekman and Davis 2016). Full coordination among SC members, while desirable, is often impractical, since it is deemed to be too costly or too risky (Geunes et al. 2016). Making information available to other enterprises and managing the information requires investment in Information Technology (IT) and entails significant resource investments, which could result in a negative cost–benefit analysis (Chan and Chan 2010, Kembro et al. 2014). Additionally, companies need to bear the risk that information may be leaked intentionally or unintentionally by suppliers (Kong et al. 2013, Huang et al. 2016). Finally, resulting benefits of IS may be difficult to allocate in a reasonable way among SC partners (Shih et al. 2015). Evidence of these barriers to achieve full collaboration among SC members can be found in practice. Accordingly, the Retailer-Direct Data Report of the Grocery Manufacturers Association (GMA) pointed out that retailers may not have an incentive to share data with suppliers (GMA 2009, Shang et al. 2016). Additionally, a study performed by Forrester Research on 89 retailers in 2006 reported that only 27% of retailers shared POS data (Shang et al. 2016). In this context, achieving a full IS (i.e., all SC members participate in IS, referred to as FIS in the following) is not always possible. Thus, in practice, partial IS is found to be prevalent (Shnaiderman and Ouardighi 2014, Xu et al. 2015). However, in the scientific literature, partial IS has been rarely analysed because the majority of studies dealing with IS assume a full collaboration practice among all members (Holmstrőm et al. 2016). In light of these considerations, studying the dynamics of SC in scenarios where FIS cannot be achieved represents a challenge for researchers and may bring potential benefits for industry. Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 4 To the best of the authors’ knowledge, up to now, partial IS has been addressed in literature in five relevant studies. Ganesh et al. (2014a,b) and Costantino et al. (2014) analyse the impact of different degrees of collaboration on SC performance (i.e., inventory holding and shortage costs, bullwhip effect and/or customer service level) in a serial SC, while Lau et al. (2004) analyse partial IS in more complex SCs, in particular in three divergent SCs. Finally, Huang and Iravani (2005) focus on one capacitated manufacturer and two retailers under a (Q,R) inventory policy, where the former receives demand and inventory information from only one of the retailers. The above-mentioned works have significantly contributed to the unexplored topic of partial IS by showing two novel insights: (1) Retailers should be the first members to be involved in IS (Ganesh et al. 2014a,b, Costantino et al. 2014, Lau et al. 2004), since they report the highest performance improvement to the SC. (2) The operational factors (OFs) of retailers, such as market shares and order sizes, may have a significant impact on the benefits provided by the IS practice under partial collaboration (Huang and Iravani 2005). The former insight reasserts the central role of retailers for the efficacy of IS, while the latter suggests that SCs characterized by heterogeneous retailers (i.e., retailers with different OFs such as lead times, order policies, market demand, etc.), may perform differently under the same IS practice. Both insights open interesting challenges for researchers and advocate important implications for industry, as they point out the relevance of exploring the efficiency of partial IS at retailers when these are heterogeneous. According to these insights, we formulate the following research questions: how retailers with different OFs may impact on SC performance when they share information about customer demand? Which retailers’ OFs are more relevant in order to consider a retailer as a potential partner for the IS scheme and at what extent? 1.3 Objective Motivated by the above considerations, in this paper we aim to contribute to the existing literature by assessing how heterogeneous retailers, characterized by different critical OFs (i.e., demand variability, average lead time, forecasting period and inventory Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 5 policy), may improve SC performance by sharing (or not) true demand information. We assume that due to the decentralized nature of modern SCs, companies and, specifically, the retailers, are autonomous members who work for their own goals and interests and thus, retailers’ OFs are considered as exogenous factors. In this manner we aim to provide recommendations to SC managers on how to properly exploit the benefits of implementing IS practices with retailers by identifying which retailers provide a higher contribution to SC performance. To fulfil the research objective, we focus on a four echelon SC (i.e., Factory, Distributor, Wholesaler and Retailer) in which each echelon is characterized by one member with the exception of the Retailer’s echelon, which is constituted by four members. We compare different partial IS scenarios (some retailers may share demand information, while some others may not share information) under two different hypothesis: (1) homogeneous retailers and (2) heterogeneous retailers. Under the former hypothesis we analyse the SC performance when identical retailers are involved in IS one by one, on variety of SC configurations. Under the latter hypothesis we assess the impact on SC performance of involving retailers with different OFs in IS. SC performance is measured using a set of system level metrics (i.e., Bullwhip Slope, Inventory Slope and Systemic Inventory Level), which provide a clear, comprehensive and structured assessment of the SC performance at systemic level and the “internal process efficiency”, as well as provide information on the potential benefits of partnerships, collaboration and information productivity of SC members (Cannella et al. 2013). Due to the exploratory nature of this research, we adopt an appropriate and structured methodology for studying the dynamic of SCs, i.e., computer simulation (Oliveira et al. 2016), and more specifically the Multi-Agent Systems (MAS) modelling approach (Chatfield et al. 2006, Rahmandad and Sterman 2008). MAS has been recognized as a useful methodology to perform complex prospective SC analysis, and findings obtained with its proper adoption have been significantly contributing to understand the dynamics in SC (see e.g., Swaminathan et al. 1998, Long and Zhang 2014, Hilletofth et al. 2016 or Ponte et al. 2017). In order to perform a systematic simulation analysis we adopt reasonable assumptions and data inputs for simulations obtained from different cases to emulate real-world logistic systems (Rabinovic and Cheon 2011, Cannella et al. 2017). Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 6 The results obtained reveal new insights on the impact of IS in SC by showing the need of individually estimating the potential value of retailers’ information prior to the implementation of IS. When retailers are homogeneous, their collaboration may provide equal potential benefits to SC performance (they contribute the same to improve SC performance when they are involved in IS). Under this hypothesis, benefits of IS increase with the number of retailers involved and a full IS approach is recommended. On the contrary, when retailers are heterogeneous they have different potential value depending on their operational configuration. Under this hypothesis, performance achieved by different partial IS structures with the same number of retailers might be significantly different (e.g., we found that involving half of the total number of retailers into IS may lead to obtain over 70% of the total benefits of a FIS under the boundary conditions). In fact, retailers with (1) higher demand variance, (2) lower forecasting period, and (3) higher average lead time, are potentially the most beneficial partners when implementing IS. The remainder of this paper is as follows: Section 2 describes the SC model and methodology. Section 3 presents the design of experiments and performance metrics. Section 4 analyses the results obtained. Section 5 presents managerial implications. Finally, Section 6 draws the conclusions, limitations of the study and future research lines. 2 SC MODEL AND METHODOLOGY In order to analyse the partial IS scenarios, we develop a SC model to conduct the experiments. In SC dynamics literature, the most used SC model is the four-echelon serial SC (see e.g. Sterman 1989, Chatfield et al. 2004, Croson et al. 2014, Cannella et al. 2015). Echelons are referred as Factory (i=1), Distributor (i=2), Wholesaler (i=3), and Retailer (i=4). In order to analyse scenarios where only some of the retailers participate in IS (referred as partial IS) we extend this SC model by increasing the number of retailers to four, thus resulting a divergent SC (Lau et al. 2004, Dominguez et al. 2015a, Rached et al. 2016), as shown in Figure 1. Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 7 Figure 1. SC configuration. In addition, we make the following assumptions regarding IS: 1. As we focus our analysis of partial IS at retailers’ stage, only retailers share information on customer’s demand. 2. Assuming that, due to some barriers (as described in Section 1) each enterprise is willing to share its local information only to its immediate upstream enterprise (see Lau et al. 2004, Kembro and Selviaridis 2015, for similar assumptions), only the wholesaler will be able to receive information from retailers. 2.1 Supply Chain model The SC general model has been adapted from Chatfield et al. (2004) so as to model a generic divergent SC (Dominguez et al. 2015a,b, Cannella et al. 2017) and to include partial IS (i.e., any node at any echelon of the SC may share information with an upstream linked node). The notation is described in Table 1. This general model is adapted in Section 3.1 for the SCs under study with specific parameters values and experimental factors. Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 8 Table 1. Notation. i Echelon position in the SC 𝜏𝑖𝑗 Forecasting period of 𝑛𝑖𝑗 j Node position within a given echelon 𝑂𝑖𝑗 𝑡 Orders placed by 𝑛𝑖𝑗 at time t 𝑛𝑖𝑗 Node at position j in echelon i 𝐼𝑖𝑗 𝑡 Inventory on hand of 𝑛𝑖𝑗 at time t E Total number of echelons 𝑊𝐼𝑃𝑖𝑗 𝑡 Work in progress of 𝑛𝑖𝑗 at time t 𝑁𝑖 Total number of nodes in echelon i 𝐵𝑖𝑗 𝑡 Backlog of 𝑛𝑖𝑗 at time t 𝑁𝐶 Total number of customers 𝑆ℎ𝐷𝑖𝑗 𝑡 Shared demand of 𝑛𝑖𝑗 at time t 𝐶𝑗 Customer at position j 𝛿𝑖𝑗 𝛿𝑖𝑗=1 if 𝑛𝑖𝑗 is involved in IS, 0 otherwise.” t Current simulation time 𝐼𝑃𝑖𝑗 Inventory policy of 𝑛𝑖𝑗 T Total simulation time (excluding warm-up) 𝑉𝑖𝑗 Set of downstream linked partners of 𝑛𝑖𝑗 𝐷𝐶𝑗 𝑡 Demand placed by customer 𝐶𝑗 at time t 𝑠𝑂𝑖𝑡 2 Estimated variance of orders placed by echelon i 𝜇𝐷𝐶𝑗 Average demand placed by 𝐶𝑗 𝑂 𝑖𝑡 Estimated average of orders placed by echelon i at time t 𝐷 𝐶𝑗 𝑡 Estimated average demand placed by 𝐶𝑗 at time t 𝜎𝑂𝑖𝑗 2 Variance of orders placed by 𝑛𝑖𝑗 𝜎𝐷𝐶𝑗 2 Variance of demand placed by 𝐶𝑗 𝑠𝑂𝑖𝑗 𝑡 2 Estimated variance of orders placed by 𝑛𝑖𝑗 𝑠𝐷𝐶𝑗 𝑡 2 Estimated variance demand placed by 𝐶𝑗 𝑠𝐼𝑖𝑡 2 Estimated variance of inventory at echelon i 𝐷𝑖𝑗 𝑡 Demand faced by 𝑛𝑖𝑗 at time t 𝐼𝑖𝑡 Estimated average of inventory at echelon i at time t 𝐷 𝑖𝑗 𝑡 Estimated average demand faced by 𝑛𝑖𝑗 at time t 𝑠𝐼𝑖𝑗 𝑡 2 Estimated variance of inventory at 𝑛𝑖𝑗 𝑠𝐷𝑖𝑗 𝑡 2 Estimated variance demand faced by 𝑛𝑖𝑗 at time t 𝐼𝑖𝑗 𝑡 Estimated average of inventory at 𝑛𝑖𝑗 at time t 𝐿𝑖𝑗 𝑡 Lead time of 𝑛𝑖𝑗 at time t 𝐷 𝐶 𝑡 Estimated average demand placed by customers at time t 𝜇𝐿𝑖𝑗 Average lead time of 𝑛𝑖𝑗 𝜋𝑖 Position of the i-th echelon 𝐿 𝑖𝑗 𝑡 Estimated average lead time of 𝑛𝑖𝑗 at time t 𝑂𝑅𝑉𝑟𝑅𝑖 Order Rate Variance Ratio echelon i 𝜎𝐿𝑖𝑗 2 Variance of the lead time of 𝑛𝑖𝑗 𝐼𝑛𝑣𝑉𝑟𝑅𝑖 Inventory Variance Ratio echelon i 𝑠𝐿𝑖𝑗 𝑡 2 Estimated variance of the lead time of 𝑛𝑖𝑗 at time t 𝐼𝑛𝑣𝐴𝑣𝑖 Inventory Average at echelon i R Inventory review period BwSl Bullwhip slope 𝑆𝑖𝑗 𝑡 Desired level of stock of 𝑛𝑖𝑗 at time t InvSl Inventory slope z Safety factor for the OUT policy SysInvAv Systemic inventory average General Modelling Assumptions  At period t, each customer 𝐶𝑗 places an independent stochastic demand 𝐷𝐶𝑗 𝑡 following a normal distribution with mean 𝜇𝐷𝐶𝑗, estimated by 𝐷 𝐶𝑗 𝑡, and variance 𝜎𝐷𝐶𝑗 2, estimated by 𝑠𝐷𝐶𝑗 𝑡 2. Customers do not fill orders. Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 9  The factory places orders to an outside supplier with unlimited capacity.  Stocking and transportation capacities are unlimited.  The demand received by node 𝑛𝑖𝑗 (𝐷𝑖𝑗 𝑡), with mean estimated by 𝐷 𝑖𝑗 𝑡 and variance estimated by 𝑠𝐷𝑖𝑗 𝑡 2, equals the total orders received by downstream (linked) partners (denoted by 𝑉𝑖𝑗), i.e., 𝐷𝑖𝑗 𝑡=∑𝑂𝑖+1,𝑟 𝑡 𝑟∈𝑉𝑖𝑗 . Demand received by retailers is customer demand 𝐷𝐸𝑗 𝑡=𝐷𝐶𝑗 𝑡.  When the stock is not enough to fill an order completely there is a stock-out situation and partial replenishment is used (Chatfield et al. 2004).  If a stock-out situation at the retailers’ echelon occurs, we assume that backordering is not allowed and unfilled demand is lost. However, true demand received at retailers is recorded (𝐷𝐶𝑗 𝑡), and shared with the upstream partner in case of participating in IS (see a detailed description of IS below) (Chatfield et al. 2004, Agrawal et al. 2009, Choudhary and Shankar 2015). Upstream members of the SC are allowed to backorder.  We assume that returns of excess inventory to upstream partners are not permitted since the allowance of returns, although a common assumption in the bullwhip effect literature, may not be realistic and may overestimate the bullwhip effect (Chatfield and Pritchard 2013, Dominguez et al. 2015b). Lead Times Lead times (𝐿𝑖𝑗 𝑡) are defined as the time elapsed between order and receipt, and may include manufacturing time, shipment to port, ship transit time, unloading, transfer to rail and/or truck, etc. (Disney et al. 2016). We assume stochastic lead times, which are stationary, independent, and identically distributed. In line with previous literature works and industrial data sets, lead times are assumed to follow a Gamma distribution (Chatfield et al. 2004, Kim et al. 2006, Hayya et al. 2011, Chatfield and Pritchard 2013, Bischak et al. 2014, Dominguez et al. 2015b, Cannella et al. 2017, among others) with mean 𝜇𝐿𝑖𝑗 and variance 𝜎𝐿𝑖𝑗 2. Since we use a periodic Order-Up-To (OUT) replenishment policy (see below), and this policy operates on a discrete time basis, lead times must be integers (Disney et al. 2016, Wang and Disney 2017). Therefore, values obtained from the Gamma distribution are discretized. Consequently, each time an order is generated, Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 16 extreme values of the factors (Costantino et al. 2014, Cannella et al. 2017). These values are chosen according to two principles: (1) In order to satisfy the hypothesis of heterogeneous retailers, OFL and OFH need to be significantly different. (2) In order to produce comparable results, OFL and OFH need to adopt values from other similar studies in SC dynamic literature. OFH values for 𝜎𝐷𝐶𝑗 2, 𝜏𝑖𝑗, and 𝜇𝐿𝑖𝑗, can be found in Chatfield et al. (2004), Chatfield et al. (2013), Costantino et al. (2014) and Dominguez et al. (2015b). OFL values of these factors are obtained by significantly reducing the OFH values. For IPij, OFH is set to S2 (see e.g. Chatfield et al. 2004, Nachtmann et al. 2010, Chatfield et al. 2013, Dominguez et al. 2015b), while OFL is set to S1 (see e.g. Chatfield et al. 2004, Dominguez et al. 2014, Costantino et al. 2014). This is an arbitrary choice without impact in the results. These values can be found in Table 2. Table 2. Operational factors, model parameters, simulation parameters and performance metrics. OFs Retailers Upstream Members Low (OFL) High (OFH) Demand variance (𝜎𝐷𝐶𝑗 2) 100 (𝜎𝐷𝐶𝑗=10) 400 (𝜎𝐷𝐶𝑗=20) N.A. Forecasting period (𝜏𝑖𝑗) 5 15 15 Lead time average (𝜇𝐿𝑖𝑗) 2 4 2 Inventory policy (IPij) S1 S2 S1 General model parameters Value Simulation parameters Value Demand average (𝜇𝐷𝐶𝑗) 50 Simulation time (T) 4000 Lead time c.v. (𝜎𝐿𝑖𝑗/𝜇𝐿𝑖𝑗) 0.50 Warm-up 1000 Review period (R) 1 Number of replications 20 Safety factor (z) 2 Performance Metrics Echelon position (i) i=1…4 BwSl InvSl SysInvAv Node position in echelon i (j) j=1 ∀i<4 j=1…4 ∀i=4 IS (𝛿𝑖𝑗) 𝛿𝑖𝑗=0 ∀i<4 𝛿𝑖𝑗=0,1 ∀i=4 Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 17 Upstream members of the SC (i.e., Wholesaler, Distributor and Factory) are not subject of analysis in this work. Hence we simplify the DoE by maintaining the operational configuration of these members fixed in all experiments (Table 2). The parameters of the general model –summarised in Table 2– are chosen as usual values used in SC dynamics literature (see, e.g., Chatfield 2013, Chatfield and Pritchard 2013, Costantino et al. 2014, Dominguez et al. 2015a). The value of the safety factor (z=2) corresponds with a customer service level of 97.72% when using the normal approximation. In order to adapt the model presented in Section 2.1 to the divergent SC under study (Figure 1), we establish the boundaries of 𝛿𝑖𝑗 and subscripts i and j, as in Table 2. 3.2 Simulation parameters Uncertainty is inherent to many of the SC’s processes (Heckmann et al. 2015). In order to account for randomness, multiple replications of the experiments were performed, and the simulation outputs were statistically analysed. According to Kelton et al. (2007), when the half-width of confidence interval is smaller than a user-specified value (e.g. within 10% of the mean, Yang et al. 2011), the number of replications is acceptable for statistical analysis. As suggested by these authors, simulations were first conducted with 10 replications. Due to the use of systemic performance metrics (see Section 3.3), we obtained results with very low variances, and thus the half width was below 10% of the average in all cases. Even though, in order to increase precision of results, we have performed 20 replications of each experiment (see e.g. Nair and Vidal 2011, Yang et al. 2011). Total simulation time (T) was set to 4,000 periods to ensure that a steady state of the system is reached. Also, the first 1,000 periods were removed from the results, as a warm-up time, to eliminate system’s initialization effects. 3.3 Performance metrics In order to capture the dynamics of the SC, we adopt a structured non-financial performance measurement system, given by three common metrics, namely: Order Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 18 Variance Ratio, Inventory Variance Ratio and Inventory Average (see e.g. Cannella et al. 2013, Costantino et al. 2014, Wang and Disney 2016, among others). These metrics are computed at echelon’s level. Due to the high number of SCs that result from the DoE (see Section 3.4), we focus instead on the global performance of the SC, allowing for an easy comparison among the different SCs (Cannella et al. 2017). To do so, we use systemic metrics (i.e., SC-level metrics), which are computed from their corresponding echelon’s metrics, i.e., Bullwhip Slope, Inventory Slope, and Systemic Inventory Average, respectively. A reduction of this set of metrics reflects improved cost effectiveness of members’ operations. They provide a comprehensive and structured assessment of the internal process efficiency of the SC at systemic level and provide information on the potential benefits of partnerships, collaboration and information productivity of SC members (Cannella et al. 2013). A detailed description of each metric is provided below. 3.3.1 Order Rate Variance Ratio - Bullwhip Slope At echelon’s level, Order Rate Variance Ratio (𝑂𝑅𝑉𝑟𝑅𝑖) accounts for order variance amplification upstream in the SC. In the long-term run it is computed as 𝑂𝑅𝑉𝑟𝑅𝑖= 𝑠𝑂𝑖𝑇 2/𝑠𝐷𝐶 𝑇 2 (Chen et al. 2000, Chatfield et al. 2004, Dejonckheere et al. 2004). In order to apply this metric to a divergent SC, we use aggregate measures for each echelon (Dominguez et al. 2015b). Therefore, assuming that all customers’ demands are independent and that each node places orders independently, we can aggregate order variances at each echelon and thus 𝑂𝑅𝑉𝑟𝑅𝑖 for a divergent SC can be written as in Equation (9): 𝑂𝑅𝑉𝑟𝑅𝑖=∑𝑠𝑂𝑖𝑗 𝑇 2 𝑁𝑖 𝑗=1 ∑𝑠𝐷𝐶𝑗 𝑇 2 𝑁𝐶 𝑗=1 (9) At system’s level we use the Bullwhip Slope (BwSl) (Cannella et al. 2013, Dominguez et al. 2015b). BwSl is computed as the slope of the linear interpolation of the set of 𝑂𝑅𝑉𝑟𝑅𝑖 values for a given SC (Equation (10)), where 𝜋𝑖 is the position of the i-th echelon in Dejonckheere’s et al. curve. This metric measures the magnitude of the bullwhip propagation across the SC and allows for a concise and holistic comparison between different SCs. A high value of BwSl indicates a fast propagation of the bullwhip effect through the SC, whereas a low value indicates a smooth propagation. Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 19 BwSl provides information on potential unnecessary costs for suppliers, such as lost capacity or opportunity costs, and on all other unexpected costs generated by the bullwhip effect (Cannella et al. 2013, Trapero and Pedregal 2016). 𝐵𝑤𝑆𝑙=𝑡𝑔𝜗𝑂𝑅𝑉𝑟𝑅 =𝐸∑𝜋𝑖𝑂𝑅𝑉𝑟𝑅𝑖− 𝐸 𝑖=1 ∑𝜋𝑖 𝐸 𝑖=1 ∑𝑂𝑅𝑉𝑟𝑅𝑖 𝐸 𝑖=1 𝐸∑𝜋𝑖2𝐸 𝑖=1 −(∑ 𝜋𝑖 𝐸 𝑖=1 )2 (10) 3.3.2 Inventory Variance Ratio - Inventory Slope At echelon’s level, the Inventory Variance Ratio (𝐼𝑛𝑣𝑉𝑟𝑅𝑖) (Disney and Towill 2003), assesses the stability degree of the inventory and it can be associated with the variation and the potential increment of the holding costs per unit (Cannella et al. 2015). It is computed as the ratio between the inventory variance at echelon i and the customer demand variance: 𝐼𝑛𝑣𝑉𝑟𝑅𝑖=(𝑠𝐼𝑖𝑇 2/𝐼𝑖𝑇)/(𝑠𝐷𝐶 𝑇 2/𝐷 𝐶 𝑇). Following the same procedure as with 𝑂𝑅𝑉𝑟𝑅𝑖, we derive 𝐼𝑛𝑣𝑉𝑟𝑅𝑖 for a divergent SC, resulting the expression shown in Equation (11). 𝐼𝑛𝑣𝑉𝑟𝑅𝑖=∑𝑠𝐼𝑖𝑗 𝑇 2 𝑁𝑖 𝑗=1 /∑𝐼𝑖𝑗 𝑇 𝑁𝑖 𝑗=1 ∑𝑠𝐷𝐶𝑗 𝑇 2 𝑁𝐶 𝑗=1 /∑𝐷 𝐶𝑗 𝑇 𝑁𝐶 𝑗=1 (11) At system’s level we use the Inventory Slope (InvSl) (Cannella et al. 2013). This metric is similar to BwSl (Equation (12)), but accounts for inventory instability propagation across the SC. An increased InvSl results in higher holding and backlog costs, inflating the average inventory costs per period (Disney and Lambrecht 2008), increasing holding unit costs, missing production schedules, job sequencing and resource re-allocation (Cannella et al. 2013, Duong et al. 2015). 𝐼𝑛𝑣𝑆𝑙=𝑡𝑔𝜗𝐼𝑛𝑣𝑉𝑟𝑅 =𝐸∑𝜋𝑖𝐼𝑛𝑣𝑉𝑟𝑅𝑖− 𝐸 𝑖=1 ∑𝜋𝑖 𝐸 𝑖=1 ∑𝐼𝑛𝑣𝑉𝑟𝑅𝑖 𝐸 𝑖=1 𝐸∑𝜋𝑖2𝐸 𝑖=1 −(∑ 𝜋𝑖 𝐸 𝑖=1 )2 (12) 3.3.3 Inventory Average - Systemic Inventory Average At echelon’s level, Inventory Average (𝐼𝑛𝑣𝐴𝑣𝑖) can be associated to the average holding cost over the observation time (Cannella et al. 2013), and it is commonly used in production-distribution systems analysis to assess concise information on inventory investment (Cannella and Ciancimino 2010, Ganesh et al. 2014a). It can be viewed as a metric complementary to 𝐼𝑛𝑣𝑉𝑟𝑅𝑖. For a divergent SC this metric can be expressed as follows: Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 20 𝐼𝑛𝑣𝐴𝑣𝑖=∑ ∑ 𝐼𝑖𝑗 𝑡 𝑇 𝑡=1 𝑁𝑖 𝑗=1 𝑇 (13) At system’s level we use the Systemic Inventory Average (SysInvAv) (Cannella et al. 2013). This metric accounts for the average inventory of the whole SC. As it is common to model holding costs as linearly dependent from stock levels (Sharma 2010, Cachon and Olivares 2010), this metric quantifies the average holding costs across the observation time (Cannella et al. 2013). Since all SCs under analysis have the same number of nodes, we can use the following expression: 𝑆𝑦𝑠𝐼𝑛𝑣𝐴𝑣=∑ ∑ ∑ 𝐼𝑖𝑗 𝑡 𝑇 𝑡=1 𝑁𝑖 𝑗=1 𝐸 𝑖=1 𝑇 (14) 3.4 Experiments We perform two sets of experiments. In the first one we assume homogeneous retailers, and intends to assess the contribution of each retailer involved in IS on improving SC performance when all of them have identical operational configurations. In order to increase the generality of results, we consider a wide range of possible operational configurations for the retailers by analysing the full factorial set of the OFs. Since each OF has two levels, we analyse 24 different retailers’ operational configurations. Then, each retailers’ operational configuration is evaluated under five IS structures: (1) no IS (NIS), (2) 1 retailer shares information (1retIS), (3) 2 retailers share information (2retIS), (4) 3 retailers share information (3retIS), and (5) 4 retailers share information (FIS). Therefore, we analyse a total of 5x24=80 SCs in this set of experiments. The second set of experiments is performed under the hypothesis of heterogeneous retailers, and intends to assess the contribution of each retailer involved in IS on improving SC performance when they have different operational configurations, and how retailers’ OFs may influence to their contribution. To this aim, for each of the four OFs, we model a set of SCs where there are two groups of two retailers. The two retailers in each group have the same OF value (OF=OF* from now on), but the OF is different among the two groups. More specifically, the first pair of retailers have the OFL value and the second pair have the OFH value (e.g. if OF*=𝜎𝐷𝐶𝑗 2, then the first pair of retailers will have 𝜎𝐷𝐶𝑗 2=100 and the second pair of retailers will have 𝜎𝐷𝐶𝑗 2=400). The other three OFs remain the same for all the retailers. To increase the generality of the Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 21 results, for a given OF=OF* we analyse the full factorial set of the other three OFs (OF≠OF*). Therefore, we have a total of 4 (OF=OF*) x 23 (OF≠OF*) = 32 retailers’ operational configurations. Finally, each retailers’ operational configuration is evaluated under four IS structures: (1) NIS, (2) first pair of retailers share information (referred as OFLIS), (3) second pair of retailers share information (referred as OFHIS), and (4) FIS. We analyse a total of 4x32=128 SCs in this set of experiments. A summary of the DoE is presented in Table 3. Table 3. Summary of experiments (DoE). Full factorial set of the OFs Retailers’ operation al configurat ions IS structures Analysed SCs Performance Metrics Homogeneous Retailers 𝜎𝐷𝐶𝑗 2(OFL, OFH) 𝜏𝑖𝑗 (OFL, OFH) 𝜇𝐿𝑖𝑗(OFL, OFH) IPij(OFL, OFH) 24=16 NIS 1retIS 2retIS 3retIS FIS 5x24=80 BwSl InvSl SysInvAv (OF=OF*) (2retailers - OFL, 2retailers - OFH) Full factorial set of OF≠OF* (same for all retailers) Heterogeneous Retailers 𝜎𝐷𝐶𝑗 2 [𝜏𝑖𝑗(OFL, OFH), 𝜇𝐿𝑖𝑗(OFL, OFH), IPij(OFL, OFH)]= =23=8 4x23=32 NIS 4x32=128 BwSl InvSl SysInvAv 𝜏𝑖𝑗 [𝜎𝐷𝐶𝑗 2(OFL, OFH), 𝜇𝐿𝑖𝑗(OFL, OFH), IPij(OFL, OFH)]= =23=8 2retIS (OFLIS) 𝜇𝐿𝑖𝑗 [𝜎𝐷𝐶𝑗 2(OFL, OFH), 𝜏𝑖𝑗(OFL, OFH), IPij(OFL, OFH)]= =23=8 2retIS (OFHIS) IPij [𝜎𝐷𝐶𝑗 2(OFL, OFH), 𝜏𝑖𝑗(OFL, OFH), 𝜇𝐿𝑖𝑗(OFL, OFH)]= =23=8 FIS The simulations were performed on an Intel Core 2 Duo P8600 2.40GHz computer with 2GB RAM. The effective simulation time was 14 hours and 49 minutes for the set of homogeneous retailers (1,600 simulation runs), and 26 hours and 4 minutes for the set of heterogeneous retailers (2,560 simulation runs). Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 22 4 ANALYSIS OF RESULTS This section presents the results obtained by the simulations performed with SCOPE according to the DoE presented in Section 3. We also derive meaningful findings on the implementation of IS on a SC with several retailers. 4.1 Homogeneous retailers Herein we present the results obtained for the set of experiments under the hypothesis of homogeneous retailers. Table 4 shows a legend, labelling the 16 retailers’ operational configurations from #1 to #16. For each retailers’ operational configuration, the SC is analysed under five IS structures (Table 3). The metrics obtained from all scenarios are averaged over the 20 replications, and results are plotted in Figure 3. For clarity, results obtained for each performance metric are divided in 4 plots. Also, they are displayed from the highest value of the metric to the lowest value of the metric. Table 4. Retailers’ operational configurations. H= OFH L= OFL #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 𝜇𝐿𝑖𝑗 H H H H H H H H L L L L L L L L IPij H H H H L L L L H H H H L L L L 𝜏𝑖𝑗 H H L L H H L L H H L L H H L L 𝜎𝐷𝐶𝑗 2 H L H L H L H L H L H L H L H L Due to the use of system’s metrics, the results obtained over the 20 replications are very close to the average with very low variances. To ensure the significance of results obtained we performed an ANOVA for each metric and each retailers’ operational configuration. All tests were significant at the 95% confidence level. Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 23 BwSl InvSl SysInvAv Figure 3. SC performance under the hypothesis of homogeneous retailers. 0 5 10 15 20 NIS 1retIS 2retIS 3retIS FIS #2 #6 #14 #1 0 2 4 6 8 10 12 NIS 1retIS 2retIS 3retIS FIS #10 #5 #8 #9 0 1 2 3 4 5 6 7 8 NIS 1retIS 2retIS 3retIS FIS #16 #4 #13 #3 0 1 2 3 4 5 NIS 1retIS 2retIS 3retIS FIS #12 #7 #11 #15 0 5 10 15 20 25 30 35 40 NIS 1retIS 2retIS 3retIS FIS #2 #10 #6 #4 0 5 10 15 20 25 NIS 1retIS 2retIS 3retIS FIS #14 #12 #8 #16 0 5 10 15 20 NIS 1retIS 2retIS 3retIS FIS #1 #9 #5 #3 0 2 4 6 8 10 NIS 1retIS 2retIS 3retIS FIS #13 #11 #7 #15 0 200 400 600 800 1000 1200 1400 1600 NIS 1retIS 2retIS 3retIS FIS #1 #5 #9 #3 0 100 200 300 400 500 600 700 800 NIS 1retIS 2retIS 3retIS FIS #2 #13 #11 #7 0 100 200 300 400 500 600 NIS 1retIS 2retIS 3retIS FIS #6 #10 #15 #4 0 50 100 150 200 250 300 350 400 450 NIS 1retIS 2retIS 3retIS FIS #14 #8 #16 #12 Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 24 Results show a quasi-linear performance improvement in BwSl from NIS to FIS, with all curves yielding a coefficient of determination (R2) over 0.99. In fact, since retailers are identical and transmit demand information, it is expected that the impact of IS on reducing demand variability would be linear with the number of retailers. However, curves related to the inventory metrics (InvSl and SysInvAv) are not strictly linear, with 67% of all curves yielding a coefficient of determination over 99%, and the rest of the curves showing small deviations from linearity, with 0.90< R2<0.99. This result suggests that the impact of transmitting demand information on inventory performance improvement is linear with the number of retailers in most cases, but it may present some non-linearity. Performance curves show different slopes depending on retailers’ operational configurations. Thus, benefits of incorporating a retailer to IS may depend on current retailers’ operational configuration. In order to appreciate this phenomenon, we compute the percentage of performance improvement for each metric from NIS to 2retIS and from NIS to FIS for each of the 16 retailers’ operational configurations and plot the results in Figure 4. A generic formulation of this measure is shown in Equation (15), where ‘metric’ can be either BwSl, InvSl or SysInvAv, and A,B represent any of the IS structures. ∆𝑚𝑒𝑡𝑟𝑖𝑐𝐴→𝐵(%)=(𝑚𝑒𝑡𝑟𝑖𝑐𝐴−𝑚𝑒𝑡𝑟𝑖𝑐𝐵) 𝑚𝑒𝑡𝑟𝑖𝑐𝐴∗100 (15) From Figure 4 it can be seen that the benefits obtained in terms of BwSl reduction are less dependent on retailers’ operational configuration than those related to InvSl and SysInvAv. In fact, performance improvement in terms of BwSl is very similar for all scenarios. This result indicates that the expected bullwhip reduction from adding retailers to IS weakly depends on retailers’ operation. Nevertheless, the performance improvement related to InvSl and SysInvAv show a stronger dependence on retailers’ operational configuration. Additionally, BwSl reduction is higher than InvSl and SysInvAv reductions: there is an average BwSl reduction of around 20%-25% for 2retIS and around 40%-50% for FIS, while average InvSl and SysInvAv reductions are around 5%-16% for 2retIS and 10%-32% for FIS. We can summarize the above findings as follows: Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 25 (1) The improvement in BwSl in a SC with homogenous retailers obtained by information sharing is linear with the number of retailers sharing information. Nevertheless some (weak) non-linearity appears for InvSl and SysInvAv metrics. (2) The improvement in BwSl in a SC with homogeneous retailers obtained by information sharing: a. It is higher than for InvSl and SysInvAv metrics. b. It is less dependent on retailers’ operational configuration than for InvSl and SysInvAv metrics. Figure 4. SC performance improvement for all the retailers’ operational configurations. 0 10 20 30 40 50 60 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 ΔBwSl_NIS->2retIS(%) ΔBwSl_NIS->FIS(%) 0 5 10 15 20 25 30 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 ΔInvSl_NIS->2retIS(%) ΔInvSl_NIS->FIS(%) 0 5 10 15 20 25 30 35 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 ΔSysInvAv_NIS->2retIS(%) ΔSysInvAv_NIS->FIS(%) Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 32 performance improvement by partial IS. In the case of OF*= IPij it can be seen that the results are highly dependent on retailers’ operational configuration and it is not clear which retailers are more favourable. OF*=𝜎𝐷𝐶𝑗 2 OF*= IPij OF*=𝜇𝐿𝑖𝑗 OF*=𝜏𝑖𝑗 Figure 6. SC performance increase (BwSl) under partial IS and FIS for heterogeneous retailers. 4.2.1 Sensitivity analysis on retailers’ demand variance and forecasting period In order to enhance the simulation models and to extend the applicability of the results obtained, we perform a sensitivity analysis (Kleijnen 2008) with respect to the more relevant OFs (i.e., OF*=𝜎𝐷𝐶𝑗 2 and OF*=𝜏𝑖𝑗). Since the values assumed by the OFs in 0 10 20 30 40 50 60 #1 #2 #3 #4 #5 #6 #7 #8 0 10 20 30 40 50 60 #1 #2 #3 #4 #5 #6 #7 #8 0 10 20 30 40 50 #1 #2 #3 #4 #5 #6 #7 #8 0 10 20 30 40 50 60 #1 #2 #3 #4 #5 #6 #7 #8 Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 33 Table 2 are different in order to ensure a heterogeneous scenario, in this further analysis we aim to address the following question: how much the results will change if the differences between retailers’ OFs are reduced? To do so, we analyse (1) two new variants for demand variance, with the OFH value reduced to 𝜎󰇗𝐷𝐶𝑗=17.5 (𝜎󰇗𝐷𝐶𝑗 2=306.25) in the first variant and to 𝜎󰇘𝐷𝐶𝑗=15 (𝜎󰇘𝐷𝐶𝑗 2=225) in the second variant; and (2) two new variants for the forecasting period, with the OFL value increased to 𝜏󰇗𝑖𝑗=7 in the first variant and to 𝜏󰇘𝑖𝑗=9 in the second variant. For each new variant we analyse the full factorial combination of the OF≠OF*, which maintains the original values, as in Table 7. Therefore we analyse a total of 4 (variants) x 8 (full factorial OF≠OF*) x 4 (IS structures) = 128 SCs (2560 simulation runs). Following the same procedure carried out in Section 4.2, we compute Equations (16) and (17) and show the average values for each metric in Table 8. As it could be expected, the advantages or disadvantages obtained from OFLIS or OFHIS structures (i.e., differences between ∆𝑚𝑒𝑡𝑟𝑖𝑐𝑂𝐹𝐿𝐼𝑆 𝐹𝐼𝑆 ⁄(%) and ∆𝑚𝑒𝑡𝑟𝑖𝑐𝑂𝐹𝐻𝐼𝑆 𝐹𝐼𝑆 ⁄(%)) are lower as the differences between OFs decrease. Table 7. DoE for the sensitivity analysis on 𝜎𝐷𝐶𝑗 2 and 𝜏𝑖𝑗. OFs 𝜎𝐷𝐶𝑗 2 sensitivity 𝜏𝑖𝑗 sensitivity 1st variant 2nd variant 1st variant 2nd variant 𝑂𝐹𝐿 󰇗 𝑂𝐹𝐻 󰇗 𝑂𝐹𝐿 󰇘 𝑂𝐹𝐻 󰇘 𝑂𝐹𝐿 󰇗 𝑂𝐹𝐻 󰇗 𝑂𝐹𝐿 󰇘 𝑂𝐹𝐻 󰇘 𝜎𝐷𝐶𝑗 2 100 306.25 100 225 100 400 100 400 𝜏𝑖𝑗 5 15 5 15 7 15 9 15 𝜇𝐿𝑖𝑗 2 4 2 4 2 4 2 4 𝐼𝑃𝑖𝑗 S1 S2 S1 S2 S1 S2 S1 S2 For OF*=𝜎𝐷𝐶𝑗 2, differences between ∆𝑚𝑒𝑡𝑟𝑖𝑐𝑂𝐹𝐿𝐼𝑆 𝐹𝐼𝑆 ⁄(%) and ∆𝑚𝑒𝑡𝑟𝑖𝑐𝑂𝐹𝐻𝐼𝑆 𝐹𝐼𝑆 ⁄(%) smoothly decrease as the OFH value decreases. In the first variant, where the c.v. of the demand faced by OFH retailers changes from 0.4 to 0.35 and the c.v. of demand faced by OFL retailers remains the same (i.e., c.v.=0.2), the benefits obtained from OFHIS still represent over 70% of the benefits of a FIS for the three metrics. In the second Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 34 variant, where the c.v. of the demand faced by OFH retailers is reduced to 0.30, benefits obtained from OFHIS are still significantly higher than benefits obtained from OFLIS. For OF*=𝜏𝑖𝑗, the difference between ∆𝑚𝑒𝑡𝑟𝑖𝑐𝑂𝐹𝐿𝐼𝑆 𝐹𝐼𝑆 ⁄(%) and ∆𝑚𝑒𝑡𝑟𝑖𝑐𝑂𝐹𝐻𝐼𝑆 𝐹𝐼𝑆 ⁄(%) decreases as the OFL value increases. It is known that a high value of 𝜏𝑖𝑗 produces a more stable forecast, while a low value of 𝜏𝑖𝑗 produces a more nervous forecast. Therefore, as 𝜏𝑖𝑗 increases for the OFL retailers, forecast patterns of both pairs of retailers become more aligned, and the advantages obtained by choosing the OFLIS structure are consequently reduced. Table 8. Results of the sensitivity analysis. OF*=𝜎𝐷𝐶𝑗 2 OF*=𝜎󰇗𝐷𝐶𝑗 2 OF*=𝜎󰇘𝐷𝐶𝑗 2 OF*=𝜏𝑖𝑗 OF*=𝜏󰇗𝑖𝑗 OF*=𝜏󰇘𝑖𝑗 ∆𝐵𝑤𝑆𝑙𝑂𝐹𝐿𝐼𝑆 𝐹𝐼𝑆 ⁄(%) 24,88 31,02 37,88 71,71 65,47 58,26 ∆𝐵𝑤𝑆𝑙𝑂𝐹𝐻𝐼𝑆 𝐹𝐼𝑆 ⁄(%) 74,24 71,18 65,40 31,94 38,80 49,75 ∆𝐼𝑛𝑣𝑆𝑙𝑂𝐹𝐿𝐼𝑆/𝐹𝐼𝑆(%) 21,94 24,92 29,75 77,60 74,91 66,81 ∆𝐼𝑛𝑣𝑆𝑙𝑂𝐹𝐻𝐼𝑆/𝐹𝐼𝑆(%) 85,62 71,46 56,20 26,03 30,53 46,56 ∆𝑆𝑦𝑠𝐼𝑛𝑣𝐴𝑣𝑂𝐹𝐿𝐼𝑆/𝐹𝐼𝑆(%) 20,33 27,91 35,35 70,71 63,79 55,06 ∆𝑆𝑦𝑠𝐼𝑛𝑣𝐴𝑣𝑂𝐹𝐻𝐼𝑆/𝐹𝐼𝑆(%) 73,79 72,33 65,31 26,36 35,45 45,85 5 DISCUSSION AND MANAGERIAL INSIGHTS In this section we discuss the managerial implications derived from our work. We focus on how SC mangers may successfully implement IS at retailers’ stage, since it reports higher benefits to the SC (Lau et al. 2004, Ganesh et al. 2014a, Costantino et al. 2014). In this way we provide practical insights for the estimation of the potential value of each retailer (i.e., estimating the potential contribution of each retailer if they join IS to improve SC performance). There are two possible approaches when implementing IS: a FIS approach, or a partial IS approach. The former always results in a higher improvement of SC performance than the latter, as we have seen in Section 4. However, implementing IS in a SC costs time (negotiations and physical installation of IT) and cash (IT is expensive), and retailers may ask for a large discount to share their information (Huang and Iravani 2005). Therefore, in terms of the net benefits our work highlights the need to consider Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 35 retailers’ operational characteristics in order to decide on which type of IS could be adopted. If retailers are similar in terms of variance of customer demand, inventory policy, forecasting period and lead time average, the potential value of all of them is also similar when they are involved in IS. Therefore, a FIS approach should be pursued, since benefits increase with the number of retailers involved. Additionally, since all retailers have similar potential value, managers may start negotiations with those that are more prone to collaborate. In case that a retailer, or group of retailers, significantly differs from the others in one or more of the aforementioned OFs, the benefits achieved by partial IS may significantly depend on the participant retailer/s. As shown in Section 4, a partial IS structure is able to achieve a significant part of the total benefits obtained by FIS if retailers are significantly different (e.g., we found that involving half of the total number of retailers into IS may lead to obtain over 70% of the total benefits of a FIS under the boundary conditions). Assuming a linear increase of costs with the number of retailers involved in IS, a cost-benefit analysis may reveal that a partial IS approach is more beneficial for the SC than a FIS approach, thus saving costs related to the involvement of additional retailers. On the other hand, an erroneous choice of the partial IS structure may result in a very low performance increase, undermining all efforts and investments. Consequently, a prior evaluation of the potential value of retailers may help managers to efficiently select a partial IS structure, constituted by the most beneficial retailers. To do so, retailers should be evaluated in this order of importance: (1) (higher) demand variance; (2) (lower) forecasting period; (3) (higher) average lead times. Naturally, these results are less significant as the differences between retailers’ OFs decrease. Once the partial IS structure to be adopted has been decided, managers may start implementing IS according to retailers’ potential value. By doing so, the benefits obtained by each new retailer involved in IS are maximal and thus an efficient implementation of IS can be achieved. Even though it has been shown that considering retailers’ operation during the implementation of partial IS may provide important benefits for the SC, obtaining such information may present some difficulties. Only the lead time average of each retailer could be accessed (through the wholesaler). However, results obtained in this paper Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 36 show that retailers’ demand variance and retailers’ forecasting period are the most significant OFs. Since these factors are retailers’ private information, a precollaboration strategy to share these data needs to be developed with retailers prior to the implementation of partial IS. In this case, SC managers should start by developing channels of trust and/or revenue contracts. To sum up, we suggest managers to implement partial IS at heterogeneous retailers using the following steps: 1. Analyse retailers’ operational characteristics. 2. If they are significantly different in one or more OFs, estimate the potential value of each retailers’ collaboration in IS and rank them accordingly. 3. Estimate costs of involving retailers into IS and perform a cost/benefit analysis. 4. Decide the best IS structure using results from 3) and proceed involving retailers according to 2). 6 CONCLUSIONS AND FUTURE RESEARCH This work presents an exploratory study on partial information sharing at retailers level, i.e., some retailers may not participate in information sharing. We analyse the potential contribution of the participation of each individual retailer in information sharing under two different hypothesis: (1) retailers are homogeneous (i.e., they have identical operational configuration), and (2) retailers are heterogeneous (i.e., they have different operational configuration). Using a Multi-Agent Systems simulation approach, we model a four echelon supply chain with four retailers, with stochastic demands and lead times, using two common Order-Up-To inventory policies. Retailers’ operation is characterized by four operational factors: demand variance, forecasting period, lead time average, and inventory policy. We measure the supply chain performance using systemic supply chain metrics: Bullwhip Slope, Inventory Slope and Systemic Inventory Average. Supply chain performance is measured for different partial information sharing structures and different retailers’ operational configurations. The results of our study emphasize the need of individually estimating the potential value of retailers’ information prior to the implementation of information sharing, and provides the following insights: Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 37 - When retailers are homogeneous they have equal potential value if they are involved in information sharing (i.e., they identically contribute to improve supply chain performance). Thus, a full information sharing approach is recommended. - When retailers are heterogeneous they have different potential value if they are involved in information sharing, depending on their operational configuration. As a consequence o The performance improvement achieved by different partial information sharing structures with the same number of retailers might be significantly different. o A partial information sharing structure involving retailers with high potential value may capture a substantial part of the benefits of full information sharing. o Assuming a linear increase of costs with the number of retailers involved in information sharing, a cost-benefit analysis may reveal that a partial information sharing approach is more beneficial for the supply chain than a full information sharing approach, thus saving costs related to the involvement of additional retailers. - Retailers’ operation need to be carefully examined in order to develop an efficient implementation of information sharing. In this order of importance, retailers with (1) higher demand variance, (2) lower forecasting period, and (3) higher average lead time, are potentially more beneficial partners for implementing information sharing. Due to the complex relationships between retailers’ operational factors and retailers’ potential value when become participants of information sharing, it was not possible to come up with a single and precise rule for identifying the most beneficial information sharing structure. In fact, properly balancing each operational factor is still an issue. Nevertheless, the findings reported in this paper should help managers to better understand the opportunities for partial information sharing and put them in a stronger position in their negotiations about establishing information sharing links. The present study has some limitations that may create room for improvement and further research. Also, due to the exploratory nature of this work, there are many ways of possible extensions: Dominguez R., Cannella S., Póvoa A.P., Framinan J.M. 2017. Information sharing in supply chains with heterogeneous retailers. Omega. DOI: https://doi.org/10.1016/j.omega.2017.08.005 38 - Deepening the analysis of each operational factor by increasing the number of intermediate values, and considering other different set ups of supply chain (i.e., different demand or lead time distributions, different forecast methods, etc.) would provide additional results that might be useful to precisely balance the importance of each operational factor on a wide variety of conditions and to look for a single rule for choosing the best information sharing structure. - Analysing scenarios where retailers may differ in more than one factor at the same time would provide more realistic results. - This work analyses either homogeneous or heterogeneous retailers. The “grey zone” that falls in the middle of both scenarios has been briefly analysed through a sensitivity analysis. Determining the limits between both scenarios would be a significant contribution in this line of research. - A similar analysis to that conducted in this work on other operational factors (e.g. lead time variance, forecast method, safety factor, etc.) would provide a wider perspective of this problem to supply chain managers. - Results of this work are scalable to higher or lower number of retailers. However, it could be interesting to analyse how the upstream part of the supply chain may impact on the results obtained. More specifically, it should be addressed how the upstream supply chain structure and upstream member’s operational configuration may impact on the implementation of information sharing at retailers. 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