Duy Tan Nguyen
email: duy-tan.nguyen@hec.ca

Yossiri Adulyasak
email: yossiri.adulyasak@hec.ca

Sylvain Landry
email: sylvain.landry@hec.ca

Duy Tan

The Bullwhip Effect in rule-based supply chain planning systems-A case-based simulation at a hard goods retailer

Keywords: Flowcasting, Distribution, Logistics, Bullwhip Effect, Simulation, Factor Analysis, Regression Analysis

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In 1958, Forrester explored the amplified demand variability in supply chain (SC) upper tiers and pointed out the importance of retail point-of-sale (POS) information in diminishing this effect. Since then, many scholars, such as Lee et al. (1997a), [START_REF] Christopher | Mitigating supply chain risk through improved confidence[END_REF] and [START_REF] Wei | Linking inter-organizational trust with logistics information integration and partner cooperation under environmental uncertainty[END_REF], have discussed and emphasized the role of information sharing, especially via SC collaboration and integration, in driving SC efficacy. Yet, several challenges persist, including lack of trust, difficulty in coordinating information and material flows, and integrating business processes [START_REF] Näslund | Supply chain management integration: a critical analysis[END_REF][START_REF] Palma-Mendoza | Business process re-design methodology to support supply chain integration[END_REF]. A study by [START_REF] Shang | Information sharing in a supply chain with a common retailer[END_REF] found that only a quarter of retailers share their data with suppliers. Per reviews by [START_REF] Näslund | Supply chain management integration: a critical analysis[END_REF] and [START_REF] Sethi | Integrating business-to-business customers in original equipment manufacturers: supply chains through information systems integration[END_REF], only a few papers address integration with SC clients, while [START_REF] Fawcett | The rhetoric and reality of supply chain integration[END_REF] state that integration with suppliers is more commonly studied. Indeed, prior publications study integration primarily from the manufacturer's perspective rather than the retailer's [START_REF] Bhakoo | Supply chain structures shaping portfolio of technologies: exploring the impact of integration through the 'dual arcs' framework[END_REF]. Examples include such practices as Vendor-Managed Inventory (VMI) and Advanced Continuous Replenishment, which are often mentioned in the literature to regard vendors as primary decision-makers [START_REF] Guimarães | The twoechelon multi-depot inventory-routing problem[END_REF][START_REF] Simchi-Levi | Designing and Managing the Supply Chain: Concepts, Strategies, and Case Studies[END_REF]. Meanwhile, [START_REF] Martin | Flowcasting the retail supply chain: slash inventories, out-of-stocks and costs with far less forecasting[END_REF] emphasize that the final POS is the only place where demand uncertainty truly exists and that stores are better positioned to grasp the retail environment and share this insight upstream the SC. These same authors therefore recommend a bottom-up approach rather than a top-down one as in VMI.

Inspired by the integrated SC vision predicated on Forrester's 1958 paper, André Martin proposed the Retail Resource Planning (RRP) concept in the 1990s, also known as Store-Level Distribution Resource Planning (DRP) and renamed it Flowcasting in 2006 [START_REF] Landry | Flowcasting : Une percée dans l'intégration de la chaîne logistique[END_REF][START_REF] Roy | The implementation of flowcasting between CPGA and Sam's Club[END_REF]. This approach extends the DRP logic, which stems from Material Requirements Planning (MRP) logic but in the distribution context [START_REF] Masters | On the adoption of DRP[END_REF], to the storefront and shifts the focus to this customer-facing actor as a central player [START_REF] Martin | Flowcasting the retail supply chain: slash inventories, out-of-stocks and costs with far less forecasting[END_REF]. In Flowcasting, demand forecast and planned replenishment from stores cascade upstream as a basis for upper-tier node demand planning. [START_REF] Janamanchi | Control theory concepts applied to retail supply chain: a system dynamics modeling environment study[END_REF] indicate from their optimization model that suppliers do not need their own forecast but instead can use that of retailers, a finding that indirectly supports Flowcasting.

While there is a large body of literature on the benefits of seamless information sharing across the SC, only some, such as [START_REF] Ma | The bullwhip effect under different information-sharing settings: a perspective on price-sensitive demand that incorporates price dynamics[END_REF] and Wang et al. (2016), specifically state that sharing both order schedules and POS data, which is in line with the Flowcasting logic, is more advantageous to reduce the Bullwhip Effect (BWE) compared to sharing consumer demand information alone. Despite the great potential of its integration into the SC, Flowcasting is understudied and remains uncommon in practice [START_REF] Koh | Enterprise networks and logistics for agile manufacturing[END_REF][START_REF] Sahin | Rolling horizon planning in supply chains: review, implications and directions for future research[END_REF]). Thus, our paper will be among the first attempts to provide empirical insight into the effect of Flowcasting versus Reorder Point (ROP) as well as a combination of ROP and DRP on various BWE dimensions. The main objective of this paper is to analyze SC-wide integrated DRP logic (Flowcasting) in BWE reduction at a firm versus two traditional inventory fulfillment methods: ROP and a combination of ROP and DRP (ROP/DRP or partially integrated DRP), whereby we emphasize the retailer's role and help confirm the value of sharing specific information on replenishment plans compared to generic data on retail sales history.

FIGURE 1: Illustration of the three inventory fulfillment systems in this study

We refer to the ROP settings hereinafter when all tiers run as per the ROP logic (see LITERATURE REVIEW). In the ROP/DRP system, we assume that the DRP logic applies to distribution centers (DCs) and upper tiers, while stores are assumed to adopt the ROP logic. In the third system, all tiers use the DRP logic (see FIGURE 1). In this paper, we refer to this replenishment system based on the DRP logic used in the entire SC network as "Flowcasting."

The case used for this study is Princess Auto Ltd. (PA), a Canadian hard goods retailer. Since its inception, the firm has intently followed an organic growth path by opening new company-owned stores. PA now has over forty stores in nine Canadian provinces and three regional DCs, each of which stocks from a different vendor base. Despite the firm's relatively small size, its steady growth has come to the attention of bigger market players, and it must therefore act to sustain its growth and competitiveness. Due to the ROP practices applied at the time, its SC was experiencing a severe capacity shortage. Thus, in 2013 it decided to invest in ROP replacement and core processes that fitted or were closely linked with a Flowcasting-based replenishment system, which entailed hiring two consulting resources and an implementation team of three business professionals and one IT professional. Their program started with educating the executives and then operational team members and suppliers/partners in small groups of 8 to 10 at a time ( software. + Provide support to staff to help them overcome their anxiety and inertia during the pilot and actual work. + Get everyone involved in the consensus process for the forecasting and demand planning throughout the Flowcasting implementation. + Conduct pilot work with the most difficult vendor base to work out cases with the most concerns + Go-live with this vendor base. + Go-live with all domestic vendors, phased in with one group/category at a time. + Go-live with overseas vendors. + Build stability into the planned replenishment to gain vendor trust and buy-in. point where PA could integrate the outcomes and benefit from more significant value and planning opportunities as they moved forward: better in-stock inventory vs. lean inventory. + Resume measuring and communicating forecast accuracy and other KPIs for improvement.

TABLE 1: Timeline of Flowcasting Implementation at Princess Auto

The contributions in this paper are fourfold. First, we establish hypotheses on how the implementation of Flowcasting logic has improved PA's SC performance based on qualitative interviews with the executives and planners involved in the implementation of this SC-wide integrated system. Second, we develop a simulation based on the data obtained from the company (PA) to quantitatively evaluate the performance of three different rule-based replenishment systems, i.e., the previously employed ROP system, a combined ROP/DRP system, and Flowcasting. Third, we deploy multivariate regression to statistically compare these methods as a way to evaluate the performance of the simulated systems under different operational factors and to obtain insights. Fourth, we discuss managerial implications based on the data and results obtained in this study. This paper has six sections: section 1 is the Introduction; section 2 consists of a review of the literature on the three inventory fulfillment tools in question as well as hypotheses about their relative efficacy; section 3 provides the methodology and the simulation of the three methods in operating mode; section 4 presents multivariate regressions to statistically compare performance and provide empirical insights; section 5 includes a discussion of the implications of this paper's findings and the limitations of the research; and section 6 is the conclusion.

LITERATURE REVIEW

Inventory Fulfillment Methods

This paper focuses on three rule-based inventory fulfillment approaches with comparable operational logic based on POS data sharing to varying degrees: Flowcasting, ROP/DRP and ROP. Comparing these methods can support the link between data sharing and BWE reduction.

The ROP system

ROP system policies have been formalized and popularized since Galliher et al.'s seminal 1959 article and Hadley and Whitin's classic 1963 textbook [START_REF] Federgruen | An efficient algorithm for computing an optimal (r, Q) policy in continuous review stochastic inventory systems[END_REF].

There is a large body of literature on the conditions under which each ROP policy best fits [START_REF] Wensing | Periodic review inventory systems: performance analysis and optimization of inventory systems within supply chains[END_REF]. When the order quantity must meet certain batch sizes given the linear and unimodular holding and backordering costs, it is advisable to adopt the (R, s, Q=nq) policy, where R is the review interval, s is the reorder level and nq is the smallest multiple of the batch size q (Wensing 2011). These parameters can be approximated by the continuous review system method [START_REF] Nahmias | Production and operations analysis[END_REF] or by our case firm's tactics. For compatibility with time-phased DRP, we selected the periodic review system (R, s, nq) for analysis, where n follows PA's logic. More details are given in 3.1. Simulation.

The DRP system

The 1970s saw the emergence of DRP, which hinges on the logic of dependent demand that stems from another item's forecast [START_REF] Martin | Flowcasting the retail supply chain: slash inventories, out-of-stocks and costs with far less forecasting[END_REF]. Inspired by Orlicky's insight into dependent demand through the MRP logic, Martin espoused the DRP approach (Roy and Landry 2010), which was initially proposed by Whybark [START_REF] Masters | On the adoption of DRP[END_REF]) and is defined as a time-phased management process that consists of identifying inventory demand at each inventory stocking location and matching supply and demand [START_REF] Martin | DRP: Distribution resource planning: the gateway to true quick response and continuous replenishment[END_REF]. In DRP, independent demand, i.e. end-user demand, is forecasted. Distribution demand, which stems from customer demand, is then calculated according to the order lot size, lead time and safety stock rather than the forecast. According to [START_REF] Samaranayake | A conceptual framework for supply chain management: a structural integration[END_REF], this logic helps link SC processes and contributes to SC integration. Ganeshan et al.'s (2001) simulation of a 4echelon SC and ANOVA test show that, compared with the periodic review ROP, DRP boosts service levels without much impact on cycle time. In terms of cutting inventory and maintaining service levels, the simulation study and ANOVA test by [START_REF] Suwanruji | Evaluating the effects of capacity constraints and demand patterns on supply chain replenishment strategies[END_REF] reveal that DRP is superior under seasonal demand but inferior to ROP with unconstrained capacity. Overall, however, only a few studies compare DRP and ROP [START_REF] Grewal | Comparative evaluation of supply chain replenishment strategies in a capacitated supply chain[END_REF]) under practical settings.

Flowcasting

As mentioned, in the 1990s André Martin developed RRP, which was later renamed Flowcasting. This approach is also called store-level DRP and consists of applying the DRP logic to stores as central actors in a multi-tier retail inventory fulfillment process [START_REF] Landry | Flowcasting : Une percée dans l'intégration de la chaîne logistique[END_REF][START_REF] Roy | The implementation of flowcasting between CPGA and Sam's Club[END_REF]. In Flowcasting, stores forecast demand and 52-week replenishment that cascade upstream the SC so that upper-tier partners can plan operations accordingly without having to repeat the forecast [START_REF] Martin | Flowcasting the retail supply chain: slash inventories, out-of-stocks and costs with far less forecasting[END_REF]). Although upstream actors may risk using inaccurate forecasts from the stores, Cannella et al. (2018a) find that in integrated SCs with shared cost, such risk-taking strategies are favored for controlling SC instability and likely beneficial for customer service, provided that the stores are risk-averse. This requires closer collaboration among SC actors in information sharing and decision making [START_REF] Martin | Meeting the promise of flowcasting[END_REF]. This entails trust [START_REF] Näslund | Supply chain management integration: a critical analysis[END_REF], which necessitates time and effort to build (Almeida et al. 2015). Yet, Flowcasting benefits both parties since it enhances SC visibility, thereby avoiding forecast distortions due to abnormal demand signals caused by retailer promotions. By preventing such distortions, the supplier can stabilize its master schedule, which, per [START_REF] Martin | Meeting the promise of flowcasting[END_REF], could boost productivity, which was the case for Proctor & Gamble (P&G). Enhanced visibility also helps cut down on buffers and therefore inventory while lifting service levels, as demand can be tracked and satisfied in a timely manner; still, an average inventory cut may be less obvious at stores compared to DCs, in light of the retail display rule [START_REF] Martin | Meeting the promise of flowcasting[END_REF].

The Bullwhip Effect (BWE)

Since the BWE is a common concept in supply chain management (SCM) [START_REF] Wang | The bullwhip effect: progress, trends and directions[END_REF], we therefore include BWE measures as assessment criteria for the operations of the three inventory fulfillment methods to be analyzed. [START_REF] Forrester | Industrial dynamics: a major breakthrough for decision makers[END_REF] was one of the first scholars to observe that a volume fluctuation of 10% at the store level leads to a 40% volume variation at the manufacturing level about six months later. The term BWE was coined by P&G, which observed an order variability rise in upper tiers [START_REF] Wang | The bullwhip effect: progress, trends and directions[END_REF]. Due to scant retail data, Hewlett-Packard had to use their immediate clients' orders for operations planning, which was vitiated by inflated demand variability (Lee et al. 1997a).

Per Lee et al. (1997a), there are four BWE triggers: demand forecast updating, order batching, price fluctuations, and rationing and shortage gaming. [START_REF] Simchi-Levi | Designing and Managing the Supply Chain: Concepts, Strategies, and Case Studies[END_REF] add lead time as another BWE cause. For their part, [START_REF] Chopra | Supply chain management: strategy, planning, and operation[END_REF] categorize BWE causes as operational, pricing and behavioral obstacles. What these scholars all agree on is that the lack of information sharing between SC partners is the main driver of the BWE. An example of their recommended measures against the BWE is seamless POS data sharing across SC actors. This recommendation is supported by several studies. [START_REF] Dejonckheere | Production, manufacturing and logistics: the impact of information enrichment on the bullwhip effect in supply chains: a control engineering perspective[END_REF] combine control systems engineering and spreadsheet simulation to illustrate that information enrichment cuts the BWE magnitude. Similar results are produced in Chatfield et al.'s simulation and ANOVA test (2004) on the impact of variable lead time, information sharing and data quality in BWE reduction. In Barlas and Gunduz's 3-tier SC model (2011), sharing demand data and forecasts contribute to BWE depletion, which is in line with Sandhu et al.'s simulation study (2013).

Quantitative Measures of the Bullwhip Effect

The literature describes several ways to quantify the BWE [START_REF] Cannella | Metrics for bullwhip effect analysis[END_REF]. Lee et al. (1997b), who were among the first scholars to explore the BWE, measure it as the ratio of the variance of replenishment order quantities to the variance of sales volumes at an echelon (store, DC, etc.). We call this measure Lee et ) 708-3 9:8/;-3 4 /6 708-3 9:8/;-3 (Equation 2)

Still, this measure is regarded by [START_REF] Disney | On the bullwhip and inventory variance produced by an ordering policy[END_REF] as representing only half of the BWE, given the impact of the replenishment rule. [START_REF] Disney | On the bullwhip and inventory variance produced by an ordering policy[END_REF] therefore introduced the Inventory Variance Ratio (IVrR) as an added measure, where the dispersion index of order quantities in the ORVrR is replaced with the coefficient of dispersion of inventory at echelon i.

Inventory Variance Ratio =

) ?1@-12:+A 4 /6 ?1@-12:+A

) 708-3 9:8/;-3 4 /6 708-3 9:8/;-3

(Equation 3)

To measure the BWE on the whole SC and compare different SCs, [START_REF] Cannella | Metrics for bullwhip effect analysis[END_REF], based on the study by [START_REF] Dejonckheere | Production, manufacturing and logistics: the impact of information enrichment on the bullwhip effect in supply chains: a control engineering perspective[END_REF], developed a number of linear slope metrics; the two most pertinent to this paper are the Bullwhip Slope and the Inventory Instability Slope. The Bullwhip Slope measures the order amplification on average when we move upstream the SC, while the Inventory Instability Slope quantifies the inventory fluctuation trend across SC tiers. A positive slope means order or inventory fluctuation rises upstream the SC, while a negative one shows a variation decrease in upper tiers. The formulas given by [START_REF] Cannella | Metrics for bullwhip effect analysis[END_REF] apply to measuring the amplification from tier 2 up, as tier 1 acts as the base for calculation 4) 5)

Bullwhip Slope = H ∑ J K K L MN O∑ J L MN ∑ K K L MN H ∑ J 4 L MN OP∑ J L MN Q 4 (Equation
Inventory Instability Slope = H ∑ J S K L MN O∑ J L MN ∑ S K L MN H ∑ J 4 L MN OP∑ J L MN Q 4 (Equation
where K is the total number of echelons in the SC in question, and pi is the position of echelon T in the SC (tier 1, tier 2, tier 3).

All of these BWE metrics can give a holistic measure of Flowcasting efficacy in BWE reduction compared to ROP and ROP/DRP. [START_REF] Cannella | Metrics for bullwhip effect analysis[END_REF] also recommend assessing the average inventory and backlog at each node as complementary criteria, which are adopted by many scholars in inventory fulfillment system reviews [START_REF] Wensing | Periodic review inventory systems: performance analysis and optimization of inventory systems within supply chains[END_REF]. In this case, we choose out-of-stock (OOS) and average inventory to assess the performance. OOS is the number of periods where demand cannot be fully satisfied by the on-hand inventory but is to be met by expedited shipment, which is commonly discussed in the literature as an indicator of SC vulnerability, begetting an unintended BWE [START_REF] Avci | A multi-objective simulation-based optimization approach for inventory replenishment problem with premium freights in convergent supply chains[END_REF]. Average inventory is the average on-hand inventory at a node during the time period considered [START_REF] Tsai | A simulation-based multi-objective optimization framework: a case study on inventory management[END_REF].

Hypotheses

While grappling with ROP operations, which had "choked" the SC in its expanding retail network with e-commerce and mail catalogs and attempting to grasp the dynamics of multiechelon replenishment and the current push to EDI, PA decided to begin the Flowcasting process in 2014 to improve the quality of its inventory management, especially in the areas of overstock and seasonal carryover. After several phases of the Flowcasting implementation portfolio (see TABLE 1), the firm was able to start integrating the outcomes of these projects and see initial value. Notably, in-stock went up with leaner inventory. This set a good condition for us to compare Flowcasting with some prior methods.

ROP determines when and how much to reorder based on historical data, which may inaccurately reflect upcoming demand. Moreover, ROP echelons do not share information on real-time sales, and ROP/DRP is not integrated with retail outlets, whereas Flowcasting replenishes as per real-time demand and forecast cascading from retail shops. According to [START_REF] Li | A strategic analysis of inter organizational information sharing[END_REF], demand information sharing improves service levels, which is in keeping with the findings of [START_REF] Boone | The benefits of information sharing in a supply chain: an exploratory simulation study[END_REF] and [START_REF] Chatfield | The bullwhip effectimpact of stochastic lead time, information quality, and information sharing: a simulation study[END_REF]. Linking upper tiers to the stores, Flowcasting provides better information sharing and therefore higher service levels. This enables suppliers to better prepare for demand changes. We therefore hypothesize that,

given the same safety stock level:

H1a: Versus ROP, Flowcasting helps reduce OOS.

H1b: Versus ROP/DRP, Flowcasting helps reduce OOS.

Christopher and [START_REF] Christopher | Mitigating supply chain risk through improved confidence[END_REF] This implies that fluctuation upstream its SC is stabilized. Thus, under our assumption:

H3a: Versus ROP, Flowcasting helps cut the Bullwhip Effect Magnitude.

H3b: Versus ROP/DRP, Flowcasting helps cut the Bullwhip Effect Magnitude.

For the Bullwhip Slope and Inventory Instability Slope, we developed two hypothesis groups.

In accordance with recommendations by Lee et al. (1997a, b) we assume that all the information is correct and timely (if shared) in our simulation.

METHODOLOGY

For this study, we performed qualitative interviews as well as a quantitative analysis of the contact firm's data, as this combination is deemed vital in working on empirical studies and gives a more comprehensive illustration of the research topic [START_REF] Jick | Mixing qualitative and quantitative methods: triangulation in action[END_REF]. With regards to the qualitative methodology, we conducted semi-structured interviews with executives and consultants involved in the implementation of Flowcasting and with relevant staff. The interview results were used to develop the simulation rules and quantitative hypotheses, as proposed by [START_REF] Chandrasekaran | Managing R&D project shifts in high-tech organizations: a multi-method study[END_REF] (Cannella et al. 2018a). In addition to the qualitative data based on the interviews, PA gave us its 52-week forecast for five merchandise categories, i.e. slow-moving, faster-moving/regular, seasonal, highly promoted and new, along with two items for each category that the firm currently forecasts individually. For comparison, we simulated all three inventory fulfillment method operations based on the case firm's settings, including historical average demand, demand estimates, lead time, etc. This allowed us to reflect on the company's operations in practice, ensure comparable operating conditions, and control the impact of confounding factors [START_REF] Evers | Systems analysis using simulation[END_REF]. As our assumption for comparison, we hold constant the safety stock level given by PA across the three methods. In the literature, several scholars follow a similar methodology by adopting real-life parameters from a case firm to assess the efficacy of their proposed algorithms. An example is Avci and Selim's (2018) paper on their simulationoptimization approach to inventory replenishment in an automotive case.

Simulation has been widely utilized to study SC dynamics (Cannella et al. 2017b), given its capability to allow for stochasticity, which better represents the increased complexity of reallife situations [START_REF] Wu | Decision making in enterprise risk management: a review and introduction to special issue[END_REF][START_REF] Tsai | A simulation-based multi-objective optimization framework: a case study on inventory management[END_REF]. As such, simulation can be complementary to empirical studies in operations management [START_REF] Davis | Developing theory through simulation methods[END_REF]Cannella et al. 2018a). According to [START_REF] Sandhu | Steel supply chain management by simulation modelling[END_REF], simulation helps foresee a system's behaviors under preset parameters/conditions, thereby helping to illuminate the dynamics of processes and even such phenomena as the BWE. It is a useful decision-making tool in such SCM areas as inventory control and network configuration and has been adopted and endorsed by several scholars [START_REF] Winch | Constructing multivariate simulation metamodels for supporting supply chain management[END_REF]). Forrester originally used simulation to propose BWE solutions [START_REF] Sandhu | Steel supply chain management by simulation modelling[END_REF] in 1958. This paper adopts the spreadsheet simulation [START_REF] Jahangirian | Simulation in manufacturing and business: a review[END_REF] to illustrate the inventory fulfillment methods concerned, whose operationalization will be discussed in the next section.

Based on the simulation results, we collected performance data on different scenarios and ran In our paper, we use regression, rather than ANOVA, to incorporate continuous control variables for analysis and implicitly take into account the correlations among variables [START_REF] Jawlik | Statistics from A to Z: confusing concepts clarified[END_REF].

Simulation

As discussed above, we adopted simulation to examine the efficacy of ROP, ROP/DRP and Flowcasting. First, for each item, we selected three to four stores, all of which are supplied by one DC. This DC might be supplied by another DC, possibly a manufacturer or primary DC.

We call the former Direct DC (DDC) and the latter Indirect DC (IDC). In total, for the 10 products in our data, there are 11 stores, 3 DDCs and 1 IDC, which account for one quarter of PA's retail network. This network follows the divergent structure as per Giard and Sali's classification (2013), which is commonly adopted in consumer-oriented SCs (Cannella et [START_REF] Kelton | Methodological expectations for studies using computer simulation[END_REF] suggestions on non-stationarity and random-number generation in stochastic simulation inputs. We set the expected forecast error rate at 25%, which is measured by the mean absolute percentage error (MAPE) and deemed an acceptable threshold by PA. In line with Cannella et al. (2017a) and Domínguez et al. (2018a, b), this divergent structure, member heterogeneity and demand stochasticity of the SC under analysis justify our choice of methodology, as simulation is deemed most effective to study system complexity and dynamics in detail. In addition, the use of simulation rather than an analytical framework is appropriate here since several important assumptions do not apply in our case, namely base stock policy, normally distributed demand and economic order quantity, which are commonly used in studies that focus on analytical results (such as the seminal paper of Lee et al. 1997b).

Let U V J denote the probabilistic demand distribution at location T in period W for product X.

The distribution of the demand is based on the predefined uniform distribution, where the expected demand at period W, Y U V J , equals the demand estimate Z ̅ J at period W provided by the company, and the distribution is set up so that the forecast, computed with a similar formula in [START_REF] Boone | The benefits of information sharing in a supply chain: an exploratory simulation study[END_REF], has a MAPE theoretically equal to 25%. The long-term demand is estimated as Z \ J , equaling average historical sales. Let Z J] denote the demand value of product X associated with scenario ^ at period W, which is drawn from U V J . The demand simulated is POS demand. Upper-tier demand is based on lower tier replenishment.

In this paper, we assume the simulated time to be in the frozen horizon, meaning that there is no re-planning within this time. In particular, the simulation horizons include 26, 38 and 50 weeks.

The order lead time to fulfill the inventory of product X for location T is _ J , and the fulfillment lot size at location T is set at _`a J . Note that the initial inventory at location T is b c . The replenishment policy at location T is to fulfill the inventory to cover the number of periods of coverage d`e J . This level is set differently at each location but consistently across systems (ROP, ROP/DRP, and Flowcasting). The inventory review interval for all systems is f.

In the simulation, the inventory of product X at the beginning of period W at location T for scenario ^, denoted by b J] , is calculated in all three systems as

b J] = b , Oh J] + j J] + k J] -Z J]
where j J] is the order quantity received of product X at location T in period W, which is calculated differently based on the fulfillment system, k J] is the quantity of the expedited shipment of product X at location T in period W in the OOS event b , Oh J] + j J] -Z J] < 0. In case of excess inventory, there is no return to upper tiers to avoid BWE inflation [START_REF] Chatfield | Returns and the bullwhip effect[END_REF]. We assume that j J] and k J] arrive at the beginning of the period and/or prior to demand consumption. The expedited quantity is set for all three systems as

k J] = o -min {0, b , Oh J] + j J] -Z J] } _`a T X s × _`a T X
The order quantity received j J] is calculated as per each system's rule. The key gap among the three inventory fulfillment methods herein is the information sharing level. Particularly, the ROP system makes no forecast and there is no replenishment schedule shared. Despite the lack of data on PA's holding and backordering costs, given its period of coverage (POC) policy requiring replenishment orders to be equivalent to certain batch sizes, we can assume the simulated ROP system should follow the (R, s, nq = Q) rule. In the ROP/DRP setting, the DDC gives its forecasts and planned order releases to the IDC, which uses this information to plan its operations. Nevertheless, store replenishment schedules are not shared with the DDC.

We assume that ROP/DRP stores operate based on the ROP logic and that the DRP logic only applies from the DDC to IDC, as indicated by [START_REF] Martin | DRP: Distribution resource planning: the gateway to true quick response and continuous replenishment[END_REF]

The ROP system

The inventory fulfillment at location T is controlled by the reorder point u J = Z \ J × P_ J + fQ + v hO w 4

x J yP_ J + fQ, where v hO w 4 is the z-score associated with the predefined cycle service level 1 -{ | and x J is the standard deviation of the single period demand of product X at location T. Since the ROP system is reactive, this order quantity is calculated separately for each demand scenario ^ of the realized demand values. If the inventory at the start of period t at location T for scenario ^, b ] , is equal to or less than u J , an order is computed as

j J = } d`e T X ×Z ~T X _`a T X • × _`a T X
to cover demand for a predefined number of periods (d`e J ), whose logic differs from EOQ. ). We therefore used the mean squared error (MSE), which is calculated in sample and is thus optimizable, to assess which of the two forecasting methods is more appropriate to our case. Our calculation shows the H-W method MSE is lower. Thus, we proceed with this method in Configuration 1. In Configuration 2, the DDC plans its operations as per the stores' aggregate demand estimates given by PA without forecasting the replenishment. In this configuration, DDC planners are unsure when or how much each store will order but assume the stores' aggregate demand will be deducted from the DDC inventory for replenishment scheduling.

The ROP/DRP system

At the DDC and IDC, the replenishment order quantity does not depend on the demand realization in each scenario. The fulfillment plan is proactively created based on the demand forecast. To calculate the planned order quantity received j J , we first determine the net requirement of product X in period W, € J , which is calculated as follows

€ J = max {Z ' TW X + ƒƒ T X -b T,W-1 X , 0}
where ƒƒ J is the safety stock quantity of product X, ƒƒ J = v hO w 4

x J yP_ J + fQ, and b , Oh J is the projected inventory of product X at period W -1, which is calculated as follows

b J = b , Oh J + j J -Z ̅ J 20
The planned order quantity received j J is then calculated as:

j J = " € TW X + ∑ Z ̅ J W+d`e T X -1 W+1 _`a T X … × _`a T X
to bring the inventory level to cover d`e J periods. ∑ Z ' TW X † ‡ ˆ ‰ Oh †h equals 0 if d`e J = 1. In the simulation of inventory flow, the replenishment quantity based on the DRP logic for all scenarios is set to j J , i.e., j J] = j J , ∀^∈ OE.

The Flowcasting system

In the Flowcasting planning spreadsheet, stores take PA's demand estimates as forecasts for operations planning. As replenishment schedules are shared upstream in Flowcasting, the We note a strong correlation of 0.76 and 0.61 between products n001 and n002, and between products l001 and r002, respectively. However, these products are supplied by different DCs and forecast and managed by PA on an item-by-item basis as per the designs of the Flowcasting system [START_REF] Doherty | A digitally-connected, consumer-driven supply chain[END_REF]. [START_REF] Martin | Flowcasting the retail supply chain: slash inventories, out-of-stocks and costs with far less forecasting[END_REF] recommend not aggregating stock-keeping units (SKUs) at checkout to avoid confounding forecast and reordering unwanted SKUs while running out of demanded ones. Also, since retailers constantly alter their product assortment (Doherty and Landry 2019) with newly-launched and gradually phased-out items, planning by product is preferred in this retail context, where goods are usually not ordered by their generic materials/components as in Raghunathan et al.'s theoretical analysis (2017). Even with such category-level management, the BWE does not necessarily decrease, depending on the sign and magnitude of demand auto-and crosscorrelation of the items under aggregation [START_REF] Raghunathan | Analysis of the bullwhip effect in a multiproduct setting with interdependent demands[END_REF]. In Bray and

Mendelson's robustness checks ( 2012), BWE estimates under product aggregation do not differ statistically from those averaged over item-level measures. Although the BWE measures averaged over positively-correlated items are shown to theoretically decrease when the number of products increases [START_REF] Raghunathan | Analysis of the bullwhip effect in a multiproduct setting with interdependent demands[END_REF], these aggregate measures are uninformative if the firm uses item-level planning [START_REF] Raghunathan | Bullwhip effect of multiple products with interdependent product demands[END_REF]. Thus, we decide to repeat the simulation item by item for each product type in the database. Items with yearly sales below 24 units at any store are slow-movers, and sales of seasonal merchandise last no more than five months. No replenishment is performed outside that time period, and unsold units become carryovers until the next selling season. PA also promotes seasonal products, but its highly promoted articles are subject to more promotional events per year.

Newly or not yet launched items have little sales history and are predicated on similar articles on PA's list of existing goods. Other products are called faster-moving/regular.

Our model generates demand independently of price, and the demand data received from PA were also cleaned of price-related fluctuations. In Cachon et al.'s study (2007), price variance in retail industries is lower than its counterparts in manufacturing and wholesale and does not correlate significantly with BWE measures. Yet, these results are subject to mixed evidence in the literature, depending on price elasticity of demand and autocorrelation in price [START_REF] Wang | The bullwhip effect: progress, trends and directions[END_REF][START_REF] Tai | Measure of bullwhip effect in supply chain with price-sensitive and correlated demand[END_REF]. Since each node in our simulation orders from its supplier as per its replenishment logic rather than pricing, only the storefront, which handles the independent demand of final customers, directly suffers price-induced demand shock. As our paper studies how different inventory fulfillment methods can tackle unanticipated demand fluctuations, which may be caused by both price and nonprice factors, we do not specifically include price in our model. We note that demand forecast adjustment due to price change can practically be done in the preprocessing process (e.g. through demand elasticity functions, sales history at discounted prices or human judgment) as typically treated in the real-world fulfillment system [START_REF] Martin | Flowcasting the retail supply chain: slash inventories, out-of-stocks and costs with far less forecasting[END_REF].

Our simulation yields an array of BWE and efficacy indices varying by forecast error and product type. At the stores, where demand is forecasted in Flowcasting, we measured the MAPE of demand forecast as a forecast error indicator, and the resulting MAPE is around 25% across stores. With the dataset generated, we conducted a z-test for the two ROP/DRP configurations and found that Configuration 2 significantly surpasses Configuration 1, which is based on H-W technique, in terms of OOS and average inventory. With respect to the Bullwhip Slope and Inventory Instability Slope, the former slightly underperforms the latter.

We analyze Configuration 2 in the next section and use Configuration 1 for robustness tests.

QUANTITATIVE TEST

Variable Definition

Since we would like to statistically compare the impact of the three inventory fulfillment methods on the BWE, we include these variables in our regression tests as follows:

Dependent variable(s): Lee's BWE, ORVrR, IVrR, Bullwhip Slope, Inventory Instability Slope, OOS and Average Inventory.

Explanatory variable: Inventory Fulfillment Method (variable of interest), which equals 0 if the method is Flowcasting, 1 if ROP, and 2 if ROP/DRP. For result robustness, we include operational factors as control variables, which also impact the benefits of information sharing (Domínguez et al. 2018a).

Variable Symbol/definition SC Complexity " ∑ •• O - - ' 4 ˜Oh ˜
with k being the number of tiers, ™ and ™ denoting the number of nodes in total and at tier T, respectively. This is the divergence factor proposed by [START_REF] Domínguez | The impact of the supply chain structure on bullwhip effect[END_REF]. Simulation Horizon 26 weeks (≈ 6 months), 38 weeks (≈ 9 months), 50 weeks (≈ 1 year).

Flowcasting MAPE

The mean absolute percentage error of Flowcasting [START_REF] Boone | The benefits of information sharing in a supply chain: an exploratory simulation study[END_REF].

Product Type* 0 = highly promoted item (Px); 1 = faster-moving/regular item (Rx); 2 = seasonal item (Zx); 3 = slow-moving item (Lx); 4 = new item (Nx).

Product Code* 1,2 = faster-moving/regular item; 3,4 = slow-moving item; 5,6 = highly promoted item; 7,8 = new item; 9,10 = seasonal item.

Location*

How the store/DDC/IDC is numbered in the firm's data (1-928). Tier 1 = Retail Outlet; 2 = Direct DC; 3 = Indirect DC.

Average Demand

The average of historical sales

Lead Time

The number of weeks from replenishment order placement to actual delivery (Cannella et al. 2017a;Domínguez et al. 2018a).

Order Lot Size

The replenishment order quantity must be a multiple of this amount.

Period of Coverage (POC)

The number of weeks whose demand must be covered by the replenishment order placed (PA's system).

Safety Stock

The inventory level to buffer uncertainty in demand [START_REF] Boone | The benefits of information sharing in a supply chain: an exploratory simulation study[END_REF], Cannella et al. 2017a). Note: *Categorical variables are often deployed in international business studies to control for the impact of firms, sectors and/or countries [START_REF] Gibson | The antecedents, consequences, and mediating role of organizational ambidexterity[END_REF][START_REF] Galan | Factors determining the location decisions of Spanish MNEs: an analysis based on the investment development path[END_REF][START_REF] Click | Resource nationalism meets the market: political risk and the value of petroleum reserves[END_REF].

TABLE 3: Control variables

As the retail networks in question epitomize high complexity, which likely impacts the efficacy of the systems under analysis [START_REF] Domínguez | The impact of the supply chain structure on bullwhip effect[END_REF]Cannella et al. 2017a), we have incorporated this control variable in line with the cited studies. However, we compute this factor at each tier, which is consistent with our tier-based model. Complexity at tier 1 equals zero. Furthermore, as Domínguez et al. (2018a, b) note that the simulation horizon may affect the simulated results, we run the models at different numbers of periods and include this indicator in the model as a control variable. According to [START_REF] Chen | How accurate are professional forecasts in Asia? Evidence from ten countries[END_REF] and [START_REF] Kunze | The usefulness of oil price forecasts: evidence from survey predictions[END_REF], accuracy declines as the forecast horizon extends.

To address the endogeneity issue, all control variables remain unchanged across Inventory Fulfillment Methods to create treatment and control groups that are the same by the beginning of the simulation (Antonakis et al. 2010;[START_REF] Kim | Environmental pressure and the performance of foreign firms in an emerging economy[END_REF]. Except for Flowcasting MAPE, which is randomly generated during the simulation for random sampling, other control factors are preset before the dependent variables are simulated to avoid reverse causality (Antonakis et al. 2010;[START_REF] Chang | A quasi-experimental approach to the multinationalityperformance relationship: an application to learning-by-exporting[END_REF]. These explanatory variables differ by product but stay constant across simulation iterations. Product Code is numbered in a different manner from Product Type to avoid multicollinearity. Location and Product Code are included to tackle endogeneity issues owing to location-specific or product-specific effects, but their coefficients are not presented in the results for concision purposes. Full results can be provided on request.

To avoid multicollinearity among independent numeric variables, we conducted a correlation test (TABLE 4). There is high correlation between Tier, Lead Time, Safety Stock, Order Lot Size, Average Demand and Complexity, which is as expected since one upstream actor handles many downstream nodes. As our regression is run by tier, much of the correlation with Tier can be avoided. We conducted the Variance Inflation Factor (VIF) test after each regression to see which control variables, especially categorical ones, should be excluded. If the VIF indicator of one variable is greater than 10, that factor should be dropped [START_REF] Marquardt | Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation[END_REF][START_REF] Hair | Multivariate data analysis: Pearson new international edition[END_REF].

(Observations =1098000) (1) (2) (3) (4) (5) (6) (7) (8)
(

Dependent Variable Aggregation

To ease interpretations, we conducted a factor analysis to ensure the three BWE measures are capturing the same thing to reduce regression numbers to be tested [START_REF] Rummel | Applied factor analysis[END_REF].

The Pairwise Correlations test showed a statistically significant correlation among all BWE measures in question. It is therefore possible for a factor analysis to capture the BWE through these indicators. To identify the number of factors fitted by the given variables, there are four common methods, namely eigenvalues [START_REF] Kaiser | The application of electronic computers to factor analysis[END_REF], factor rotation [START_REF] Rummel | Applied factor analysis[END_REF], scree plot [START_REF] Cattell | The scientific use of factor analysis in behavioral and life sciences[END_REF]) and maximum likelihood (ML) [START_REF] Tabachnick | Using multivariate statistics[END_REF].

With the eigenvalues method, the criterion is that factors with eigenvalues greater than 1 should be fit [START_REF] Kaiser | The application of electronic computers to factor analysis[END_REF]. Our test produces only one eigenvector with an acceptable eigenvalue (2.76314). With factor rotation at the 0.3 threshold, all variables also belong to one factor. The scree plot method proposes the eigenvectors before the last big drop, after which the eigenvalues become stable [START_REF] Cattell | The scientific use of factor analysis in behavioral and life sciences[END_REF]. The result suggests one factor, which is in line with the first two methods. The ML test also retains one factor. Hence, we can use the factor aggregated by Lee's BWE, ORVrR and IVrR to measure the BWE Magnitude for analysis.

Next, we build a scale for the BWE Magnitude on the non-weighted mean of Lee's BWE, ORVrR and IVrR. To test the scale's internal consistency, we conduct the Cronbach alpha test, and the result is 0.7427, which is greater than the 0.6 threshold considered adequate when only a few items are contained in the scale [START_REF] Dunn | From alpha to omega: a practical solution to the pervasive problem of internal consistency estimation[END_REF]). Thus, this scale is deemed consistent and acceptable. We also create a score for the BWE Magnitude based on the weighted average of Lee's BWE, ORVrR and IVrR. The correlation between the scale and the score is 0.9979, which is high, indicating the interchangeability between the scale and score. We use the scale as an independent variable for the regression, as it is easier to repeat.

Regression Result Summary

In schedules, we also emphasize the central role of retailers rather than vendors or distributors in improving the system's performance. Nonetheless, according to [START_REF] Ye | Drivers and barriers of omni-channel retailing in China: a case study of the fashion and apparel industry[END_REF], franchised outlets are less likely to buy into a new operational model unless they receive a fair share of the benefits. This is aligned with our interviews with PA, in that their ownership structure with solely company-owned outlets facilitates their implementation of Flowcasting, as franchisees are less likely to realize system-wide benefits of Flowcasting. Although we did not explicitly study franchising in the model, our quantitative analysis shows that the direct advantages of Flowcasting at the storefront are less statistically significant compared to those at upstream levels. Compared to company-owned stores, franchised outlets are less likely to receive the benefits redistributed from upstream partners. Thus, franchising retailers must ensure that these benefits are properly shared to incentivize their franchisees.

According to Almeida et al. (2015) and Domínguez et al. (2018a), information-sharing measures to cut the BWE require investment in trust and collaboration, for which the return is not readily apparent. PA's executive cited a learning curve of two to three years from planned implementation to tangible benefits. Therefore, as an information sharing method, Flowcasting should be adopted with foresight, diligence and mutuality [START_REF] Martin | Meeting the promise of flowcasting[END_REF]. With today's growing trend towards omnichannel retailing, i.e. integrating different retail channels so that customers can experience seamless cross-channel shopping [START_REF] Rigby | The future of shopping[END_REF][START_REF] Verhoef | From multi-channel retailing to omnichannel retailing: introduction to the special issue on multi-channel retailing[END_REF], end-user orders can be filled from multiple channels, nodes or tiers, which increases the complexity of information system management (Hübner et al. 2016a;Hübner et al. 2016b). The Flowcasting logic of assigning sales from different selling channels to the store closest to the customer and cascading this blended information upstream for SC operations planning can be an appropriate approach [START_REF] Doherty | Flowcasting: in-stock -whenever, wherever[END_REF]. However, more research is needed to investigate the combinability of these models.

Managers should also take measures to balance the service level against SC fluctuation.

Assuming unconstrained holding capacity, all the simulated nodes can accommodate an enormous BWE-triggered fluctuation in inventory or replenishment to meet the service level.

In real life, this assumption does not usually hold, and a sizeable order for certain periods may not be feasible. Order placement and delivery should therefore be scheduled thoroughly to avoid both OOS and excess inventory, which may incur higher handling and holding costs, as additional capacity may be needed. Such financial implications should be kept in mind to avoid over-optimism and ignorance of hidden costs.

The successful implementation of Flowcasting involved a significant focus on people and process. To facilitate buy-in, the implementation team spent considerable time educating employees on the thinking behind Flowcasting -specifically understanding consumer-centric planning and how the extended organization could work to a single set of numbers. They delivered process-and principles-based education to both employees, starting from the CEO level, and vendors [START_REF] Doherty | A digitally-connected, consumer-driven supply chain[END_REF]. In addition to this, technological advances undeniably facilitate Flowcasting implementation. For instance, increased digital connection allows real-time information flow and thus visibility within the entire SC for planning and recalibration [START_REF] Doherty | A digitally-connected, consumer-driven supply chain[END_REF]. Retailers can now access substantial volumes of product-location data, which can arrive at a high velocity from various sources and formats and reach the Big Data level [START_REF] Megahed | Statistical perspectives on "Big Data[END_REF]. Forecasting as well as the system can benefit from Big Data analytics (BDA) in several ways. First, short-term forecast can be refined based on the recently observed demand signals, e.g. weather, traffic and events [START_REF] Tiwari | Big data analytics in supply chain management between 2010 and 2016: Insights to industries[END_REF], enabling fulfillment adjustments in real time. Second, in addition to the forecasted demand, safety stock and lead time, two important parameters in the Flowcasting/DRP system, can also be adaptive based on analyzing causal factors through probabilistic predictive models [START_REF] Engeland | Probabilistic postprocessing models for flow forecasts for a system of catchments and several lead times[END_REF] with BDA [START_REF] Dinis | Valuing data in aircraft maintenance through big data analytics: A probabilistic approach for capacity planning using Bayesian networks[END_REF].

Third, PA has already benefited from the feedback mechanism where demand planners flag irregular demand with the labels indicating its most probable underlying causes. These labels are then used in the data cleansing process (outlier detection) prior to demand prediction. These types of information (indicators and labels of irregular demand) can be further leveraged in more complex predictive models which use advanced machine learning techniques to improve the quality of demand forecast and fulfillment plans. The growing literature in this area has discussed several algorithms and approaches to BDA, e.g. parallel computing [START_REF] Lau | Parallel aspect-oriented sentiment analysis for sales forecasting with Big Data[END_REF], cloud computing [START_REF] Neaga | Cloud enabled Big Data business platform for logistics services: a research and development agenda[END_REF] and other machine learning algorithms [START_REF] Nguyen | Big data analytics in supply chain management: a state-of-the-art literature review[END_REF][START_REF] Singh | Social media data analytics to improve supply chain management in food industries[END_REF].

In terms of limitations, we employed simulation for data generation, which means that the dataset may not fully reflect real-life decisions. For example, it is difficult to incorporate human behaviors into a simulation [START_REF] Evers | Systems analysis using simulation[END_REF]. Indeed, some orders may not follow the predefined logic when demand planners believe the actual demand will differ from the programmed forecast. In Mostard et al.'s study (2011), the expert-based forecasting methods surpass all of the algorithm-based ones considered. In PA, demand planners in charge of a product category can autonomously modify the forecast insofar as they believe it will better represent true demand. Exceptions due to promotional activities or abnormal sales, which deviate largely from normally recorded figures, are flagged automatically or manually by the demand planners and processed by software to achieve a clean sales history. Seasonal item sales that occur outside the season through markdowns or seasonal clearances are also excluded from the clean history. As expert adjustment for input data can improve forecast accuracy [START_REF] Käki | What to do when decision-makers deviate from model recommendations? Empirical evidence from hydropower industry[END_REF], the forecast made by PA's planners is likely more accurate, and real-life data analysis may have different results and expound inconclusive results in our simulation. After the frozen horizon, the demand recorded becomes data and changes the forecast result and replenishment schedule [START_REF] Dolgui | Supply planning under uncertainties in MRP environments: a state of the art[END_REF]. Nevertheless, in this simulation, we do not incorporate intra-frozen period adjustments. In addition, our paper analyzes operational benefits of Flowcasting without considering its financial implications, e.g. training, installation and maintenance. Yet, according to PA's consultant, the Flowcasting process and logic are simple and do not require the firm's partners to change their transactional systems. PA spent 60% to 70% of its time educating staff and partners on Flowcasting in small groups. The implementation team gave one example of spending months helping a demand planner overcome her anxiety and inertia. As with any other organizational change, the process started with feasibility analysis and staff education. The firm used spreadsheets to show staff how the process and system would work so that they could understand the process principles and system logic before learning how to execute the new business process and supporting software. The company and consultants stated that staff who received principles-based education were better prepared to learn and use the software system, which confirmed the effectiveness of their roll-out approach. PA's consultant added that the service level rose from 91.7% to around 98% while inventory investment decreased by 10% and that the firm was able to leverage the system for omnichannel retailing -by planning and delivering online demand from the nearest store. This confirmed that the payback surpassed the required costs and effort.

CONCLUSION

In this paper, we used the forecast demand of a Canadian hard goods retailer to simulate how ROP, ROP/DRP and Flowcasting would perform under uncertain demand. Our interview results and regression tests on the simulated datasets corroborate the hypotheses:

• Out-of-Stock: Flowcasting outperforms both ROP and ROP/DRP in reducing OOS.

• Bullwhip Effect: Since the BWE is manifested upstream from the SC, Flowcasting impact on BWE depletion against ROP and ROP/DRP is more noticeable in upper tiers, such as the IDC level.

• Average Inventory: With the amplified BWE at tiers 2 and 3, ROP and ROP/DRP simultaneously faces OOS and high average inventory compared to Flowcasting.

Our study confirms the value of sharing both retail sales and order schedules in reducing the BWE and emphasizes the central role of retailers rather than the role of vendors or distributors in this process. However, these downstream players may see fewer direct benefits than their upstream partners; the system-wide yields should therefore be shared properly to incentivize their engagement. It should be noted that our simulation may not fully reflect reallife Flowcasting efficacy against ROP and ROP/DRP, given the costs and benefits of the Flowcasting software and possible human intervention during implementation. However, we hope this paper's findings will further inform practices and research in SC integration through an implementation of SC-wide integrated DRP logic. .6892 -3.4224 -3.4102 -4.0347 -3.496 -3.4796 -3.5320

  STATA 15.1 to statistically test the efficacy of the three inventory fulfillment methods. This combined simulation-regression/statistics method has been adopted by several scholars in SCM. According to[START_REF] Kelton | Methodological expectations for studies using computer simulation[END_REF], "since most simulations are stochastic[…], the results are also stochastic"; thus, simulated datasets should be statistically analyzed to reach meaningful and valid conclusions.[START_REF] Ma | Study of the bullwhip effect under various forecasting methods in electronics supply chain with dual retailers considering market share[END_REF] use simulation to study the BWE under three forecasting methods in the electronics industry. Hayya et al. (2011) perform simulation based on three statistical distributions to derive regression between cost and measures of fluctuating demand and lead time. Likewise, Haughton (2008) deploys simulation to analyze the BWE on carriers at various levels of capacity flexibility, forecasting capability and replenishment policy. This same author also applies two-way ANOVA and sensitivity analysis to test the impact of the distortional BWE on carriers in different scenarios.

  stores' planned order releases become DDC demand estimates. DDC planned order releases then become IDC demand estimates. The planning follows the DRP logic. Next, the inventory flow spreadsheet simulates how this system tackles demand changes. Actual store requirements come from the simulated demand Z J] . Lower tiers' actual order releases in week t are upper tiers' actual requirements that week.Next, we use the simulation outputs from the three systems to assess the efficacy of the outputs based on Equation 1 to Equation 5. The lower the indices, the better the inventory fulfillment method considered in addressing the BWE, OOS and average inventory. When the forecast error changes, we have a different set of BWE and efficacy indices. To identify the optimal number of replications REP, we compute the margin of error and use the threshold of 10% of the mean suggested by[START_REF] Yang | Evaluation of robustness of supply chain information-sharing strategies using a hybrid Taguchi and multiple criteria decisionmaking method[END_REF] and cited byCannella et al. (2018c) andDomínguez et al. (2018a). Where the mean is zero, we useBurton et al.'s formula (2006) being the accuracy level we would like to target in the simulation. After a comparison of these two approaches, we select the bigger number (REP=2000) for all the simulations.

TABLE 1 )

 1 . PA's industry is characterized by slow-moving and/or heavy-weight items, which are expensive to ship to customers from a central DC or fulfillment center via e-commerce or omnichannel retailing [PA's Vice President (VP) of SC Planning], making stores the proper information consolidating point. This meshes with the Flowcasting logic. With the current large-scale implementation in 45 stores and 3 DCs as of 2017, PA is a good candidate for a case study on

	Flowcasting.
	2013 -2014: Phase 1	The 3-year learning curve: Phase 2	2017: Phase 3
	Initial considerations	Implementation	Full implementation
	+ First decision to	+ Educate the CEO, internal staff (IT, demand planners,	+ 15,000 items, 45 stores,
	implement	merchants, S&OP, etc.) and vendors, first using	3 DCs and 400 suppliers.
	Flowcasting.	spreadsheets and examples and then the Flowcasting	+ These projects came to a

  [START_REF] Roy | The implementation of flowcasting between CPGA and Sam's Club[END_REF] show that Flowcasting helped Sam's Club raise inventory turnover by 10%, thus cutting the average inventory. PA's VP of SC Planning said, "Our DC inventories are as lean as they've ever been. In-store inventories are down." The company's Senior VP of SC added, "This is a clear indication of the value of Flowcasting being able to forecast inventory at individual stores, which allows the inventory at each store to come down, particularly in the area of overstock and seasonal carryover." Thus, we hypothesize that, given the same safety stock level:

state that improved SC visibility helps prevent buffer buildups, thereby cutting inventory. According to

[START_REF] Boone | The value of information sharing in the retail supply chain: two case studies[END_REF]

and

Domínguez et al. (2018a)

, information sharing lowers the average inventory. Flowcasting directly links upper tiers to POS data rather than only to immediate client orders, as in ROP and ROP/DRP, which means that SC visibility in Flowcasting is not limited to 1st-tier partners, as in ROP, or upstream nodes, as in ROP/DRP. An initial Flowcasting version adopted at Giant Foods in the US contributed to inventory curtailing at this supermarket chain

[START_REF] Landry | Flowcasting : Une percée dans l'intégration de la chaîne logistique[END_REF]

.

H2a: Versus ROP, Flowcasting helps cut the average inventory level.

H2b: Versus ROP/DRP, Flowcasting helps cut the average inventory level.

As per the simulation studies by

[START_REF] Dejonckheere | Production, manufacturing and logistics: the impact of information enrichment on the bullwhip effect in supply chains: a control engineering perspective[END_REF]

and

[START_REF] Sandhu | Steel supply chain management by simulation modelling[END_REF]

, the BWE magnitude can be cut by information enrichment, which is more likely to occur with Flowcasting than with the other two methods, since store-level demand data is shared upstream. Furthermore, economic order quantity is often cited as a way to identify order quantity in ROP systems

[START_REF] Zhang | Kroger uses simulationoptimization to improve pharmacy inventory management[END_REF]

, which may lead to order batching, a cause of the BWE. Flowcasting, on the other hand, involves reordering as per the forecasted demand. This can prevent order batching and hence cut the BWE. Yet, there are five BWE measures given in the literature: Lee's BWE, ORVrR and IVrR measure the BWE magnitude at each node, while the Bullwhip Slope and Inventory Instability Slope quantify, on average, the BWE slope from retail outlets to the upper-tier echelon. The five indicators are possibly incompatible to be captured in a single hypothesis, so we presume Lee's BWE, ORVrR and IVrR are more likely to be combined into one single factor associated with the hypothesis group for the BWE Magnitude. According to PA's Senior VP of Customer Experience, the aggregate calculated demand is what the company plans to do in the DC. "The vendors took a little while to adapt to the schedule, and that gave PA time to build more stability into the planning process that produces the vendor schedule," said the implementation team leader.

  , we assume the BWE Magnitude in Flowcasting plummets in upper tiers, as these tiers make no forecast. It then becomes difficult to compare Flowcasting with ROP, because no echelon in the latter case

makes use of demand forecast. In ROP/DRP, the only upstream nodes that forecast are the DC that directly supply stores. Nonetheless, as in

Domínguez et al. (2018a)

, information enrichment, as in Flowcasting in our study, can help upper tiers in this system surpass their counterparts in the other two. As the slopes are measured from tier 2 upwards, we hypothesize under our assumption: H4a: Versus ROP, Flowcasting helps cut the Bullwhip Slope at tiers 2 & 3. H4b: Versus ROP/DRP, Flowcasting helps cut the Bullwhip Slope at tiers 2 & 3. H5a: Versus ROP, Flowcasting helps cut the Inventory Instability Slope at tiers 2 & 3. H5b: Versus ROP/DRP, Flowcasting helps cut the Inventory Instability Slope at tiers 2-3. Note that Cannella et al. add that the impact of information sharing on stockout, ORVrR and IVrR (2015), average inventory, Bullwhip Slope and Inventory Instability Slope (2017a, 2018b) are subject to the accuracy and/or timeliness of the information shared. In our paper,

  al. 2017a). As perDomínguez et al.'s formula (2015) (see TABLE3), our network has a divergence factor of 5.29, which exceeds the index for the high-complexity SC inCannella et al.'s (2017a) simulation-based study. To avoid increasing staff nervousness, PA postponed measuring forecast errors until recently. We therefore had to randomize this figure using the uniform distribution as perCannella et al.'s simulations (2017aCannella et al.'s simulations ( , 2018b) ) and

TABLE 2 : Methods for demand estimates and inventory control of the three systems

 2

  Since PA has not implemented ROP/DRP but instead decided to implement the fully integrated Flowcasting process, we did not have its DDC forecast and therefore developed

	two ROP/DRP configurations. In Configuration 1, DDC planners forecast store
	replenishment as per sales history. In PA's data, we observed seasonality and sometimes
	trend in the DDC demand. Per Petropoulos et al.'s review (2014), the Holt-Winters (H-W)
	and Decomposition methods are the most suitable for such cases. MAPE, which is a common
	indicator of forecast error, cannot be optimized, as it is measured out of sample (de
	Myttenaere et al. 2016

TABLE 4 : Correlation among independent numeric variables

 4

TABLE 5 ,

 5 ROP correlates positively with OOS, and this correlation is significant across Denotes the statistical significance of the variable at the 1% level. No VIF is greater than 10.

	Order Lot Size	because of	because of	because of	because of
	Safety Stock	collinearity)	collinearity)	collinearity)	collinearity)
	Average Demand
	POC
	SC Complexity
	Horizon	-0.0411* 0.000	0.0053* 0.000	0.0100* 0.000	-0.0001 0.720
	Cons	1.3195* 0.000	-0.6791* 0.000	-4.5458* 0.000	0.0072 0.265
	*

ACKNOWLEDGEMENTS

We would like to take this opportunity to thank PA's executives and staff and especially Mike Doherty, PA's consultant for their invaluable insights into our research topic. We also want to thank the Deputy Editor and peer reviewers for their insightful feedback and our colleagues for their proofreading to enhance the professional quality and contribution of our paper. This research was partially funded by the Canadian Natural Sciences and Engineering Research Council [Grant 2016-05822]. This support is gratefully acknowledged. REFERENCE LIST Almeida, M., Marins, F., Salgado, A., Santos, F., and Silva, S. 2015. "Mitigation of the bullwhip effect considering trust and collaboration in supply chain management: a literature review." International Journal of Advanced Manufacturing Technology 77 (1-4): 495-513. Antonakis, J., Bendahan, S., Jacquart, P., and Lalive, R. 2010. "On making causal claims: a

APPENDIX

Product

Code

Tier

tiers. This denotes that, compared to Flowcasting, ROP raises OOS at all tiers. In other words, Flowcasting reduces OOS compared to ROP regardless of the tier. This lends support to H1a, as better SC visibility in Flowcasting helps avoid OOS arising from unexpectedly high demand. At tiers 1 and 2, Flowcasting also outperforms ROP/DRP in cutting OOS, which concurs with Wang et al. (2016) that sharing information on both order schedules and retail sales is more effective in improving than sharing POS data alone. Yet, this comparison is not significant at tier 3. The possible reason is that the DRP logic applied at tiers 2 and 3 in ROP/DRP may deplete OOS. This supports H1b at tiers 1 and 2 and, indirectly, the DRP logic.

TABLE 5: Regressions of OOS at each tier

The control variables included and retained are significant but do not override the impact of Inventory Fulfillment Method. As regards Horizon, its length raises OOS as an expected result of decreased forecast accuracy and less relevant historical data, but this does not impact the significance of Inventory Fulfillment Method. Separate regressions (TABLE 11) show that Flowcasting overperformance relative to ROP and ROP/DRP even goes up as Horizon rises.

Regarding TABLE 6, H2a and H2b are rejected at tier 1 as both ROP and ROP/DRP cuts inventory compared to Flowcasting. This can be explained by the generally positive correlation between the service level and the inventory level [START_REF] Jeffery | Determining a cost-effective customer service level[END_REF][START_REF] Salam | Retail supply chain service levels: the role of inventory storage[END_REF]. With less OOS, signifying a higher service level, Flowcasting tends to have more onhand inventory. This disparity between Flowcasting and the other methods remains significant across horizons, although the magnitude drops as Horizon expands (TABLE 11).

At tier 2, ROP has less inventory, while ROP/DRP incurs more inventory than Flowcasting; however, when Horizon hits 50 weeks, Flowcasting outperforms both ROP and ROP/DRP (TABLE 11). Likewise, Flowcasting has progressively lower inventory than ROP and ROP/DRP at tier 3 as Horizon increases (TABLE 11). Note that, at tiers 2 and 3, ROP and ROP/DRP have generally more inventory while experiencing more OOS. This is possibly a sign of the BWE accumulated in upper tiers over time due to disconnected information and low visibility of downstream nodes (Lee et al. 1997a). Overall, H2a and H2b are partially supported at tiers 2 and 3. Regarding the Inventory Instability Slope, at tier 2, ROP and ROP/DRP are more effective than Flowcasting. The ROP and ROP/DRP) order quantity Q=nq from tier 1 to tier 2 may explain this lower slope. Calculated as per the long-term historical average demand, Q (or n) is fixed across orders at a node, which means there are fewer huge inventory fluctuations, whereas Flowcasting order quantities vary by forecast. Yet, at tier 3, ROP and ROP/DRP raise the Inventory Instability Slope compared to Flowcasting, which is a sign of a rising BWE in upper tiers (Lee et al. 1997a). While ROP has fixed Q (or n), ROP/DRP and Flowcasting both have Q (or n) varying by forecast from tier 2 to tier 3. The result shows that Flowcasting benefits are robust against the variability of Q (or n) at tier 3. H5a and b are therefore confuted at tier 2, but they are both attested at tier 3. Slope, ROP/DRP pushes these indicators higher compared to ROP at tiers 2 and 3.

Robustness Tests

The above regressions are built on the demand dataset generated uniformly with a 25% MAPE. In other words, the simulated demand is uniformly dispersed from the forecast with a 28.87% σ in percentage terms. Although we had already included the MAPE as a control variable, to guarantee the result robustness, we reran the simulation with the demand based on forecast errors under normal distribution (as in Cannella et al. 2018a, c), where the mean is PA's forecast and the σ is the mean times 28.87% to be consistent with the tests under uniform distribution. This is consistent with Evers and Wan's advice ( 2012) that multiple distributions should be considered. Overall, the new store-level MAPE of forecast in Flowcasting is 23%. The summary of the robustness test results is presented below.

Hypothesis

First Test Result Robustness/Consistency H1a: impact on OOS versus ROP Supported at all tiers.

Stably supported at all tiers. H1b: impact on OOS versus ROP/DRP Supported at tiers 1 and 2;

Inconclusive at tier 3.

Stably supported at tiers 1 and 2.

Not statistically stable at tier 3.

H2a: impact on Average Inventory versus ROP Rejected at tier 1; Partially supported at tier 2;

Fully supported at 3.

Stable results: Rejected at tier 1; Partially supported at tier 2; Fully supported at 3. H2b: impact on Average Inventory versus ROP/DRP Rejected at tier 1; Partially supported at tiers 2 and 3.

Stable results: Rejected at tier 1; Partially supported at tiers 2 and 3. H3a: impact on Bullwhip Effect Magnitude versus ROP Inconclusive at tier 1; Rejected at tier 2;

Stable results: Inconclusive at tier 1; Rejected at tier 2;

Fully supported at tier 3. Fully supported at tier 3.

H3b: impact on Bullwhip Effect Magnitude versus ROP/DRP Inconclusive at tier 1; Fully supported at tiers 2 and 3. Inconclusive at tier 1; Fully supported at tier 2; But partially supported at tier 3. H4a: impact on Bullwhip Slope versus ROP Fully supported at tiers 2 and 3. Stable results: Fully supported at tiers 2 and 3. H4b: impact on Bullwhip Slope versus ROP/DRP Fully supported at tiers 2 and 3. Stable results: Fully supported at tiers 2 and 3. H5a: impact on Inventory Instability Slope versus ROP Rejected at tier 2; Fully supported at tier 3.

Stable results: Rejected at tier 2;

Fully supported at tier 3. H5b: impact on Inventory Instability Slope versus ROP/DRP Rejected at tier 2; Fully supported at tier 3.

Stable results: Rejected at tier 2;

Fully supported at tier 3.

DISCUSSION AND MANAGERIAL IMPLICATIONS

We have quantitatively demonstrated the benefits of Flowcasting perceived by PA (as stated in the hypotheses). With the hypotheses mostly supported at tier 3, retailers can use this insight to convince their suppliers to adopt Flowcasting, a system more likely to benefit suppliers since decreased fluctuation helps them avoid unnecessary nervousness and costly adjustments [START_REF] Dolgui | Supply planning under uncertainties in MRP environments: a state of the art[END_REF], such as expedited shipments. In addition to reduced average inventory and thus holding costs, replenishment schedules sent in advance and automatically cascaded upstream in the system may augment planning efficacy to reduce ordering and handling costs, as demonstrated by [START_REF] Boone | The value of information sharing in the retail supply chain: two case studies[END_REF].

In addition to confirming the importance of information sharing, especially replenishment