The Role of Execution in Managing Product Availability

APPENDIX 1

4.1.1 DeHoratius and Raman (2008)

Research Site: The authors examine the drivers of inventory record inaccuracy using data from Gamma Corporation, a large specialty retailer with over ten billion dollars in annual sales. Gamma uses electronic point-of-sale scanning for all its sales and an automated replenishment system for inventory replenishment.

Data: The authors collected data from physical audits of 37 Gamma stores in 1999. These data included detailed information about each stock-keeping-unit (SKU) contained in each store, amounting to a total of 369,567 observations, or SKU-Store combinations. Physical audits revealed the recorded quantity (the recorded number of inventory units for each SKU at a specific store) as well as the on-hand quantity (the actual number of inventory units present at the store for each SKU). In addition to SKU level data, the authors collected both store and product category data and complemented their quantitative analysis with extensive fieldwork.

Dependent Variable: The dependent variable is the inventory record inaccuracy of each SKU in each store. Inventory record inaccuracy (IRI) is measured as the absolute difference between the recorded and actual quantity for each SKU-store combination.

Independent variables: SKU level variables are: the cost of the item, its annual selling quantity, and whether the item had been shipped to the store from one of Gamma’s distribution centers or directly from the vendor. Store level variables are: total number of units in a given selling area, product variety, and the number of days between the current and previous physical audit.

Empirical Model: Because these data have a multi-level structure (SKUs are contained within stores and product categories), the authors fit a series of hierarchical linear models to examine the drivers of IRI. In addition to the independent variables noted above, the empirical model includes the following control variable, a dummy for each region in which a store is located (REGION_ONE_k,REGION_TWO_k). Equation (1) below summarizes their model.

$$\begin{aligned}{\rm IRI}_{\rm ijk} = &\Theta_0+ {\rm b}_{00{\rm j}} +{\rm c}_{00{\rm k}} + {\rm e}_{\rm ijk}+ \pi_1{*}({\rm QUANTITY}_{-}{{\rm SOLD}_{\rm ijk}})\\&+ \pi_2{*}({\rm ITEM_{-}COST}_{\rm ijk}) + \pi_3{*}({\rm DOLLAR}_{-}{\rm VOLUME}_{\rm ijk}) \\&+ \pi_4{*}({\rm VENDOR}_{\rm i}) +\pi_5{*}({\rm VENDOR_{-}COST}_{\rm ijk}) \\&+ \gamma_{001}{*}({\rm REGION_{-}ONE}_{\rm k}) + \gamma_{002}{*}({\rm REGION_{-}TWO}_{\rm k})\\&+\gamma_{003}{*}({\rm DENSITY}_{\rm k})+ \gamma_{004}{*}({\rm VARIETY}_{\rm k})+ \gamma_{005}{*}({\rm DAYS}_{\rm k})\end{aligned}$$

((1))

where

• IRI_ijk is the record inaccuracy of item i (i = 1…..,n_jk) in product category j (j = 1……,68) and store k (k = 1, ……,37).

• Θ₀ is a fixed intercept parameter.

• The random main effect of product category j is b_00j ∼ N(0, τ_boo).

• The random main effect of store k is c_00 k ∼ N(0, τ_coo).

• The random item effect is e_ijk ∼ N(0, σ²).

• τ_boo, τ_coo, and σ² define the variance in IRI between product categories, stores, and items, respectively.

• π₁–π₅ are the fixed item level coefficients and γ₀₀₁-γ₀₀₅ are the fixed store level coefficients.

Each of the variables is defined below:

• QUANTITY_SOLD_ijk is the annual selling quantity of item i in product category j and store k

• ITEM_COST_ijk is the cost of item i in product category j and store k

• DOLLAR_VOLUME_ijk is the interaction between the cost of the item and its annual selling quantity

• VENDOR_i is a dichotomous variable that takes the value of one if the item is shipped direct to the store from the vendor and takes the value of zero if the item is shipped to the store from the retail-owned distribution center.

• VENDOR_COST_ijk is an interaction term between the way in which an item was shipped to the store and its cost

• DENSITY_k is the total number of units in a store divided by that store’s selling area (units per square foot)

• VARIETY_k is the number of different merchandise categories within a store

• DAYS_k measures the number of days between audits for a given store.

Findings: The authors find significant positive relationships between IRI and an item’s annual selling quantity, store inventory density, store product variety, and the number of days since the last store audit. A significant negative relationship exists between IRI and an item’s cost as well as its dollar volume. The way in which an item is shipped to the store is a significant predictor of IRI such that items shipped direct to the store from the vendor are more accurate than items shipped from the retail distribution center. This relationship, however, depends on the cost of an item. Specially, the difference between vendor-shipped and DC-shipped items is greater for inexpensive items than for expensive ones.

4.1.2 Ton and Raman (2006)

Research Site: The authors examine the drivers of misplaced products using data from Borders Group, a large retailer of entertainment products such as books, CDs, and DVDs. To ensure product availability, the retailer has invested heavily in information technology and merchandise planning to make sure that the right product is sent to the right store at the right time.

Data: The authors collected data from physical audits of 242 Borders stores in 1999. Physical audits provide data on the total units of inventory at the store, total number of products at the store, and the number and dollar value of the products that were present in storage areas but not on the selling floor. In addition to physical audit data, the authors collected data on store attributes and human resource characteristics. The authors complemented their empirical data with extensive fieldwork.

Dependent Variable: The dependent variable, % phantom products, is the percentage of products that are in storage areas but not on the selling floor. The authors call these products “phantom” because they are physically present in the store and often shown as available in retailers’ merchandising systems, but in fact are unavailable to customers.

Independent variables: The authors use the following independent variables: inventory level per product, total number of products in a given area, size of the storage area, employee workload, employee turnover, store manager turnover, and the number of trainers at the store.

Empirical Model: The authors estimate the parameters of equation (2) using ordinary least square estimator to examine the drivers of % phantom products. In addition to all independent variables, the empirical model includes the following control variables: store sales, store age, seasonality, unemployment rate, and a dummy variable for each region. Note that, one variable, store sales, is an endogenous variable and hence the authors employ instrumental variable estimation to cope with endogeneity. The authors use corporate sales as an instrument for store sales.

$$\begin{aligned}\% PHANTOM\_PRODUCTS_i = &\;\beta _0 + \beta _1\, SEASONALITY_i + \beta _2\, UNEMPLOYMENT\_RATE_i + \beta _3\, LN(AGE)_i \\&+\beta _4\, SALES_i + \beta _5\, WAGE_i + \beta _{6j}\, REGION_i + \beta _7\, INVENTORY\_DEPTH_i \\&+\beta _8\, PRODUCT\_DENSITY_i + \beta _9\, STORAGE\_SIZE_i\\& + \beta _{10}\, LABOR\_INTENSITY_i + \beta _{11}\, SM TURNOVER_i + \beta _{12}\, FT TURNOVER_i\\& + \beta _{13}\, PT TURNOVER_i + \beta _{14}\, TRAINING_i + \varepsilon _i \\\end{aligned}$$

((2))

Each of the variables is defined below:

• %PHANTOM_PRODUCTS _i is the number of products in storage but not on floor in store j divided by the total number of products in store i.

• SEASONALITY _ij is the seasonality index for month j in which the audit is conducted at store i. The seasonality index for month j is calculated as:

  $$\theta _j=\frac{{\sum\limits_{i = 1}^{242} {S_{ij} } }}{{\left( {{{\sum\limits_{j = 1}^{12} {\sum\limits_{i = 1}^{242} {S_{ij} } } } \mathord{\bigg/ \kern-\nulldelimiterspace} {12}}} \right)}}$$

• UNEMPLOYMENT_RATE _i is the unemployment rate of the metropolitan statistical area in which the store is located in 1999.

• LN (AGE) _i is the natural log of the age of store i (in months) during the time of the audit.

• SALES _i is the total sales at store i in 1999.

  WAGE _i is the average hourly wage at store i in 1999.

• REGION _j are 17 dummy variables indicating region in which store i is located.

• INVENTORY_DEPTH _i is the total number of units in store i divided by the number of products in store i.

• PRODUCT_DENSITY _i is the number of products in store i divided by the total selling area of store i.

• STORAGE_SIZE _i is the backroom area of store i divided by the total selling area of store i.

• LABOR_INTENSITY _i is the payroll expenses at store i in 1999 divided by sales at store i in 1999.

• SM TURNOVER _i is a dummy variable indicating the departure of store manager at store i in 1999.

• FT TURNOVER _i is the total number of full-time employees in store i that departed in 1999 divided by the average number of full-time employees in store i.

• PT TURNOVER _i is the total number of part-time employees in store i that departed in 1999 divided by the average number of part-time employees in store i.

• TRAINING _i is the total number of “trainer months” at store i in 1999.

Findings: The authors find significant positive relationships between % phantom products and inventory level per product, total number of products in a given area, employee workload, and store manager turnover. The authors find partial support for the positive relationship between employee turnover and % phantom products. The authors also find a significant negative relationship between % phantom products and the amount of training at the store.

4.1.3 Ton and Raman (2007)

Research Site: The authors examine the effect of product variety and inventory levels on store sales using data from Borders Group.

Data: The authors collected data from physical audits of all Borders stores from 1999 to 2002. The dataset includes 356 stores, some of which opened between 1999 and 2002. As a result the authors do not have four years of data for all 356 stores.

Dependent Variables: The authors use two dependent variables. First is the percentage of phantom products, products that are in storage areas but not on the selling floor. The second dependent variable is store sales.

Independent variables: The authors use the following independent variables: inventory level per product, total number of products at a store.

Empirical Model: The authors estimate the parameters of equation (3) to examine the effect of product variety and inventory levels on % phantom products and estimate the parameters of equation (4) to examine the effect of % phantom products on store sales. In both equations, the authors control for factors that vary over time for stores and are different across stores (seasonality, unemployment rate in the store’s metropolitan statistical area, amount of labor used in a month, employee turnover, full-time employees as a percentage of total employees, store manager turnover, and the number of competitors in the local market), factors that vary over time but are invariant across stores (year fixed effects), and factors that are time-invariant for a store but vary across stores (store fixed effects).

The authors use ordinary least squares (OLS) estimators in estimating both equations (3) and (4) and report the heteroskedasticity robust standard errors for OLS. In addition to OLS estimators, the authors also treat equations (3) and (4) as seemingly unrelated regressions (SUR) allowing for correlation in the error terms across two equations. In addition, because of autocorrelation in the error terms of equation (4), the authors consider a flexible structure of the variance covariance matrix of the errors with first-order autocorrelation and estimate the parameters of (4) using maximum likelihood estimation.

$$\begin{aligned}\%PHANTOM\_PRODUCTS_{it}=\ & \alpha_i+\lambda_t+ \beta_1\,PRODUCT\_VARIETY_{it}\\ &+\beta_2INVENTORY\,\_LEVEL_{it}+ X_{it}\beta+\varepsilon_{it}\end{aligned}$$

((3))

$$\begin{aligned}SALES_{it} =\ & \eta_{i}+\theta_t+\gamma_1\, \%PHANTOM\_PRODUCTS_{it}+\gamma_2\,PRODUCT\,\_VARIETY_{it}\\&+\gamma_3\, INVENTORY\,\_LEVEL_{it}+X_{it}\gamma+\varepsilon_{it}\end{aligned}$$

((4))

Each of the variables is defined below:

• %PHANTOM_PRODUCTS _it is products that are in storage areas but not on floor at store i in year t at the time of the physical audit divided by the # of products at store i in year t at the time of the physical audit

• SALES _it is sales during the month preceding the audit at store i in year t

• PRODUCT_VARIETY _it is the # of products at the store at the time of the physical audit at store i in year t

• INVENTORY_LEVEL _it is the # of units at the store at the time of the physical audit at store i in year t divided by the # of products at the store at the time of the physical audit at store i in year t

• The vector X _it represents the following control variables:

• SEASONALITY _j is the seasonality index for month j in which the audit is conducted at store. Let $S_{ijt}$=sales at store i in month j in year t. Then the seasonality index for month j is.

  $$\frac{{\sum\limits_{t = 1}^4 {\sum\limits_{i = 1}^{267} {S_{ijt} } } }}{{\left( {{{\sum\limits_{t = 1}^4 {\sum\limits_{j = 1}^{12} {\sum\limits_{i = 1}^{267} {S_{ijt} } } } } \mathord{\bigg/ \kern-\nulldelimiterspace} {48}}}\right)}}$$

• UNEMPLOYMENT _it is the unemployment rate of the metropolitan statistical area in which the store is located during the month preceding the audit at store i in year t.

• LABOR _it is the payroll expenses during the month preceding the audit at store i in year t.

• EMPLOYEE_TURNOVER _it is the fraction of employees that are charged with managing inventory that had left during the month preceding the audit at store i in year t.

• PROPORTION_FULL _it is the fraction of full-time employees during the month preceding the audit at store i in year t.

• SM_TURNOVER _it is a dummy variable that has a value of 1 if the store manager had left the company voluntarily since the last physical audit at store i in year t.

• COMPETITION _it is the total number of Barnes & Noble and Borders stores in the area during the month preceding the audit at store i in year t.

• PLAN_SALES _it is the forecasted sales during the month preceding the audit at store i in year t.

Findings: The authors find that increasing both product variety and inventory level per product at a store is associated with an increase in % phantom products. The authors also find that an increase in % phantom products is associated with a decrease in store sales. Consequently, increasing product variety and inventory levels has an indirect effect on store sales. This indirect negative effect, however, is smaller than the direct positive effect of increasing inventory levels and product variety on store sales.