Vendor-managed inventory in fresh-food supply chains
Post, Roel
DOI:
10.33612/diss.130028783
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Post, R. (2020). Vendor-managed inventory in fresh-food supply chains. University of Groningen, SOM research school. https://doi.org/10.33612/diss.130028783
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The performance effects of
retailer driven Vendor-Managed
Inventory with Consignment
Abstract. In retail supply chains, either the supplier or the retailer can hold control and
own-ership of inventory. Multiple studies have shown how vendor-managed inventory (VMI), where control of inventory is transferred to the supplier, can lead to lower inventories and higher demand fulfillment. Earlier work on this phenomenon has been dominated by studies of large suppliers that have taken control of their retailers’ inventory, which we call supplier-driven VMI. In practice, there are also many VMI initiatives supplier-driven by a large retailer. The setup of retailer-driven VMI is usually very different and often involves a transfer of both control and ownership of inventory to suppliers. Retailer-driven VMI affects suppliers’ in-centives and decision latitude to determine inventory levels and the resulting demand ful-fillment performance in the supply chain. This chapter describes a study of a retailer-driven VMI initiative. Using unique transaction data that allow observation of inventory levels in the entire supply chain, we show how retailer-driven VMI leads to performance outcomes that differ from what is known from studies of supplier-driven VMI. Suppliers in our empirical context focus strongly on improving product availability and on efficient use of their produc-tion and transportaproduc-tion resources. This leads to a remarkable improvement of the retailer’s demand fulfillment, albeit at the expense of an increase in inventory.
2.1
Introduction
Strategic decisions to allocate the control and ownership of inventory across actors in the supply chain have been a main topic in the management science literature for two decades (e.g. Cachon, 2004; Davis et al., 2014; ¨Ozer et al., 2017). In traditional retail supply chains, control and ownership of inventory are usually allocated to the retailer, this is known as retailer-managed inventory (RMI). In RMI, the retailer makes the inventory management decisions and owns the inventory, incurring both the holding costs and the costs of any unsold products. Today, control of inventory is often transferred to suppliers as part of vendor-managed inventory (VMI) initia-tives. In VMI, the supplier of goods is responsible for ensuring sufficient inventory at the retailer’s stock point. In many cases, VMI also includes a transfer of inventory ownership in the form of consignment inventory (CI), where the suppliers own the inventory at the retailer’s stock point (Wang et al., 2004).
Over the last decades, VMI and consignment inventory have become very pop-ular in practice due to advances in information technology (Bichescu and Fry, 2009). One of the first reported VMI implementations was a joint initiative of Wall-mart and Proctor Gamble (Waller et al., 1999). Interestingly, later VMI initiatives have both been driven by large suppliers and retailers, meaning both supplier’s and re-tailer’s see opportunities in VMI for their organizations. Campbell Soup and Barilla are well known examples of large suppliers that implemented VMI for its retail out-lets (Clark and Hammond, 1997; Cachon and Fisher, 1997; Lee et al., 1999), while large retailers such a K-mart and Home Depot have initiated VMI for their suppliers (Dong et al., 2014).
Insights into the supply chain performance impact of VMI initiatives mostly stem from analytical modelling studies (Cetinkaya and Lee, 2000; Ketzenberg and Fergu-son, 2008; Ru et al., 2018), with only a few studies using empirical data to validate the expected VMI performance effects. The outcomes of those empirical studies unan-imously show that VMI is associated with lower inventory levels at the retailer’s stock point, while demand fulfillment remains similar or even improves (Clark and Hammond, 1997; Dong et al., 2014; Lee et al., 1999). We note that these studies all consider a large supplier, which drove the VMI initiative for its retail outlets. More-over, the VMI initiatives studied involved only a transfer of inventory control from the retailers to the supplier, but not a transfer of inventory ownership. To our
knowl-edge, no studies have empirically measured the supply chain performance effects when a retailer drives a VMI implementation. On the basis of currently available empirical studies on supplier-driven VMI, one may expect that retailer-driven VMI will also lead mainly to lower inventory levels. However, a number of important contrasts between supplier-driven and retailer-driven VMI may result in different performance outcomes.
The motivation for the arrangements of a VMI initiative can differ markedly, de-pending on whether the supplier or the retailer drives the initiative. In supplier-driven VMI initiatives, the supplier takes control of the inventory of some or all of the retailers in its supply network. The motivation for doing so is to lower inventory and optimize production and distribution processes. A supplier that drives a VMI initiative has little incentive to take over the ownership of inventory at its retailers’ stock points. Therefore, it is not surprising that, for instance, Campbell only took over the control of inventory, not the ownership of inventory (Clark and Hammond, 1997; Lee et al., 1999). When a large retailer drives the VMI initiative, however, the retailer has an incentive to also transfer ownership of inventory to the supplier (Bich-escu and Fry 2009). Indeed, the resulting decrease in inventory costs could form a main motivation for the retailer. The costs and risks of owning inventory affect sup-pliers’ incentives to choose an inventory level for the supply chain (Cachon, 2004; Kremer and Van Wassenhove, 2014) and also makes the suppliers less dependent on the retailer in their inventory management decisions, as the retailer is less likely to impose restrictions on inventory (Fry et al., 2001). This condition could motivate a supplier to make a different trade-off between demand fulfillment and inventory levels than in a situation where a VMI initiative would be supplier-driven.
In this chapter, we evaluate how retailer-driven VMI affects supply chain inven-tory levels and demand fulfilment. Specifically, we use unique, longitudinal trans-action data together with interviews, surveys, and observations of a VMI initiative driven by a large European grocery retailer transferring inventory control and own-ership to all its fresh food suppliers. Understanding how such a transfer affects the performance of a supply chain requires measuring stockouts and supply chain inventory levels. Owing to limitations in data availability (Ho et al., 2017), the in-ventory measures used in most empirical operations management studies capture the inventory levels in only part of the supply chain. In empirical studies on VMI, data about inventory at the supplier’s facility and in-transit inventories has so far
re-mained out of scope (Clark and Hammond, 1997; Dong et al., 2014; Lee et al., 1999), even though the focus of VMI has always been on supply chain improvement. In order to extend focus to inventory in the entire supply chain, we present and ap-ply a novel inventory measure capturing the number of days a product has been in inventory in the supply chain.
The findings from our study suggest that retailer-driven VMI indeed leads to supply chain performance outcomes that differ from the supplier-driven VMI initia-tives reported in the literature. Most notably, while prior studies strongly focused on inventory reduction, we observe that suppliers tend to increase supply chain in-ventory to realize still greater demand fulfilment while also enabling a better uti-lization of their production and logistics resources. The findings seem to somewhat contradict prior empirical studies, but can be explained well if we take differences between supplier- and retailer-driven context into account. In the retailer-driven context, suppliers are on average smaller and less powerful organizations compared to a supplier-driven situation. These smaller suppliers do not necessary feature large networks of buyers and advanced planning abilities. Our results suggest that these suppliers use the decision latitude provide in a way that differs from prior work that focused on inventory reduction. However, the findings are in line with analyt-ical studies that study contracts of VMI with consignment inventory (Cachon, 2004; Bernstein et al., 2006) from a financial incentive perspective. Our study thus empha-sizes the importance of considering the supply chain context when studying VMI (Kulp, 2002; De Toni and Zamolo, 2005).
2.2
Background
Multiple research streams in the operations management literature have provided insights into how the allocation of inventory ownership and control can affect sup-ply chain performance. In recent decades, these discussions have focused on how these strategic decisions serve to reduce inventory in the supply chain. This focus is logical, given the generally positive relation between inventory reduction and finan-cial performance (Chen et al., 2005, 2007). A limit exists, of course, on the extent to which inventory can be reduced. Below a certain inventory level, increased stock-outs start to hurt financial performance more than excess inventory would (Lee et al., 1999). Because of the long-term emphasis on supply chain inventory reduction, in
many cases this limit may have already been reached (Eroglu and Hofer, 2011). The results from analytical studies suggest that transferring control of inven-tory to a supplier has two types of advantages. First, considering a single sup-plier–retailer dyad, control of inventory allows the supplier to synchronize its pro-duction and transportation processes with customer demand (Chaouch, 2001; Hol-weg et al., 2005). Therefore, suppliers can ship the goods directly after production and use a single stock position closer to the demand (Ketzenberg and Ferguson, 2008), enabling a faster response to sudden changes in demand. Second, control of inventory offers a supplier flexibility when supplying products to multiple buyers (Fry et al., 2001). The supplier can prioritize production and shipments so that the buyer with the lowest inventory level is served first, or it can hold shipments until economic quantities are reached (Cetinkaya and Lee, 2000; Cheung and Lee, 2002). This so-called uncertainty pooling effect can reduce the overall demand variability for the supplier and therefore reduce its need to hold safety stock. Also, the supplier can realize higher transportation cycle times at lower costs by combining shipments to multiple buyers (Cheung and Lee, 2002).
According to analytical studies, transferring not only control but also ownership from the retailer to the supplier brings a third theoretical advantage. Many VMI initiatives in practice are accompanied by a transfer of inventory ownership (Wang et al., 2004), Consignment Inventory (CI). Transfer of inventory ownership means that the retailer takes ownership of the products only when the products are shipped to their store or the end customer, a concept also called scan-based trading (Choi et al., 2019). By transferring control of ownership, the supplier gains full control and ownership over its production, transport, and inventory management processes while the retailer can reduce its holding costs. The transfer of ownership enables a situation in which the supplier controls the entire replenishment process and incurs all financial consequences of these decisions (Bernstein et al., 2006; Cachon, 2004).
When introducing VMI in a supply chain in practice, the incentives for the sup-plier or retailer to enter the VMI agreements influence how VMI will affect the per-formance of the supply chain (Fry et al., 2001). Moreover, the division of power be-tween supplier and retailer influence the contractual terms of a VMI introduction in terms of ownership and possible inventory limits and performance targets (Bichescu and Fry, 2009). Supplier-driven VMI initiatives are mainly motivated by the desire to take advantage of the flexibility that serving multiple retail outlets provides.
Fur-thermore, when the supplier takes the initiative to introduce VMI, that supplier will often be the larger and more advanced organization in the supply chain, and is thus in a better position than the retailer to leverage the point-of-sale (POS) data (Dong et al., 2014). In addition, in situations with a more powerful supplier, the supplier is not likely to take over ownership of the inventory, which implies that the retailer retains ownership of the inventories that are controlled by the supplier (Clark and Hammond, 1997; Lee et al., 1999; Dong et al., 2014). Therefore, contractual or rela-tional governance should guarantee that the retailer is not paying for inventory that is pushed by the supplier. This assurance can be achieved either through limits on the inventory levels (Fry et al., 2001) or through relational or contractual agreements under which the supplier and retailer jointly monitor inventory levels, also called co-managed inventory (Blatherwick, 1998). In their empirical analysis of transaction data of VMI implementations driven by large suppliers, Clark and Hammond (1997), Lee et al. (1999) and Dong et al. (2014) unanimously show that VMI introduction is associated with lower inventory levels at the retailer’s stock point, with similar or even higher demand fulfillment.
Retailer-driven VMI initiatives are aimed at placing suppliers in charge of opti-mizing the entire replenishment process, enabling the retailer to focus on sales and store operations. In addition, retailers that initiate VMI are usually powerful, relative to their suppliers (Bichescu and Fry, 2009). For these reasons, retailer-driven VMI of-ten involves consignment inventory (Wang et al., 2004). Prior analytical studies on VMI provide three reasons why the impact of retailer-driven VMI implementations may differ from supplier-driven VMI implementation. First, in VMI with CI, the sup-plier incurs all inventory costs in the supply chain, which could be an incentive for the supplier to lower inventory. This is particularly the case if the supplier ends up paying more inventory holding costs after VMI introduction, which partly depends on the difference between holding costs at the supplier and retailer’s warehouse (Ru et al., 2018). On the other hand, a supplier could be expected to increase inven-tory in the presence of brand competition between the VMI suppliers of a retailer, as stockouts from one supplier can lead to substitution with a competing supplier’s products (Mishra and Raghunathan, 2004). Moreover, competition between suppli-ers could be stronger in cases where the retailer introduces VMI to all its supplisuppli-ers than in cases in which a powerful supplier takes the initiative for VMI.
knowledge-able organization, which means that the advantage of transferring control to the or-ganization with the largest information-processing capability in the supply chain, that often motivates supplier-driven VMI implementation (Kulp, 2002), does not ap-ply. To overcome this disadvantage, the retailer can support its suppliers by sharing not only POS data but also forecasts or demand outlooks (Fry et al., 2001).
Third, in supplier-driven VMI, emphasis is usually on the supplier’s ability to use its network of multiple buyers to pool deliveries and inventory decisions, which favors keeping inventory at the supplier’s stock point (Cetinkaya and Lee, 2000) and thus leads to lower inventories at the retailer’s stock point (Dong et al., 2014). How-ever, when the supplier is not able to use its network in this way, the other potential advantages of VMI that are related to one-on-one synchronization between supplier and retailer are more relevant to this supplier (Ketzenberg and Ferguson, 2008). An example of this is increased synchronization of production and transportation with a specific VMI retailer, which may remove the need for inventory at the supplier’s location completely (Ketzenberg and Ferguson, 2008).
Thus, the incentives for suppliers and the advantages of optimizing their sup-ply chain network can differ markedly in retailer-driven VMI compared to supplier-driven VMI, which could favor a different trade-off over the supply chain perfor-mance measures. This study seeks to address the empirical gap in the literature by measuring the supply chain performance effects of a retailer-driven VMI introduc-tion.
2.3
Research context
The setting for this research is the fresh food supply chain of a grocery retailer in The Netherlands. The retailer is part of a leading supermarket chain in Europe with more
than a 1,000 grocery stores and overe10 billion in sales in The Netherlands alone.
The suppliers included in this study range from small businesses (30 employees) to large multinationals (over 20,000 employees). All suppliers deliver to the retailer’s central warehouse for fresh products, from which the retailer replenishes its grocery stores (Figure 2.1). Stockouts and inventories in the supply chain are low compared to industry benchmarks (Chen et al., 2005, 2007), indicating that the supply chain under study is modern and highly optimized.
Supplier - Production - Supplier inventory
Central Warehouse Retailer - Retailer inventory - Order picking
Stores
RMI: Order + forecasts
VMI: Inventory + Aggregated Demand + forecast Shipment Shipment Aggregated Demand Supplier Supplier Retailer RMI: VMI: Processes and information: Allocation of control and ownership: Performance
measures: Stock-out levelsSupply chain inventory
Retailer Retailer
Figure 2.1: Research setting and performance measures.
of inventory to all fresh food suppliers that deliver to the central warehouse. The use of VMI became a prerequisite for supplying to this retailer, although it should be noted that none of the suppliers ended their relation with the retailer for this reason. Therefore, self-selection bias with respect to the inclusion of suppliers, a factor often limiting empirical operations management studies (Ho et al., 2017), is not really an issue in our study. Moreover, all suppliers replenish the retailer’s central warehouse under the same conditions with respect to information availability and contracts. Even though this limits the external validity of our findings (as it considers one specific retailer context), it greatly improves internal validity (by allowing us to observe if the effect of VMI introduction is consistent across suppliers).
Before the introduction of VMI, all suppliers received replenishment orders from the retailer at pre-agreed times. The orders specified the exact quantity and time for each replenishment and were based on a central automatic ordering system (Kok and Fisher, 2007) according to common practice of retailers (van Donselaar et al., 2010). Similar to many modern fast-moving consumer goods supply chains, the retailer kept low inventories and required suppliers to deliver within short lead times, often within 24 hours. To this end, rolling forecasts of the expected warehouse demand for each of the following 21 days were shared daily with all suppliers. The retailer became owner of the products directly upon delivery by the suppliers at the retailer’s warehouse.
Under RMI, stockouts towards the stores were affected by both the supplier’s ability to deliver the ordered quantities in time and the retailer’s safety-stock
deci-sions for inventory in its central warehouse. The retailer communicated a service level target of 98.4% for suppliers via contracts, albeit no direct penalties were in place to enforce them. Rather, service level performance was discussed in periodic meetings, which is in line with the retailer’s aim to develop long-term partnership with their supplier base. Furthermore, account managers of the retailer emphasized that a supplier’s ability to meet a certain service level was strongly dependent on the characteristics of products and complexity of a supplier’s supply chain processes. For example, they realized that a 95% service level could already be too costly for highly perishable, slow-moving products, while for non-perishable slow-moving products service levels close to 100% can be realized at low inventory costs. Sim-ilar considerations were taken into account for the retailer’s inventory decisions in the central warehouse. The logic of the central automatic ordering system was devel-oped internally and contained many exceptions with regard to, for example, shelf life and demand volumes. In addition, supply chain planners at the retailer evaluated about 10% of all automatically generated orders to take additional product specific factors into account.
Since the introduction of VMI, suppliers no longer receive orders, but are them-selves responsible for decisions on the quantities and timing of the replenishments. The service level targets communicated to suppliers, and the retailer’s means of en-forcement remained the same as under RMI. Suppliers deliver their products to a new warehouse located close to the former warehouse. They remain owner of the products and incur a holding costs until the products are picked up to be shipped to the grocery stores. Suppliers can choose which information package they want to receive from the retailer, which is shared via a web portal and through an Electronic Data Interchange (EDI) linkage. At minimum, a supplier receives live insight into the inventory levels at the retailer’s central warehouse, daily accumulated store orders, twice daily store-demand forecast updates, and confirmations of product receipts and returns (in case of quality issues). At the supplier’s request, this information package can be extended with four additional daily forecast updates and POS data of all individual grocery stores. During the introduction phase, the retailer shared knowledge of the supply chain and inventory control in documentation and project meetings with the suppliers.
2.4
Data
For this study, we mainly rely on statistical techniques for analyzing transaction data. Insights from these analyses are extensively corroborated by conducting interviews and observations at both the retailer and its fresh food suppliers, and by studying archival data of the retailer. The retailer provided transaction data, enabled frequent interaction with project managers of the VMI initiative, operations managers, and the supply chain director, and assisted in gaining access to the suppliers. The first author was embedded in the retailer’s strategic supply chain department during the transition to VMI for the sole purpose of studying this transition.
In order to measure the supply chain inventory and stockout performance effects of VMI, we obtained transaction data of all products related to the VMI introduc-tion from at least one year before and at least one year after the transiintroduc-tion to VMI. The data was registered on an item-week level: the accumulated volume of store orders, accumulated actual volume supplied to the stores, average shelf life upon production, and average remaining shelf life of the products at the moment they were shipped to the grocery stores.
To mitigate the potential impact of data errors, and to obtain more balanced data before and after VMI introduction, we applied several data cleaning steps. We re-moved item-week observations with infeasible values, such as higher than 100% order completeness or negative inventories, which led to the removal of 1,593 item-week observations. Second, we excluded suppliers that did not occur in both the VMI and the RMI data sets, which resulted in the removal of 7,732 item-week ob-servations related to 17 suppliers. The resulting data set for analysis contains 70,343 item-week observations concerning 1,119 products of 63 suppliers. More summary statistics are provided in Tables 2.1 and 2.2. In our choices for measures and mod-els, which we will explain in detail below, we take into account that despite these cleaning efforts our data will not be completely free of errors.
Moreover, we collected additional qualitative data to corroborate our insights from analyzing the transition data. Specifically, we studied various archival docu-ments (480 pages in total) related to the VMI initiative, such as requiredocu-ments, testing procedures, and instruction presentation slides. To include the suppliers’ perspec-tives, we interviewed 10 suppliers to learn about how the transition to VMI had affected their planning, production, and transportation processes, as well as their
or-Table 2.1: Summary statistics pre-VMI introduction for supply chain inventory (INV), stockouts (SO), shelve live (SHELF), volume (VOLUME), demand variance (VAR), retailer promotions (PROMO) and stockout levels (SL).
Statistic N Mean St. Dev. Min Max
INV 25,795 4.141 7.013 0.001 99.900 SO 25,795 1.290 2.032 0.000 11.095 SHELF 25,795 22.820 25.359 3 200 VOLUME 25,795 0.917 0.276 0 1 VAR 25,795 10.309 3.538 −1.204 22.121 PROMO 25,795 0.050 0.218 0 1 SL 25,795 0.028 0.072 0.000 0.499
Table 2.2: Summary statistics post-VMI introduction for supply chain inventory (INV), stockouts (SO), shelve live (SHELF), volume (VOLUME), demand variance (VAR), retailer promotions (PROMO) and stockout levels (SL).
Statistic N Mean St. Dev. Min Max
INV 45,124 5.357 6.497 0.00001 95.908 SO 45,124 1.126 2.126 0.000 10.897 SHELF 45,124 24.944 24.913 3 200 VOLUME 45,124 0.885 0.319 0 1 VAR 45,124 10.819 3.676 −1.204 23.063 PROMO 44,124 0.078 0.269 0.000 1.000 SL 45,124 0.023 0.064 0.000 0.499
ganization as a whole. In total, we collected 18 hours of interview material. Drawing on insights from these interviews, we sent a survey to all suppliers involved in the VMI initiative (response rate 78%), in which we asked them to report on how VMI introduction affected their organization and processes on a 5-point scale, where 1 represents very negative impact and 5 very positive impact. This survey question-naire is included in Appendix A.
2.5
Measures
Supply chain performance is measured in two dependent variables that both reflect the performance measured at the moment products are shipped from the retailer’ central warehouse (henceforth referred to as warehouse) to the retailer’s stores: sup-ply chain inventory and stockouts. We use i to index products and t to index weeks. Each product can only be supplied by a single supplier.
2.5.1
Dependent variables: supply chain performance measures
We measure supply chain inventory by capturing the days of supply chain inventory(INVit), i.e., the number of days a product spent between production and pickup
from the warehouse. To measure INVitat a supply chain level, we rely on the
shelf-life registration of products. The moment a product is shipped to the grocery stores, the retailer registers the remaining shelf life. For example, a product with ten days shelf life from the moment of production is shipped to the store with five days re-maining shelf life under RMI, but four days rere-maining shelf life under VMI, has an increase of supply chain inventory of one day. The difference between the remaining shelf life and the total shelf life of the product upon production is a very good proxy for the days of inventory in the supply chain. Most importantly, by observing the change in this variable we can access the effect of VMI on the total available inven-tory in the supply chain, regardless of whether that inveninven-tory was at the supplier’s stock point, in transit, or at the retailer’s stock point, assuming transportation lead times and sales behavior of possible other buyers of the supplier remain the same before and after the transition to VMI. Using this inventory measure, our results can be compared to prior studies (Cachon and Olivares, 2010; Chen et al., 2007) and can be transformed to other inventory measures.
We define stockouts (SOit) as the difference between (1) total demand that was
ordered by stores from the warehouse and (2) the demand that was that was ful-filled. We thus use stockouts, as measured by the retailer, as a proxy for customer demand fulfillment. The retailer’s grocery stores place their order once every day. The orders are delivered at the stores the next day provided the products are avail-able in the warehouse. Backorders are not used. The retailer registers stockouts in an automated way to monitor the effect of product availability in the warehouse on the fulfillment of total store demand. To ensure that only this effect is measured, the retailer manually corrects the stockout values in case other reasons than insufficient inventory from the supplier caused store orders to be unfulfilled, such as material
handling errors or IT malfunctions. Both SOitand INVitare log transformed to
re-duce potential impact of data errors and large outliers, which is consistent with prior work (Cachon and Olivares, 2010).
Because Supply chain inventory and stockouts form a trade-off, where an in-crease in inventory is likely associated with lower stockouts and vice versa (Clark
and Hammond, 1997), we expect the two dependent measures to be correlated. However, since our supply chain inventory captures all inventory in the supply chain, the trade-off is more nuanced than in single echelon cases that are most com-mon in the literature. The supply chain inventory does not only capture inventory in the retailer warehouse inventory that directly affects the stockouts, but also inven-tory in transit and at the suppliers facility, which is not directly affecting stockouts. A Spearman’s correlation of -0.25 between stockouts and supply chain inventory confirms that the measures are indeed negatively correlated, but not very strongly.
2.5.2
Independent variables: weeks to or from VMI transition
The key independent variables in our study should capture the introduction of VMI. Previous studies on VMI (Clark and Hammond, 1997; Yao et al., 2012), as well as the qualitative data collected during our study, indicate that learning effects can be present in the first period after VMI introduction. To capture the effect of VMI over time and to capture the learning effect, we introduce a set of week-parameters j =
−k, −(k − 1), ..., 0, (k − 1), k. Using the TIMEDIFFjtvariables we define a window k
leading up to the moment VMI is introduced for a supplier s0, and a window k after
s0.
The j in the TIMEDIFFjtvariables indicate the difference between the t, the week
of the current observation, and s0, the week the supplier switched to VMI. Therefore, negative j indicate observations in the period leading up to the VMI introduction and positive j weeks after the VMI introduction. This approach is similar to prior empirical studies on VMI (Clark and Hammond, 1997). Because suppliers switched
from RMI to VMI in batches (see Figure 2.2), the relation between TIMEDIFFjtand
tdiffers between suppliers depending on the moment a supplier switched to VMI.
Using the estimated coefficients for TIMEDIFFjt we can observe if there were any
trends in the data leading up to VMI introduction and if the performance is signifi-cantly different after, regardless of when a supplier switched to VMI.
This notation has two advantages: First, it enables us to control for external ef-fects that affect the performance at a specific point in time, as the value for TIMEDIFFjt varies across suppliers and over time depending on when they transferred from RMI to VMI, similar to Dong et al. (2014). Second, this allows us to observe the trend in the performance measures for a longer period of time, so that we can check whether
Figure 2.2: Supplier transition from RMI to VMI over time.
the effect of VMI introduction was indeed a break from the ongoing trend in the stock outs and supply chain inventory.
2.5.3
Controls
In addition to the VMI variables, we measure a vector of exogenous control
vari-ables CONTROLSitto control for factors outside the VMI introduction that may
affect the dependent measures. Perishability of products is an important driver of inventory costs and sets an upper limit for the amount of inventory (Fisher, 1997;
Ketzenberg and Ferguson, 2008). We include measure SLIFEi that accounts for the
perishability (shelf life) of the products, measured in the number of days that the product can be consumed after production. At the minimum shelf life, starting from three days in our data, inventory risk is high. With longer shelf life, up to 100 days in our data, virtually no risk for perishing exists in the fast-moving supply chain under study. Our study contains products over this entire range (see Tables 2.1 and 2.2). Especially for perishable products, slow-moving products may require different inventory management than fast-moving products to prevent them from perishing
(Ketzenberg and Ferguson, 2008). VOLUMEiis a dummy variable that indicates if a
product is a (relative) slow mover, which we define as the first quartile of products when sorted on accumulated store demand per product. To control for promotions, that can lead to large and hard to forecast jumps in product demand, we include
PROMOit, a dummy variable that indicates if a product i was in promotion in week
t. Finally, we include VARi, measuring the average log demand variance in a
prod-uct’s demand.
2.5.4
Estimation strategy
We estimate two separate models, one for each dependent variable. Equation 2.1 specifies our model for supply chain inventory per product, per week:
log(INVit) = αs+ βt+ +k X j=−k γjTIMEDIFFjt+ δCONTROLSit+ it (2.1) where, • i is product, • t is week, • s is supplier,
• log(INVit)is measured in log units of product,
• αsare the supplier fixed effects, an intercept that is the same for each product of a supplier
• βtare the week fixed effects,
• sois equal to the week supplier s switched to VMI,
• TIMEDIFFjtis an indicator for the time difference since the VMI introduction:
it equals 1 if t = s0+ j, and 0 otherwise
• CONTROLSitis the vector the vector of exogenous controls: SLIFEi, VOLUMEi,
PROMOit, and VARi. δ is a vector of coefficients, • errors are clustered at the supplier level (Harrell, 2015).
In a similar way, Equation 2.2 specifies our model stockouts for each item-week, measured as the difference between products ordered by the stores and shipped:
log(SOit) = αs+ βt+ +k X
j=−k
Where SOitis also measured in log units of products, increased by 1. All other variables can be interpreted in the same way as in Equation 2.1.
For causal inference models, it is critical to take challenges of endogeneity and selection bias into account (Ho et al., 2017). Table 2.3 provides an overview of the endogeneity challenges encountered in our study and the way we have addressed them in our estimation strategy. First, we took potential censoring effect into
ac-count for the estimation method choice. The range of INVit, the supply chain
inven-tory variable, is limited to the transportation lead time of the product on one side, representing only in-transit inventory, and the shelf life of the product on the other side. We apply a linear model using the OLS method to estimate the supply chain inventory with Equation 2.1. The value of the stockouts can range from 0%, when the total store orders are fulfilled, to 100%, when none of the ordered products are supplied at all. These natural limits result in a truncated sample. In our data, stock-outs close to 100% are very rare. On the contrary, 0% stockstock-outs are very common, which causes an imbalance in the data (Figure 2.3). Stockouts of 0% can be seen as a censored or non-observed response. In other words, we can only measure the mag-nitude of a stockout if a stockout occurred in the first place. Therefore, estimating this response with the ordinary least squares (OLS) method would result in inaccu-rate estimations. To estimate stockouts including the zero stockout observations, we apply a corner solution model (Heckman, 1979), also called a tobit model, to estimate the stockouts in Equation 2.2. This model uses a latent variable that can take on any value. If this latent variable is negative, the observed dependent variable equals 0. If the latent variable is positive, the dependent variable is equal to the latent variable (Leeflang et al., 2017). In the robustness analysis we will evaluate how this choice impacts our estimations.
A second potential source of endogeneity that might affect our results is omission of variables. Since the suppliers in our data differ in many respects, we want to con-trol for unobserved supplier-specific factors that potentially affect the performance of the supply chain. This control can be modeled as either fixed or random effects (Gaur et al., 2005). We use fixed effects, because the random-effects methods assume that the random-effect terms for the suppliers are unrelated to our other explana-tory variables, which is conceptually unlikely in our case. A significant Hausman test (p < 0.01) confirms that fixed effects are preferred over random effects in our model (Wooldridge, 2010). Finally, we want to control for unobserved time-specific
Figure 2.3: Distribution of Stock Out observations.
factors, e.g., weather and holidays, that potentially affect the performance of the sup-ply chain. Following the same reasoning as above, we use fixed effects to control for time specific effects, such as demand seasonality or random factors that disturb the inventory process temporary.
Third, because we use time series data, patterns in the error terms may yield inconsistent estimates for our models. We check for serial correlation of the residu-als using the Durbin-Watson test and perform a Cochrane-Orcutt procedure to help determine consistent estimates of the regression parameters (Rajagopalan and Mal-hotra, 2001; Kennedy, 2003) in the robustness analysis.
A final important source of potential bias is selection bias, i.e., systematic errors due to reasons that cause the suppliers in our data to be non-representative of an ‘average’ supplier in a VMI introduction. We can not address this potential bias in the model specification, but we use auxiliary interview and survey data to better understand how the characteristics of our specific case may have affected the results we observe.
2.5.5
Auxiliary interview and survey data
Next to the validity checks in the econometric analysis described above, we used qualitative data to support the internal validity of our study. Our many conversa-tions with the planners and operaconversa-tions managers of the suppliers, and the respective
Table 2.3: Potential sources of endogeneity or selection bias and validity checks.
Potential bias Role in our case Validity checks
Censoring Large proportion of zero obser-vations in stockout levels
Corner solution model Omitted variables Omitted supplier and product
factors, especially in stockout es-timation (lower model fit). Risk of outside influence other than the VMI introduction.
Fixed effects to control for sup-plier specific and time related factors outside our data. In ad-dition, qualitative data is col-lected using interviews and sur-veys to control for external influ-ences outside our data.
Auto correlation Durbin-Watson test indicates 1st order auto correlation may affect consistency of the estimates
We used the Cochrane-Orcutt procedure to help in determin-ing consistent estimates of the re-gression parameters
Selection bias Limited for suppliers, all suppli-ers transferred to VMI. The fact that all suppliers deliver to the same retailer limits our scope.
The results must be carefully in-terpreted in the specific retail context. Furthermore, the qual-itative data provides more back-ground on the retailer’s motiva-tions for initiating VMI.
account managers of the retailer assured us that no major changes occurred with respect to the store replenishment policies that drove store demand, the forecasting methods, and the supply chain planning teams. Also the economic climate, the re-tailer’s market share, and sales volumes of this retailer in the Netherlands did change in any significant way that could have affected our results over the three years we collected our data. During the interviews, employees of the suppliers neither noted substantial changes in the supply chain other than VMI. Two suppliers mentioned that mergers or acquisitions affected their supply chain processes, but the influence of these events remains specific to the individual suppliers and thus can be consid-ered as noise in our estimations.
With regard to ongoing changes that affect the supply chain, multiple employees of the retailer pointed out that the retailer’s assortment is expanding continuously, especially with slow-moving products, which also reduces the average demand per individual product. Tables 2.1 and 2.2 show that the average demand volume per product was slightly lower after the introduction of VMI, while the shelf life was slightly longer (the latter being the result of innovations in processing and packag-ing improvpackag-ing the shelf life of fresh products). Both shelf life and demand volume
are included in our controls. Moreover, we used the same maximum shelf life for our supply chain inventory measure for each product over the entire measurement period to enhance comparison between VMI and RMI.
2.6
Results
Tables 2.1 and 2.2 show the summary statistics of the observations pre- and post-VMI introduction. Across the two sub-tables, the characteristics for the independent vari-ables are similar, but a clear difference is visible between the dependent varivari-ables. A mean value analysis shows that supply chain inventory increases on average by about one full day, from 4.1 to 5.4 days. The average stockouts reduce by 0.5 per-centage point from 2.8% to 2.3%. However, mean value analysis does not control for exogenous factors that might have affected the independent variables, which will be taken into account in the estimations that follow.
2.6.1
The effect of VMI on supply chain inventory and stockouts
and learning effects
Figure 2.4 provides a graphical overview of the estimated coefficients for TIMEDIFFjt
in the supply chain inventory (INVit) model. A table including all coefficients and
goodness of fit metrics is included in the first column of Table 2.5 in Appendix B (fixed effects coefficient have been omitted for readability purposes). The coeffi-cients for the supply chain inventory estimation indicate that no significant trend was present with regard to this variable before the introduction of VMI. Directly upon VMI introduction, we observe a significant increase (p<0.01) in supply chain inventory. A very slight decrease supply chain inventory can be observed in the
coef-ficients for TIMEDIFFjtover time, but supply chain inventory remains significantly
higher the entire first year after VMI is introduced.
The interview and survey responses complement these observations. The suppli-ers as well as the retailer prioritize high service levels, but differ in the way they aim to achieve this. The automated replenishment system and planners of the retailer acted under strong incentive to keep inventories in the warehouse low. To keep in-ventories low, the retailer’s planners placed frequent orders at the suppliers, asking for short delivery times from the suppliers. The planners of suppliers, by contrast,
Figure 2.4: Fitted values for the time difference between observation and VMI intro-duction coefficients for the INV model.
give priority to a higher service level while inventory holding costs playing a less important role. As long as inventory space is available at the warehouse, holding costs are relatively low compared to production costs and potential missed sales. Rather, suppliers see potential to improve on other performance indicators, such as resource utilization and reducing stress on the planning process. Only for highly perishable products, the suppliers emphasize the risk of excess inventory, and hence report to focus on reducing inventory for those products. This is also reflected in the outcomes of our survey. Suppliers reported that they especially benefited from VMI via possibilities for increased transportation efficiency (3.5 on a on a 5-point scale ranging from ’very negative impact’ to ’very positive impact’) and the ability to keep inventory at the retailer’s warehouse (3.2). Moreover, despite the increase in supply chain inventory, the impact of VMI introduction for the supplier’s organiza-tion was reported as neutral (an average value of 3.0), with a few suppliers reporting a (slightly) negative impact or (slightly) positive impact.
For the stockout model, Figure 2.5 shows a slight increase in stockouts in the weeks leading up to the introduction of VMI. However, this trend is not significant, as indicated by the insignificant, or low significance of, p-values for the TIMEDIFFjt coefficients with negative j in the second column of Table 2.5 in Appendix B. The
Figure 2.5: Fitted values for the time difference between observation and VMI intro-duction coefficients for the SO model.
first two weeks after VMI is introduced, we observe higher stockouts as indicated by
the large increase in the TIMEDIFFjt coefficients, which suggests a strong learning
effect. After this short performance dip, however, we observe a strong downward trend in the coefficients, which converts the estimates into a decrease in stockouts (compared to RMI), which is highly significant (p<0.01) from 14 weeks onward. This downward trend continues the first 30 weeks after VMI introduction, after which amount of stockouts stabilizes at a level significantly lower than before VMI.
Again, the observations in the data are in line with the responses to our inter-views and survey. As described above, both supplier and retailer prioritize low stockouts, but the qualitative data shows differences between the RMI and VMI sit-uation that may contribute to the reduction in stockouts that we observe after VMI introduction. After VMI introduction, the planners of the supplier are completely responsible for the stockout levels at the retailers wharehouse. They are under pres-sure within their own organization to maintain low stockouts, but on top of that receive external pressure from the retailer. In contrast, before VMI introduction, the planners of the retailer only had to report to management within their own organiza-tion. Moreover, responsibility for stockouts in the warehouse was always divided be-tween retailer and supplier, as the supplier’s ability to meet the inventory fulfillment
plan also affects the performance. Next to this, the survey showed that the suppliers benefit from improved access to information after introducing VMI (3.2). Arguably, in many cases suppliers simply made better use of information that was available to them before VMI as well. Furthermore, suppliers are almost unanimously positive regarding their ability to improve stockout performance after the VMI introduction (3.8) and the supply chain inventory levels needed to do so (3.9).
2.6.2
Robustness checks
To check for potential multicollinearity, we computed variance inflation factor (VIF) scores for all independent variables in the supply chain inventory and stockouts es-timation models. The generalized VIF scores for variables in all models are between 1.1 and 1.9, which is lower than the commonly accepted cutoff value of 5, indicating that multicollinearity is not a problem (De Vaus, 2013).
To investigate the robustness for alternative methodical choices concerning the censoring effect, we ran a normal OLS without the tobit correction for Equation 2.2. The results of this test are shown in Figure 2.6 and the third column of Table 2.5
in Appendix B. The general trends in the TIMEDIFFjt coefficients are similar. The
startup effect after VMI introduction that causes increased stockouts seems stronger, as now the first seven weeks after VMI introduction show a significant increase in stockout levels. Similar to the model with censoring correction this is converted in a strong decrease of stockouts that stabilize around 30 weeks after VMI is introduced at a level significantly lower than before VMI. Note that the model without censoring correction assumes a normal distribution of stockout observations, which is not the case due to the high number of 0 stockout observations in our data (see Table 2.2). This may (partly) explain why the stockout reduction effect takes longer to become significant in the method without censoring, as not only the size but also the part of item-weeks that contain a stockout reduces after VMI introduction. We conclude that our results are robust for the method of estimation.
To verify if our results based on the absolute measure of stockouts is not affected by changes in store demand volume, we tested an alternative measure for stock-outs: a relative measure describing the stockouts of each week as a fraction the total amount ordered by the stores in that week. This measure is also used to measure service levels (SL). To be consistent with our other stockout measure, we also use
Figure 2.6: Fitted values for the time difference between observation and VMI intro-duction coefficients for the SO model (without censoring correction).
the log transformed value of this stockout level, and increase all observations with 1 to avoid having to take the log of zero. We use the same tobit model to obtain
the estimated values for TIMEDIFFjt. Figure 2.7 (and the last column of Table 2.5 in
Appendix B) indicates that with this measure, we obtain similar results. After VMI is introduced, the pattern looks similar to the pattern observed using our original absolute SOitmeasure, with long term stockouts that stabilize at a level significantly lower than the level before VMI introduction.
Finally, we verify how possible autocorelation impacts our results by re-estimating both models using the Cochrane-Orcutt procedure, which solves first order relation problems using an iterative method. This procedure estimates both autocor-relation and beta coefficients recursively until we reach the convergence. A Durbin-Watson test confirms that the procedure successfully removes all significant first
or-der autocorrelation in both the stockout and inventory model. The TIMEDIFFjt
co-efficients visualised in Figure 2.8 and Figure 2.9 shows similar trends as before (the full results are included in Table 2.6 in Appendix B), hence we conclude that autocor-relation is no major threat in our study. All in all, we conclude that our main results are robust for methodological choices.
Figure 2.7: Fitted values for the time difference between observation and VMI intro-duction coefficients for relative stockout measure (Stockout Level).
Figure 2.8: Fitted values for the time difference between observation and VMI intro-duction coefficients for INV corrected for potential autocorelation.
Figure 2.9: Fitted values for the time difference between observation and VMI intro-duction coefficients for SO corrected for potential autocorelation.
2.7
Discussion and conclusion
Many retailers have implemented VMI, or are considering doing so, in an attempt to reduce inventories in their supply chains while maintaining or improving ser-vice levels. However, to date insights into the supply chain performance effects of VMI implementations have been based mainly on analytical modelling or empirical observations at large suppliers driving the VMI initiative while measuring inven-tory level changes at their buyers’ stock points. To the best of our knowledge, this study is the first to empirically measure the supply chain performance effects of a VMI introduction driven by a large retailer that also includes a transfer of inventory ownership, and covering both integral supply chain inventory and service levels.
Our study suggests that the supply chain performance effects of a retailer-driven VMI introduction differs markedly from the supplier-driven VMI that has been the focus of empirical investigations so far (Clark and Hammond, 1997; Lee et al., 1999; Dong et al., 2014). While our results underline the efficiency gains these prior stud-ies describe, a major difference lstud-ies in how suppliers use the newly gained deci-sion latitude provided by the transfer of inventory ownership and control associated with VMI. In contrast to empirical observations from supplier-driven VMI initia-tives, our study reveals that a retailer-driven VMI leads to strong improvement in
demand fulfillment performance at the expense of an increase in supply chain in-ventory. This seemingly counterintuitive result can be explained by considering that suppliers have strong incentives to realize high product availability while effectively utilizing their production and transportation resources.
The setup and characteristics of retailer- and supplier-driven VMI introductions may differ depending on whether a retailer or a supplier drives the introduction of VMI. Most notably, retailer-driven VMI is commonly combined with consignment inventory, because the retailer is often the more powerful of the two, and the sup-plier’s abilities and supply chain may be less developed compared to a supplier driving VMI introduction. With this difference in context in mind, we will evaluate how VMI is expected to provide operational gains in a supply chain (e.g. Cetinkaya and Lee, 2000; Ketzenberg and Ferguson, 2008) and the expected impact of VMI and consignment inventory on incentives in the supply chain (e.g. Cachon, 2004; Bern-stein et al., 2006).
First, our study provides empirical evidence for the assertion that assigning both ownership and control of inventory to the supplier provides contractual incentives that lead to improved demand fulfillment. After transferring inventory ownership and control to a supplier, the supplier can steer virtually all operations from produc-tion, transportation to inventory at the retailer’s stock point while also incurring all corresponding costs. Our novel supply chain inventory measure revealed that sup-pliers use this newly gained decision latitude to improve demand fulfillment at the expense of increased inventory, compared to the retailer’s control decisions before the transfer of ownership and control of inventory. Furthermore, efficiency gains that arise after introducing VMI (the learning effect) are focused on further improv-ing demand fulfillment rather than on reducimprov-ing inventories. When interpretimprov-ing these results, it should be acknowledged that all earlier studies measured inventory levels at the buyer only (Clark and Hammond, 1997; Lee et al., 1999; Dong et al., 2014). Our empirical results confirm findings of analytical studies that suggest that a supplier has greater incentives than a retailer to improve product availability (Bernstein et al., 2006), in part owing to brand competition (Mishra and Raghunathan, 2004). Also, the powerful position of the retailer, that is typical for retailer-driven VMI, provides an additional incentive to prioritize high service levels.
Second, our results emphasize the importance of efficient use of production, trans-portation, and human resources rather than improving inventory performance. VMI
implementations driven by a supplier are often motivated by a desire to better utilize the supplier’s advanced supply chain planning abilities by centralizing the replen-ishment decisions for multiple retailers. This type of supplier may differ from a sup-plier that ends up using VMI through a retailer-driven VMI introduction. Through-out our time at the retailer and during the many interviews with suppliers, infor-mants emphasized the value of stable production and transportation processes over inventory reduction, especially in situations where the inventory system is already lean. Last-minute changes in demand volumes are expensive in terms of time invest-ment required of managers and planners, as well as in terms of the extra production and transportation capacity needed to deal with such variations. This might be an aspect that is especially relevant for the smaller, less knowledgeable suppliers who are part of the retailer-driven VMI implementation but are otherwise unlikely to im-plement VMI themselves. However, we found the same argument consistently be-ing raised by larger suppliers. Furthermore, our survey data indicates that suppliers benefit from VMI via improved transport efficiency and their ability to keep inven-tory at the retailer’s stock point. Our observations underline findings from prior experimental studies showing that planners tend to avoid stockouts beyond what can be economically expected (Schweitzer and Cachon, 2000), as the extra inventory reduces complexity in decision making (Kremer and Van Wassenhove, 2014; Kremer et al., 2014).
Third, the learning effects observed in our retailer-driven are in some aspects consistent with supplier-driven VMI introductions, but in other aspects they differ. Clark and Hammond (1997) show that VMI introduction is directly followed by a reduction in inventory at the buyers location (when controlling for changes in stock-outs). Inventory continues to decrease for at least six months after VMI introduction when the latest measure is obtained. In our case, performance does not directly im-prove, both inventory and stockout first increase for two or three weeks before stock-out reduces strongly. It is likely that the suppliers involved in the retailer-driven VMI introduction took more time to adopt to the new technology involved, which causes a ‘performance dip’. This is a common phenomenon that has been observed in other IT-related implementations (Mcafee, 2002). The long learning effect we observe is similar to those reported by Clark and Hammond (1997) and Yao et al. (2012), as we observe a reducing trend in stockouts up to one year after VMI introduction. In con-trast to (Yao et al., 2012), we do not observe an inverting effect that causes stockouts
to increase again within the first year after the VMI introduction.
All in all, our findings emphasize the importance of the context a VMI implemen-tation takes place in. The results show that outcomes of a retailer-driven VMI imple-mentation with consignment inventory can be markedly different from the current view on VMI that is dominated by inventory reduction. Therefore, the assumption that decision makers involved in VMI introductions will strive to lower inventories, which is used in many analytical models of VMI, should be used with care. How-ever, at the same time our results provide empirical support for results obtained in prior studies obtained using analytical models, in particular in relation to supply chain contracting and power relations. Our results can make managers of (grocery) retailers more aware of how a retailer-driven VMI introduction, or VMI introduc-tion that include consignment, can differ from the well known cases in academia in practice.
2.8
Limitations and recommendations for future research
As in any empirical work, generalization of our results is limited by the context the study was conducted in. The results must be interpreted in the context of modern European supply chains, characterized by short delivery times, high levels of in-formation sharing prior and high service level requirements. The fact that we find markedly different results compared to prior studies, however, shows the relevance of studying the effects of a well-established concept as VMI in a context it has not been measured in before. Studying data of retailers that drive VMI introductions for suppliers in other parts of the world or other industries could deepen our un-derstanding of how introduction of VMI depends on the supply chain context it is implemented in. Finally, in this study we focused on the supply chain level effect of VMI. Future work could empirically explore how the outcomes of VMI introductions are conditional on products and suppliers characteristics.
2.9
Appendix A: supplier-survey questions and results
1. How does the introduction of Vendor Managed Inventory affect yourorgani-zation in general?
2. How does the VMI introduction affect the transportation efficiency in your or-ganization.
3. How does the VMI introduction affect the production efficiency in your orga-nization.
4. How do the following aspects of the VMI introduction affect your organization: (a) The ability to decide the delivery quantities and frequency yourself. (b) The additional information that received since the VMI introduction.
(c) The ability to keep inventory at [the buyer’s] warehouse.
All answers are provided on a 5-point scale ranging from ’very negative impact’ to ’very positive impact’
Item 1 2 3 4a 4b 4c
1: Very negative impact 0.04 0.00 0.00 0.04 0.09 0.06
2 0.23 0.08 0.06 0.13 0.11 0.06
3 0.38 0.68 0.43 0.45 0.28 0.32
4 0.21 0.11 0.30 0.25 0.28 0.36
5: Very positive impact 0.00 0.00 0.08 0.02 0.09 0.08
Average 2.96 3.08 3.51 3.15 3.19 3.47
2.10
Appendix B: estimation tables
Table 2.5: Complete Estimation Results table.
Dependent variable:
log(INV) log(SO +1 ) log(SO +1 ) log(SL +1 )
OLS tobit OLS tobit
(1) (2) (3) (4) log(SHELF) 0.645∗∗∗ (0.006) −1.695∗∗∗ (0.058) −0.425∗∗∗ (0.017) −0.041∗∗∗ (0.002) VAR −0.010∗∗∗ (0.001) 0.181∗∗∗ (0.008) 0.084∗∗∗ (0.002) 0.002∗∗∗ (0.0002) PROMO −0.080∗∗∗ (0.010) 2.178∗∗∗ (0.085) 0.962∗∗∗ (0.029) 0.057∗∗∗ (0.002) VOLUME 0.044∗∗∗ (0.009) −0.784∗∗∗ (0.078) −0.640∗∗∗ (0.027) −0.002 (0.002) TIMEDIFF -50 −0.064 (0.057) −0.103 (0.505) 0.054 (0.162) −0.002 (0.015) TIMEDIFF -45 −0.114∗∗ (0.055) 0.231 (0.492) 0.189 (0.158) 0.009 (0.014) TIMEDIFF -40 −0.080 (0.056) 0.661 (0.484) 0.290∗ (0.159) 0.021 (0.014) TIMEDIFF -35 −0.005 (0.052) −0.122 (0.461) 0.110 (0.149) 0.006 (0.013) TIMEDIFF -30 −0.065 (0.050) 0.971∗∗ (0.438) 0.436∗∗∗ (0.142) 0.035∗∗∗ (0.013) TIMEDIFF -25 −0.010 (0.051) 0.253 (0.446) 0.147 (0.144) 0.021 (0.013) TIMEDIFF -15 −0.027 (0.051) 0.396 (0.451) 0.284∗ (0.146) 0.026∗∗ (0.013) TIMEDIFF -14 −0.020 (0.052) 0.894∗∗ (0.451) 0.379∗∗ (0.148) 0.038∗∗∗ (0.013) TIMEDIFF -13 −0.021 (0.054) 1.068∗∗ (0.468) 0.554∗∗∗ (0.153) 0.045∗∗∗ (0.013) TIMEDIFF -12 0.011 (0.052) 0.173 (0.456) 0.279∗ (0.147) 0.020 (0.013) TIMEDIFF -11 0.026 (0.051) 0.398 (0.450) 0.259∗ (0.147) 0.023∗ (0.013) TIMEDIFF -10 −0.008 (0.052) 0.705 (0.455) 0.485∗∗∗ (0.147) 0.039∗∗∗ (0.013) TIMEDIFF -9 0.001 (0.051) 0.483 (0.447) 0.286∗ (0.146) 0.026∗∗ (0.013) TIMEDIFF -8 −0.021 (0.050) 0.546 (0.433) 0.281∗∗ (0.141) 0.028∗∗ (0.012) TIMEDIFF -7 0.002 (0.049) 0.924∗∗ (0.428) 0.535∗∗∗ (0.139) 0.037∗∗∗ (0.012) TIMEDIFF -6 −0.007 (0.049) 1.066∗∗ (0.427) 0.587∗∗∗ (0.139) 0.046∗∗∗ (0.012) TIMEDIFF -5 −0.048 (0.049) 1.001∗∗ (0.424) 0.596∗∗∗ (0.138) 0.042∗∗∗ (0.012) TIMEDIFF -4 0.002 (0.048) 0.800∗ (0.421) 0.502∗∗∗ (0.137) 0.039∗∗∗ (0.012) TIMEDIFF -3 −0.038 (0.048) 0.699∗ (0.418) 0.451∗∗∗ (0.136) 0.037∗∗∗ (0.012) TIMEDIFF -2 −0.015 (0.047) 0.829∗∗ (0.412) 0.388∗∗∗ (0.135) 0.048∗∗∗ (0.012) TIMEDIFF -1 0.015 (0.047) 0.619 (0.413) 0.404∗∗∗ (0.134) 0.041∗∗∗ (0.012) TIMEDIFF 0 0.042 (0.048) 3.091∗∗∗ (0.408) 1.415∗∗∗ (0.137) 0.111∗∗∗ (0.012) TIMEDIFF 1 0.185∗∗∗ (0.047) 1.872∗∗∗ (0.409) 1.048∗∗∗ (0.134) 0.075∗∗∗ (0.012) TIMEDIFF 2 0.303∗∗∗ (0.047) 0.879∗∗ (0.413) 0.707∗∗∗ (0.135) 0.050∗∗∗ (0.012) TIMEDIFF 3 0.263∗∗∗ (0.048) 0.498 (0.417) 0.519∗∗∗ (0.135) 0.037∗∗∗ (0.012) TIMEDIFF 4 0.280∗∗∗ (0.047) 0.827∗∗ (0.414) 0.630∗∗∗ (0.135) 0.042∗∗∗ (0.012) TIMEDIFF 5 0.226∗∗∗ (0.047) 0.635 (0.412) 0.610∗∗∗ (0.134) 0.042∗∗∗ (0.012) TIMEDIFF 6 0.220∗∗∗ (0.047) 0.702∗ (0.413) 0.574∗∗∗ (0.134) 0.042∗∗∗ (0.012) TIMEDIFF 7 0.234∗∗∗ (0.047) 0.230 (0.413) 0.413∗∗∗ (0.134) 0.027∗∗ (0.012) TIMEDIFF 8 0.260∗∗∗ (0.047) −0.075 (0.414) 0.297∗∗ (0.134) 0.019 (0.012) TIMEDIFF 9 0.245∗∗∗ (0.047) −0.528 (0.415) 0.121 (0.134) 0.007 (0.012) TIMEDIFF 10 0.273∗∗∗ (0.047) −0.453 (0.416) 0.175 (0.134) 0.007 (0.012) TIMEDIFF 11 0.214∗∗∗ (0.047) −0.427 (0.420) 0.138 (0.135) 0.004 (0.012) TIMEDIFF 12 0.260∗∗∗ (0.047) −0.003 (0.420) 0.275∗∗ (0.135) 0.015 (0.012) TIMEDIFF 13 0.234∗∗∗ (0.048) 0.112 (0.422) 0.372∗∗∗ (0.136) 0.019 (0.012) TIMEDIFF 14 0.225∗∗∗ (0.048) −0.653 (0.426) 0.094 (0.136) 0.001 (0.012) TIMEDIFF 15 0.252∗∗∗ (0.048) −1.377∗∗∗ (0.428) −0.083 (0.136) −0.019 (0.012) TIMEDIFF 16 0.207∗∗∗ (0.048) −0.636 (0.426) 0.098 (0.136) 0.001 (0.012) TIMEDIFF 17 0.223∗∗∗ (0.048) −0.377 (0.426) 0.121 (0.136) 0.002 (0.012) TIMEDIFF 18 0.234∗∗∗ (0.048) −0.951∗∗ (0.431) −0.053 (0.137) −0.006 (0.012) TIMEDIFF 19 0.197∗∗∗ (0.048) −0.882∗∗ (0.431) −0.021 (0.137) −0.011 (0.012) TIMEDIFF 20 0.189∗∗∗ (0.048) −0.475 (0.427) 0.136 (0.137) 0.003 (0.012) TIMEDIFF 21 0.193∗∗∗ (0.049) −0.541 (0.433) 0.147 (0.139) 0.001 (0.012) TIMEDIFF 22 0.203∗∗∗ (0.049) −0.786∗ (0.438) 0.106 (0.139) −0.007 (0.013) TIMEDIFF 23 0.204∗∗∗ (0.049) −1.167∗∗∗ (0.442) −0.062 (0.139) −0.017 (0.013) TIMEDIFF 24 0.202∗∗∗ (0.049) −0.744∗ (0.442) 0.067 (0.140) −0.005 (0.013) TIMEDIFF 25 0.148∗∗∗ (0.049) −0.307 (0.438) 0.214 (0.140) 0.005 (0.013) TIMEDIFF 30 0.230∗∗∗ (0.050) −1.751∗∗∗ (0.451) −0.262∗ (0.141) −0.030∗∗ (0.013) TIMEDIFF 35 0.224∗∗∗ (0.050) −1.786∗∗∗ (0.459) −0.149 (0.142) −0.035∗∗∗ (0.013) TIMEDIFF 40 0.193∗∗∗ (0.050) −0.901∗∗ (0.454) 0.062 (0.143) −0.012 (0.013) TIMEDIFF 45 0.176∗∗∗ (0.053) −1.590∗∗∗ (0.496) −0.162 (0.151) −0.028∗ (0.014) TIMEDIFF 50 0.186∗∗∗ (0.054) −2.238∗∗∗ (0.516) −0.219 (0.154) −0.046∗∗∗ (0.015) Log(scale) 1.524∗∗∗ (0.006) −2.038∗∗∗ (0.005) Constant −1.169∗∗∗ (0.071) 2.834∗∗∗ (0.598) 2.386∗∗∗ (0.203) 0.043∗∗ (0.017) Observations 70,382 71,656 71,656 71,656
Fixed effects suppliers Yes Yes Yes Yes
Fixed effects weeks Yes Yes Yes Yes
R2 0.512 0.214
Adjusted R2 0.510 0.211
Residual Std. Error 0.646 (df = 70083) 1.854 (df = 71357)
F Statistic 246.693∗∗∗ (df = 298; 70083) 65.231∗∗∗ (df = 298; 71357)
Table 2.6: Estimation results obtained with Cochrane Orcutt procedure. Dependent variable: log(INV) log((SO + 1) (1) (2) log(SHELF) 0.606∗∗∗ (0.012) −0.425∗∗∗ (0.022) VAR −0.004∗∗∗ (0.001) 0.074∗∗∗ (0.003) PROMO −0.144∗∗∗ (0.007) 0.976∗∗∗ (0.028) VOLUME 0.089∗∗∗ (0.010) −0.769∗∗∗ (0.031) TIMEDIFF -50 −0.129∗∗∗ (0.033) 0.050 (0.138) TIMEDIFF -45 −0.238∗∗∗ (0.047) 0.232 (0.155) TIMEDIFF -40 −0.210∗∗∗ (0.048) 0.320∗∗ (0.156) TIMEDIFF -35 −0.143∗∗∗ (0.045) 0.171 (0.146) TIMEDIFF -30 −0.135∗∗∗ (0.043) 0.486∗∗∗ (0.140) TIMEDIFF -25 −0.097∗∗ (0.043) 0.191 (0.141) TIMEDIFF -20 −0.152∗∗∗ (0.045) 0.785∗∗∗ (0.145) TIMEDIFF -15 −0.187∗∗∗ (0.045) 0.327∗∗ (0.144) TIMEDIFF -14 −0.182∗∗∗ (0.046) 0.432∗∗∗ (0.146) TIMEDIFF -13 −0.164∗∗∗ (0.047) 0.558∗∗∗ (0.151) TIMEDIFF -12 −0.140∗∗∗ (0.046) 0.339∗∗ (0.145) TIMEDIFF -11 −0.135∗∗∗ (0.045) 0.272∗ (0.145) TIMEDIFF -10 −0.164∗∗∗ (0.045) 0.529∗∗∗ (0.145) TIMEDIFF -9 −0.146∗∗∗ (0.045) 0.336∗∗ (0.144) TIMEDIFF -8 −0.111∗∗ (0.043) 0.326∗∗ (0.139) TIMEDIFF -7 −0.111∗∗∗ (0.043) 0.550∗∗∗ (0.138) TIMEDIFF -6 −0.123∗∗∗ (0.043) 0.645∗∗∗ (0.137) TIMEDIFF -5 −0.138∗∗∗ (0.042) 0.653∗∗∗ (0.137) TIMEDIFF -4 −0.123∗∗∗ (0.042) 0.523∗∗∗ (0.136) TIMEDIFF -3 −0.160∗∗∗ (0.041) 0.491∗∗∗ (0.134) TIMEDIFF -2 −0.120∗∗∗ (0.041) 0.421∗∗∗ (0.133) TIMEDIFF -1 −0.097∗∗ (0.040) 0.410∗∗∗ (0.132) TIMEDIFF 0 −0.029 (0.040) 1.457∗∗∗ (0.134) TIMEDIFF 1 0.155∗∗∗ (0.041) 1.026∗∗∗ (0.133) TIMEDIFF 2 0.268∗∗∗ (0.042) 0.738∗∗∗ (0.135) TIMEDIFF 3 0.217∗∗∗ (0.043) 0.593∗∗∗ (0.135) TIMEDIFF 4 0.232∗∗∗ (0.043) 0.638∗∗∗ (0.135) TIMEDIFF 5 0.224∗∗∗ (0.043) 0.614∗∗∗ (0.134) TIMEDIFF 6 0.195∗∗∗ (0.043) 0.586∗∗∗ (0.134) TIMEDIFF 7 0.208∗∗∗ (0.043) 0.421∗∗∗ (0.134) TIMEDIFF 8 0.219∗∗∗ (0.044) 0.323∗∗ (0.134) TIMEDIFF 9 0.222∗∗∗ (0.044) 0.146 (0.134) TIMEDIFF 10 0.261∗∗∗ (0.044) 0.195 (0.134) TIMEDIFF 11 0.198∗∗∗ (0.044) 0.166 (0.135) TIMEDIFF 12 0.248∗∗∗ (0.045) 0.305∗∗ (0.136) TIMEDIFF 13 0.203∗∗∗ (0.045) 0.396∗∗∗ (0.136) TIMEDIFF 14 0.181∗∗∗ (0.045) 0.126 (0.136) TIMEDIFF 15 0.198∗∗∗ (0.045) −0.050 (0.136) TIMEDIFF 16 0.168∗∗∗ (0.045) 0.128 (0.136) TIMEDIFF 17 0.207∗∗∗ (0.045) 0.153 (0.137) TIMEDIFF 18 0.214∗∗∗ (0.046) −0.021 (0.137) TIMEDIFF 19 0.186∗∗∗ (0.046) 0.031 (0.138) TIMEDIFF 20 0.193∗∗∗ (0.046) 0.187 (0.138) TIMEDIFF 25 0.125∗∗∗ (0.047) 0.242∗ (0.141) TIMEDIFF 30 0.213∗∗∗ (0.048) −0.244∗ (0.142) TIMEDIFF 35 0.211∗∗∗ (0.049) −0.127 (0.144) TIMEDIFF 40 0.183∗∗∗ (0.049) 0.084 (0.145) TIMEDIFF 45 0.170∗∗∗ (0.053) −0.124 (0.154) TIMEDIFF 50 0.153∗∗∗ (0.054) −0.183 (0.157) Constant −1.092∗∗∗ (0.101) 2.484∗∗∗ (0.230) Observations 70,382 71,656
Fixed effects suppliers Yes Yes
Fixed effects weeks Yes Yes
