The Decision Sciences Journal of Innovative Education

 Spreadsheet Modeling of Spatial Problems for the Classroom

 Michael M. Pearson, Ph.D.

The Stanford H. Rosenthal Distinguished Professor of Risk and Entrepreneurship, and

Professor of Marketing

College of Business Administration

Loyola University New Orleans

6363 St. Charles Avenue

New Orleans, Louisiana 70118

Phone: (504) 865-2448

Fax: (504) 865-3496

E-mail: pearson@beta.loyno.edu

Lee Mundell, Ph.D.

Associate Professor of Decision Science

College of Business Administration

Loyola University New Orleans

6363 St. Charles Avenue

New Orleans, Louisiana 70118

Phone: (504) 865-2549

Fax: (504) 865-3496

E-mail: mundeI1@beta.1oyno.edu

This is the second revised copy of an article submitted as a teaching brief to the DSJIE.

Spreadsheet Modeling of Spatial Problems for the Classroom

            A spatial problem is one that requires a decision to be made within a spatial area. Where do we put our warehouses?  Where do we locate our stores within a trade area?  How do we arrange departments in the retail store, or on the retail shelf? These are problems that are often solved by modeling, and spreadsheet models are but one of many types of models that can be used.    The use of the LOOKUP command greatly increases the potential of the spreadsheet to solve spatial problems, and especially to solve spatial problems in a classroom setting. This command changes spreadsheet modeling in the classroom from simply a number crunching exercise by students to a visual interaction between students and the spatial problem.

Objectives of Paper

            This teaching brief presents a simple spreadsheet-based spatial model, and shows how it has been used in the classroom to build student awareness of spatial problems and how the spreadsheet can be used to model these problems.

The Exercise

            Shelf-space allocation and arrangement is a typical spatial problem faced by retailers.  How do you get the most return out of an 8’x 5’ shelving unit?  How much space do you allocate to each product or each product group?  Which items should be placed at eye-level?  Which items should be placed on the left, middle and center of the shelving unit?  Should we be trying to maximize our dollar sales, percentage gross margin or dollar gross margin as our return?

Planograms

            Planograms are shelf management tools used by both retailers and manufacturers to determine the space allocation and profitability of brands within a product category.  Retailers use information from their databases to determine which products deserve more shelf space or better shelf space (eye level) based upon profitability and product movement.  Planograms provide consistency of merchandising throughout the units of a chain.  Nearly all supermarkets and mass merchandising stores use some form of planograms. 

Objectives of the Exercise  

            This particular spatial exercise has been used both in the retail management classroom and the decision sciences classroom.  From a retail viewpoint, this exercise is designed to show that (1) there are dollar and cents strategies for how items are arranged on the shelf, (2) there is a position value of various spaces on the shelving unit, and (3) there are a variety of measures that can be used for judging the return of various shelf layout strategies.  From a decision sciences viewpoint, the objectives of this exercise are to (1) make students aware of spatial problems as a category dealt with through decision sciences, and (2) show how the spreadsheet can be used to model these problems.  Both of these groups of objectives are presented and discussed in order to give the reader some background for classroom discussion arising from the use of this exercise.  

The Planogram Exercise and its Use in the Classroom

            This is a relatively simple exercise that takes students only a short time to complete.  Each student is given a copy of the handout sheet. (See Exhibit 1-Student Handout.)  The students are placed into groups of three to four and asked to come up with a group decision of where to put the products on the retailer’s shelving unit.  When they have reached their decision, they can enter their group’s decision onto a planogram, the computerized version of this shelving diagram.  When all groups have entered and saved their decisions, class discussion can begin.

            Each group is given a short time to explain the logic behind its planogram strategy.  The quantitative results of the group’s strategy is calculated by the spreadsheet underlying the exercise, showing sales, percentage gross margin, and dollar gross margin resulting from this plan-o-gram strategy. 

Student Reaction to the Exercise

Student reaction is usually focused in three areas. 

1. The logic behind the Position Value Matrix – This is always the first area of discussion.  Students seem very intrigued by how the customer views the shelving unit.  (Vertically on Exhibit 2, the eye first starts at eye-level or slightly below (rows 2 & 3).  The eye then moves below eye- level (row 4), then to above eye-level (row 1), and finally to the bottom (row 5).  Horizontally, the eye follows the same pattern, starting at left-center (columns C & D), then to right-center (columns E & F), then to far left and finally to far right.  This is deep consumer behavior material that might fit best in a marketing class rather than operations management.  However, this is where the students always start the discussion, which leads to some interesting student-generated examples about shopping behavior.
2. The workings of the LOOKUP Table – The students may not bring up this topic on their own, but because of the importance of this tool for this model, the discussion is directed to this point by the instructor. The students are shown how to use the VLOOKUP and the HLOOKUP functions.  This seems to be quite rapidly assimilated by the students because they have just worked with an application through the exercise.  We have tried to talk about the LOOKUP Table independent of this exercise.  There always seems to be less interest and assimilation of the concept by the students when they have not engaged in the exercise first.
3. The flow chart – Discussion of the model always finishes with the flow chart (Exhibit 3).  Without understanding how the entire model works there does not seem to be closure with the exercise.  Evidence of this can be seen when using this model in retailing classes.  Many of the students here are from majors outside the business area and do not have the background with spreadsheets and modeling as do business students.  While these students do think the consumer behavior elements of the Position Value Matrix are intriguing, they do not seem to grasp the concept or significance of spatial modeling.

How is the spreadsheet model underlying this exercise constructed?

            The basic construction of this spreadsheet model is shown in Exhibit 3.  The model consists of several parts:

Input Matrix  (Same as the planogram diagram on the student handout.) - The student group will enter an item number  “1” (pencils) into the A3 position on the computer spreadsheet to show where it wants to place this item on the shelf.  The group will then enter item number “2” (desk calendars) into the B4 position to show that is where it wants that item placed on the shelf. 

Lookup Table (Exactly the same in structure as the Merchandise Table on the student handout.) - When the student group places the “1” in position A3 of the Input Matrix, item values of “30%” (gross margin %), “6.5” (stock turn) and “$840” (dollar inventory) are picked up from the Lookup Table by LOOKUP Commands programmed into the A3 positions of the three storage matrices (Gross Margin % Storage Matrix, Stock Turn Storage Matrix, and $ Inventory Storage Matrix).                                                           

Position Value Matrix – This matrix is imbedded in the spreadsheet, where the students initially cannot see it.  As shown in Exhibit 2, this matrix gives a value (30% - 100%) to each position space on the shelf.  This percentage is based upon visibility of different areas on the shelf.  (Eye-level has the highest visibility.  Middle areas on the shelf have more visibility than end areas.  Left is seen before right.)  When the student group places a “1” in position A3 of the input table, the position value (.8) associated with this “1” value is picked up from the Position Value Matrix and stored in this position.  (The “.8” represents 80% of the value of the best position space (100%) on the shelf.) 

Calculations of Totals - Calculating the total dollar gross margin for a cell (A3) is simply a matter of multiplying the values in the A3 positions in each of the Gross Margin %, Stock Turn, $ Inventory and Position Value Matrices.  Calculating the total dollar gross margin for the entire planogram is a matter of simply summing all the positions (A1:D4) of the $ Gross Margin Matrix.

The LOOKUP Command – The LOOKUP Command itself needs some extra attention here.  The VLOOKUP Command searches for a value in the left-most column of a table, and then returns a value in the same row from the column you specify in the table.  (There is also a HLOOKUP Command that searches the top row of a table and returns a value from the specified column, but this will not be discussed here in order to keep the explanation as simple as possible.)   When a “1” is entered into the A1 position of the input matrix, the VLOOKUP Command built into the corresponding A1 position in the Gross Margin % Matrix (VLOOKUP(A1, A1…F10, 3)), will take the value of “1” from the Input Matrix and search the first column of the Lookup Table until it finds a “1”.  The VLOOKUP Command identifies the size of the array (A1…F10), and then jumps 3 columns to the “GM %” column.  Given the row label, “1”, and the specified third column, the VLOOKUP Command selects 35%, and enters this in the A1 position of the Gross Margin % Matrix.   (A note of caution should be made to be sure to use the LOOKUP Command rather than the LOOKUP WIZARD in the newer EXCEL versions.  The LOOKUP WIZARD simply selects a value from an array given specified values for a row and a column, and separate entries must be made each time another row and column is specified.  Therefore, the LOOKUP WIZARD does not possess all the spatial attributes of the LOOKUP Command.)

What other spatial applications can you see for spreadsheet modeling?

            The unique feature of this planogram exercise has been the fact that the LOOKUP Command has actually has actually turned the spreadsheet into a spatial tool. This feature creates interest both for the authors and for their students. The authors continue to develop and use spatial exercises in the classroom. These exercises have carried spatial spreadsheet modeling into the marketing areas of store location and advertising positioning for both the newspaper and the web site. (References for these articles and papers are available at authors’ web sites listed below.) 

            Potential applications also exist for the decision sciences and operations management classrooms.  Spatial problems exist in the areas of production layout, warehouse location, inventory management and transportation.  This exercise has also served as a logical transition into optimization through linear programming.

            The primary purpose of developing this exercise, however, was to promote modeling.  We wanted to show that spreadsheet modeling as a relatively easy way to model spatial problems.  Such models can be constructed both by instructors for classroom use, or by students as project assignments.  We feel that instructors will feel more comfortable and will present with more enthusiasm when using their own models in the classroom.  The intent of this article was not to present a model that might simply be used for demonstration purposes in the classroom, but to present a spatial model that would inspire other instructors to develop their own models.

Authors’ Note:

            The authors are very happy to share the working versions of this planogram model as well as their other spatial exercises with academics for use in their classes.  These can be downloaded from our web sites at http//cba.loyno.edu/faculty/Pearson/ or http//cba.loyno.edu/faculty/Mundell/.  We are still revising and working on new applications for spatial modeling.

Exhibit 1

Planogram Exercise

Directions:  You are an employee of a retail gift shop.  New merchandise has just been delivered to your store and you have been asked by your manager to design a planogram for how this merchandise should be placed on the 8’x 5’ shelving unit as represented below on the planogram diagram in order to achieve the best results for your store.  Use the information from the merchandise table at the bottom of this handout.  Place a product number in each planogram cell in order to develop your plan.  Use only the amount of cells allocated for each product category.  Once you have decided on your planogram strategy, enter these numbers into the computer and the computer will calculate how well you did in setting the shelving unit.

                                                            Planogram Diagram 

Spreadsheet-calculated projections from shelving unit based upon your planogram strategy:

                        Projected Percentage Gross Margin:            __________

                        Projected Sales Volume:                      __________

Projected Dollars Gross Margin:            __________                                                                           

                                                              Merchandise Table

1. Number representing a product category.  Place in the planogram diagram.
2. Product category associated with number to the left.
3. Number of spaces on the planogram diagram allocated to this product.  (e.g. You can put pencils in five (and only five) boxes on the planogram diagram.)
4. Gross Margin Percentage for this product category.  (e.g. If the retailer sells $840 of pencils, this will yield a GM% of 30% or $252 (at a cost of 70% or $588.))
5. Stock Turn represents the number of times the retailer will “turn” its inventory during the year.  (e.g. The retailer is projected to turn the $840 of pencils in one unit of the plan-o-gram diagram 6.5 times during the year.  ($840 inventory x 6.5 stock turn = $5,460 projected annual sales for this cell.))
6. Inventory represents the retail value of inventory of this product in one cell of the plan-o-gram diagram.  (e.g. $840 worth of inventory fits in one planogram cell.  Therefore, the total inventory of pencils in the entire planogram diagram will be $840 x 5 allocated cells = $4,200 dollars of inventory.)

Exhibit 2

Position Value Matrix for Planogram Model*

                           A             B            C            D            E            F             G            H     

            1

            2

            3

            4

            5

* This matrix shows the value of shelf space for an eight-foot wide by five-foot high shelving unit.  The highest valued positions are at the B2 and C2 locations, with 1.0 (100%) position value (eye-level position, slightly to the left).  Products in the B3 and C3 positions are seen slightly less by the consumer, therefore, these shelf positions are valued at only 0.9 (or 90%) of the B2 and C2 positions.

Exhibit 3

Flow Chart for Planogram Model*

                                                                  GM% Storage

                                                                                                                     A  B  C  D              

                                                                                           1

                                                             2

                                                             3  .30                                       $ Sales

                                                             4       .25                                       A    B    C    D

                                                                                   1

                                    Lookup Table                             Input Matrix     ST Storage   Position Value          2         

                                     Alloc GM% ST  $Inv.               A  B  C  D        A  B  C  D                 A   B   C  D           3 4368

                1. Pencils          5    30%   6.5  $840     1                         1                   1  .7   .8   .8  .8          4       1575

                2. Calendars       2    25%   5.0  $450           2                         2                   2  .9 1.0 1.0  .9     

                3. Note Pads       3    38%   8.0  $350     3  1                 3  6.5       3  .8   .9   .9  .8       

                4. Disks              6    41%   3.5  $400     4       2                4      5.0           4  .6   .7   .7  .6            $ GM Matrix

                                                                                       A    B    C    D

                     $ Inv. Storage                  1

                                                                              A  B  C  D                                              2

                                                             1                                                               3 1310

                                                             2                                                               4        394

                                                             3  840

                                                             4     450

* Explanation – A student selects pencils (#1) to put into the A3 position of the Input Matrix. VLOOKUP commands in the respective A3 positions in the Gross Margin %, Stock Turn and $ Inventory Storage Matrices extract values from the Lookup Table and store these in the A3 cells of these respective matrices.  The $ Sales value for A3 ($4,368) is calculated by multiplying the A3 value in the $ Inventory Matrix ($840) by the A3 value in the Stock Turn Matrix (6.5) by the A3 value in the Position Value Matrix (0.9).  The $ Gross Margin value is calculated by multiplying this result by the A3 value in the Gross Margin % Matrix ($4,368 x .30 = $394).