# Logistics and transportation

What is the meaning of logistics?

How do firms go about planning and analyzing their logistics capabilities?

Jacobs, F., & Chase, R. (2014). Operations and supply chain management (14 ed.). New York: McGraw-Hill

### LOGISTICS

The Association for Operations Management defines logistics as “the art and science of obtaining, producing, and distributing material and product in the proper place and in proper quantities.” This is a fairly broad definition, and this chapter will focus on how to analyze where we locate warehouses and plants and how to evaluate the movement of materials to and from those locations. The term international logistics refers to managing these functions when the movement is on a global scale. Clearly, if the China-made sweatshirt is sold in the United States or Europe, this involves international logistics.

Logistics

The art and science of obtaining, producing, and distributing material and product in the proper place and in the proper quantities.

International logistics

All functions concerned with the movement of materials and finished goods on a global scale.

There are companies that specialize in logistics, such as United Parcel Service (UPS), FedEx, and DHL. These global companies are in the business of moving everything from flowers to industrial equipment. Today a manufacturing company most often will contract with one of those companies to handle many of its logistics functions. In this case, those transportation companies often are called a third-party logistics company. The most basic function would be simply moving the goods from one place to another. The logistics company also may provide additional services such as warehouse management, inventory control, and other customer service functions.

Third-party logistics company

A company that manages all or part of another company’s product delivery operations.

Logistics is big business, accounting for 8 to 9 percent of the U.S. gross domestic product, and growing. Today’s modern, efficient warehouse and distribution centers are the heart of logistics. These centers are carefully managed and efficiently operated to ensure the secure storage and quick flow of goods, services, and related information from the point of origin to the point of consumption.

EACH BUSINESS DAY, FEDEX EXPRESS MOVES MORE THAN 3.5 MILLION PACKAGES THROUGH 10 AIR EXPRESS HUBS AROUND THE GLOBE.

376

LO15–2

Contrast logistics and warehouse design alternatives.

### DECISIONS RELATED TO LOGISTICS

The problem of deciding how best to transport goods from plants to customers is a complex one that affects the cost of a product. Major trade-offs related to the cost of transporting the product, speed of delivery, and flexibility to react to changes are involved. Information systems play a major role in coordinating activities and include activities such as allocating resources, managing inventory levels, scheduling, and order tracking. A full discussion of these systems is beyond the scope of this book, but we cover basic inventory control in other chapters.

Transportation Modes A key decision area is deciding how material will be transported. The Logistics-System Design Matrix shown in Exhibit 15.1 depicts the basic alternatives. There are six widely recognized modes of transportation: highway (trucks), water (ships), air (aircraft), rail (trains), pipelines, and hand delivery. Each mode is uniquely suited to handle certain types of products, as described next:

Highway (truck). Actually, few products are moved without some highway transportation. The highway offers great flexibility for moving goods to virtually any location not separated by water. Size of the product, weight, and liquid or bulk can all be accommodated with this mode.

Strategy

Water (ship). Very high capacity and very low cost, but transit times are slow, and large areas of the world are not directly accessible to water carriers. This mode is especially useful for bulk items such as oil, coal, and chemical products.

Air. Fast but expensive. Small, light, expensive items are most appropriate for this mode of transportation.

Rail (trains). This is a fairly low-cost alternative, but transit times can be long and may be subject to variability. The suitability of rail can vary depending on the rail infrastructure. The European infrastructure is highly developed, making this an attractive alternative compared to trucks, while in the United States, the railroad infrastructure has declined over the last 50 years, making it less attractive.

Pipelines. This is highly specialized and limited to liquids, gases, and solids in slurry forms. No packaging is needed and the costs per mile are low. The initial cost to build a pipeline is very high.

Hand Delivery. This is the last step in many supply chains. Getting the product in the customer’s hand is often a slow and costly activity due to the high labor content.

 exhibit 15.1 Logistics-System Design Matrix: Framework Describing Logistics Processes

377

Few companies use a single mode of transportation. Multimodal solutions are the norm, and finding the correct multimode strategies can be a significant problem. The problem of coordination and scheduling the carriers requires comprehensive information systems capable of tracking goods through the system. Standardized containers often are used so that a product can be transferred efficiently from a truck to an airplane or ship.

Warehouse Design Special consolidation warehouses are used when shipments from various sources are pulled together and combined into larger shipments with a common destination. This improves the efficiency of the entire system. Cross-docking is an approach used in these consolidation warehouses, where, rather than making larger shipments, large shipments are broken down into small shipments for local delivery in an area. This often can be done in a coordinated manner so that the goods never are stored in inventory.

Cross-docking

An approach used in consolidation warehouses where, rather than making larger shipments, large shipments are broken down into small shipments for local delivery in an area.

Retailers receive shipments from many suppliers in their regional warehouses and immediately sort those shipments for delivery to individual stores by using cross-docking systems coordinated by computerized control systems. This results in a minimal amount of inventory being carried in the warehouses.

Hub-and-spoke systems combine the idea of consolidation and that of cross-docking. Here the warehouse is referred to as a “hub” and its sole purpose is sorting goods. Incoming goods are sorted immediately to consolidation areas, where each area is designated for shipment to a specific location. Hubs are located in strategic locations near the geographic center of the region they are to serve to minimize the distance a good must travel.

Hub-and-spoke systems

Systems that combine the idea of consolidation and that of cross-docking.

Designing a system is an interesting and complex task. The following section focuses on the plant and warehouse location problem as representative of the types of logistics decisions that need to be made. Logistics is a broad topic, and its elements evolve as the value-added services provided by major logistics vendors expand. Having the proper network design is fundamental to efficiency in the industry.

### LOCATING LOGISTICS FACILITIES

The problem of facility location is faced by both new and existing businesses, and its solution is critical to a company’s eventual success. An important element in designing a company’s supply chain is the location of its facilities. For instance, 3M has moved a significant part of its corporate activity, including R&D, to the more temperate climate of Austin, Texas. Toys “Я” Us has opened locations in Japan as a part of its global strategy. Disney chose Shanghai for its Chinese theme park, and Boeing assembles the 787 Dreamliner in South Carolina. Manufacturing and service companies’ location decisions are guided by a variety of criteria defined by competitive imperatives. Criteria that influence manufacturing plant and warehouse location planning are discussed next.

LO15–3

Analyze logistics-driven location decisions.

Proximity to Customers For example, Japan’s NTN Driveshafts built a major plant in Columbus, Indiana, to be closer to major automobile manufacturing plants in the United States—whose buyers want their goods delivered yesterday. Such proximity also helps ensure that customer needs are incorporated into products being developed and built.

Strategy

Business Climate A favorable business climate can include the presence of similar-sized businesses, the presence of companies in the same industry and, in the case of international locations, the presence of other foreign companies. Probusiness government legislation and local government intervention to facilitate businesses locating in an area via subsidies, tax abatements, and other support are also factors.

Total Costs The objective is to select a site with the lowest total cost. This includes regional costs, inbound distribution costs, and outbound distribution costs. Land, construction, labor, taxes, and energy costs make up the regional costs. In addition, there are hidden costs that are difficult to measure. These involve (1) excessive moving of preproduction material between locations before final delivery to the customers and (2) loss of customer responsiveness arising from locating away from the main customer base.

378

Infrastructure Adequate road, rail, air, and sea transportation is vital. Energy and telecommunications requirements also must be met. In addition, the local government’s willingness to invest in upgrading infrastructure to the levels required may be an incentive to select a specific location.

Quality of Labor The educational and skill levels of the labor pool must match the company’s needs. Even more important are their willingness and ability to learn.

Suppliers A high-quality and competitive supplier base makes a given location suitable. The proximity of important suppliers’ plants also supports lean production methods.

Other Facilities The location of other plants or distribution centers of the same company may influence a new facility’s location in the network. Issues of product mix and capacity are strongly interconnected to the location decision in this context.

Free Trade Zones A foreign trade zone or a free trade zone is typically a closed facility (under the supervision of the customs department) into which foreign goods can be brought without being subject to the normal customs requirements. There are about 260 such free trade zones in the United States today. Such specialized locations also exist in other countries. Manufacturers in free trade zones can use imported components used in production of the final product and delay payment of customs duties until the product is shipped into the host country.

A closed facility (under the supervision of government customs officials) into which foreign goods can be brought without being subject to the payment of normal import duties.

Political Risk The fast-changing geopolitical scenes in numerous nations present exciting, challenging opportunities. But the extended phase of transformation that many countries are undergoing makes the decision to locate in those areas extremely difficult. Political risks in both the country of location and the host country influence location decisions.

Government Barriers Barriers to enter and locate in many countries are being removed today through legislation. Yet many nonlegislative and cultural barriers should be considered in location planning.

Trading Blocs The Central America Free Trade Agreement (CAFTA) is one of the new trading blocs in our hemisphere. Such agreements influence location decisions, both within and outside trading bloc countries. Firms typically locate, or relocate, within a bloc to take advantage of new market opportunities or lower total costs afforded by the trading agreement. Other companies (those outside the trading bloc countries) decide on locations within the bloc so as not to be disqualified from competing in the new market. Examples include the location of various Japanese auto manufacturing plants in Europe before 1992 as well as recent moves by many communications and financial services companies into Mexico in a post-NAFTA environment.

A group of countries that agree on a set of special arrangements governing the trading of goods between member countries. Companies may locate in places affected by the agreement to take advantage of new market opportunities.

Environmental Regulation The environmental regulations that impact a certain industry in a given location should be included in the location decision. Besides measurable cost implications, these regulations influence the relationship with the local community.

Host Community The host community’s interest in having the plant in its midst is a necessary part of the evaluation process. Local educational facilities and the broader issue of quality of life are also important.

Competitive Advantage An important decision for multinational companies is the nation in which to locate the home base for each distinct business. Porter suggests that a company can have different home bases for distinct businesses or segments. Competitive advantage is created at a home base where strategy is set, the core product and process technology are created, and a critical mass of production takes place. So a company should move its home base to a country that stimulates innovation and provides the best environment for global competitiveness.1 This concept can also be applied to domestic companies seeking to gain sustainable competitive advantage. It partly explains the southeastern states’ recent emergence as the preferred corporate destination within the United States (that is, their business climate fosters innovation and low-cost production).

379

OSCM AT WORK

Boeing Produces First 787 Dreamliner in South Carolina

Boeing has always assembled its large jets in Seattle, Washington, but that recently changed. Boeing rolled out the first jetliner made in the American South on April 27, 2012, amid fireworks and the cheers of thousands of workers. By the end of 2013, the plant should be producing about three-and-a-half of the revolutionary aircraft per month. The plant was a source of political controversy after the National Labor Relations Board brought a complaint against Boeing alleging that the nonunion South Carolina plant was built in retaliation for past union strikes at Boeing’s other plant located in Washington. The complaint was dropped after the Machinists Union approved a contract extension, and Boeing promised to build a new version of the 787 in Washington. So in the future Boeing will be building the plane in two locations, separated by 2,100 nautical miles.

Boeing workers gather around a 787 at the company’s assembly plant in North Charleston, S.C., on Friday, April 27, 2012.

#### Plant Location Methods

As we will see, there are many techniques available for identifying potential sites for plants or other types of facilities. The process required to narrow the decision down to a particular area can vary significantly depending on the type of business and the competitive pressures that must be considered. As we have discussed, there are often many different criteria that need to be considered when selecting from the set of feasible sites.

In this section, we sample three different types of techniques that have proven to be very useful to many companies. The first is the factor-rating system that allows us to consider many different types of criteria using simple point-rating scales. Next, we consider the transportation method of linear programming, a powerful technique for estimating the cost of using a network of plants and warehouses. Following this, we consider the centroid method, a technique often used by communications companies (cell phone providers) to locate their transmission towers. Finally, later in the chapter we consider how service firms such as McDonald’s and State Farm Insurance use statistical techniques to find desirable locations for their facilities.

Analytics

Keep in mind that each of the techniques described here would be used within the context of a more comprehensive strategy for locating a facility. Typically, the strategy would employ some type of search where major regions are first considered; it is narrowed down to areas, then to potential sites, and finally a choice is made between a few alternatives.

380

Think of these techniques as simple tools that are used in different ways to zero in on a site. The factor-rating system is useful when nonquantitative factors are important. The linear programming and centroid methods are quantitative and may be tied to cost and service-related criteria. The statistical techniques are good when there is significant variability in criteria measures. The techniques are often used in combination to solve a real problem.

Factor – Rating Systems Factor-rating systems are perhaps the most widely used of the general location techniques because they provide a mechanism to combine diverse factors in an easy-to-understand format.

Factor-rating systems

An approach for selecting a facility location by combining a diverse set of factors. Point scales are developed for each criterion. Each potential site is then evaluated on each criterion and the points are combined to calculate a rating for the site.

By way of example, a refinery assigned the following range of point values to major factors affecting a set of possible sites:

 RANGE Fuels in region 0 to 330 Power availability and reliability 0 to 200 Labor climate 0 to 100 Living conditions 0 to 100 Transportation 0 to 50 Water supply 0 to 10 Climate 0 to 50 Supplies 0 to 60 Tax policies and laws 0 to 20

Each site was then rated against each factor, and a point value was selected from its assigned range. The sums of assigned points for each site were then compared. The site with the most points was selected.

A major problem with simple point-rating schemes is that they do not account for the wide range of costs that may occur within each factor. For example, there may be only a few hundred dollars’ difference between the best and worst locations on one factor and several thousands of dollars’ difference between the best and the worst on another. The first factor may have the most points available to it but provide little help in making the location decision; the second may have few points available but potentially show a real difference in the value of locations. To deal with this problem, it has been suggested that points possible for each factor be derived using a weighting scale based on standard deviations of costs rather than simply total cost amounts. In this way, relative costs can be considered.

Transportation Method of Linear Programming The transportation method is a special linear programming method. (Note that linear programming is developed in detail in Appendix A.) It gets its name from its application to problems involving transporting products from several sources to several destinations. The two common objectives of such problems are to either (1) minimize the cost of shipping n units to m destinations or (2) maximize the profit of shipping n units to m destinations.

Transportation method

A special linear programming method that is useful for solving problems involving transporting products from several sources to several destinations.

EXAMPLE 15.1: U.S. Pharmaceutical Company

Suppose the U.S. Pharmaceutical Company has four factories supplying the warehouses of four major customers and its management wants to determine the minimum-cost shipping schedule for its monthly output to these customers. Factory supply, warehouse demands, and shipping costs per case for these drugs are shown in Exhibit 15.2A.

For a step-by-step walkthrough of this example, visit www.mhhe.com/jacobs14e_sbs_ch15.

The transportation matrix for this example appears in Exhibit 15.2B, where supply availability at each factory is shown in the far right column and the warehouse demands are shown in the bottom row. The shipping costs are shown in the small boxes within the cells. For example, the cost to ship one unit from the Indianapolis factory to the customer warehouse in

381

 exhibit 15.2 A. Data for U.S. Pharmaceutical Transportation Problem

B. Transportation Matrix for U.S. Pharmaceutical Problem

Columbus is \$25. The actual flows would be shown in the cells intersecting the factory rows and warehouse columns.

SOLUTION

This problem can be solved by using Microsoft Excel’s Solver function. If you are not familiar with the Solver, you should study Appendix A, “Linear Programming Using the Excel Solver.” Exhibit 15.3 shows how the problem can be set up in the spreadsheet. Cells B6 through E6 contain the requirement for each customer warehouse. Cells F2 through F5 contain the amount that can be supplied from each plant. Cells B2 through E5 are the cost of shipping one unit for each potential plant and warehouse combination.

To view a tutorial on Transportation Method Solver, visit www.mhhe.com/jacobs14e_tutorial_ch15.

Cells for the solution of the problem are B9 through E12. These cells can initially be left blank when setting up the spreadsheet. Column cells F9 through F12 are the sum of each row, indicating how much is actually being shipped from each factory in the candidate solution. Similarly, row cells B13 through E13 are sums of the amount being shipped to each customer in the candidate solution. The Excel Sum function can be used to calculate these values.

The cost of the candidate solution is calculated in cells B16 through E19. Multiplying the amount shipped in the candidate solution by the cost per unit of shipping over that particular route makes this calculation. For example, multiplying B2 by B9 in cell B16 gives the cost of shipping between Indianapolis and Columbus for the candidate solution. The total cost shown in cell F20 is the sum of all these individual costs.

To solve the problem, the Excel Solver application needs to be accessed. The Solver is found by selecting Data and then Solver from the Excel menu. A screen similar to what is shown below should appear. If you cannot find Solver at that location, the required add-in might not have been activated when Excel was initially installed on your computer.

382

 exhibit 15.3 Excel Screen Showing the U.S. Pharmaceutical Problem

For the Excel template, visit www.mhhe.com/jacobs14e.

Solver parameters now need to be set. First set the target cell. This is the cell where the total cost associated with the solution is calculated. In our sample problem, this is cell F20, which sums the values in cells B16 through E19. Next we need to indicate that we are minimizing this cell. Selecting the “Min” button does this. The location of our solution is indicated in the “By Changing Variable Cells.” These cells are B9 through E12 in our example.

Next we need to indicate the constraints for our problem. For our transportation problem we need to be sure that customer demand is met and that we do not exceed the capacity of our manufacturing plants. To ensure that demand is met, click on “Add” and highlight the range of cells where we have calculated the total amount being shipped to each customer. This range is B13 to E13 in our example. Next select “=” indicating that we want the amount shipped to equal demand. Finally, on the right side enter the range of cells where the actual customer demand is stated in our spreadsheet. This range is B6 to E6 in our example.

Excel® screen shots from Microsoft® Excel. © 2010 Microsoft Corporation.

383

The second set of constraints that ensures that the capacity of our manufacturing plants is not exceeded is entered similarly. The range of cells that indicate how much is being shipped from each factory is F9 to F12. These values need to be less than or equal to (< =) the capacity of each factory, which is in cells F2 to F5.

Two options need to be set for solving transportation problems. First, set the solving method to “Simplex LP.” This tells the Solver that there are no nonlinear calculations in our spreadsheet. This is important because the Solver can use a very efficient algorithm to calculate the optimal solution to this problem if this condition exists. Next, check the “Make Unconstrained Variables Non-Negative” box. This tells Solver that the values in our solution need to be greater than or equal to zero. In transportation problems, shipping negative quantities does not make any sense. Click “Solve” to actually solve the problem. Solver will notify you that it found a solution. Indicate that you want that solution saved. Finally, click OK to go back to the main spreadsheet. The solution should be in cells B9 to E12.

The transportation method can be used to solve many different types of problems if it is applied innovatively. For example, it can be used to test the cost impact of different candidate locations on the entire production–distribution network. To do this we might add a new row that contains the unit shipping cost from a factory in a new location, say, Dallas, to the existing set of customer warehouses, along with the total amount it could supply. We could then solve this particular matrix for minimum total cost. Next we would replace the factory located in Dallas in the same row of the matrix with a factory at a different location, Houston, and again solve for minimum total cost. Assuming the factories in Dallas and Houston would be identical in other important respects, the location resulting in the lower total cost for the network would be selected.

For additional information about using the Solver, see Appendix A, “Linear Programming Using the Excel Solver.”

#### Centroid Method

The centroid method is a technique for locating single facilities that considers the existing facilities, the distances between them, and the volumes of goods to be shipped. The technique is often used to locate intermediate or distribution warehouses. In its simplest form, this method assumes that inbound and outbound transportation costs are equal, and it does not include special shipping costs for less than full loads.

Centroid method

A technique for locating single facilities that considers the existing facilities, the distances between them, and the volumes of goods to be shipped.

Another major application of the centroid method today is the location of communication towers in urban areas. Examples include radio, TV, and cell phone towers. In this application the goal is to find sites that are near clusters of customers, thus ensuring clear radio signals. The centroid method finds a simple mathematical point. Once it is found, the problem should consider qualitative factors such as geography, roads, and utilities to find an exact location.

The centroid method begins by placing the existing locations on a coordinate grid system. Coordinates are usually based on longitude and latitude measures due to the rapid adoption of GPS systems for mapping locations. To keep it simple for our examples, we use arbitrary X, Y coordinates. Exhibit 15.4 shows an example of a grid layout.

The centroid is found by calculating the X and Y coordinates that result in the minimal transportation cost. We use the formulas

Cx=dixViViCy=diyViVi

${C}_{x}=\frac{\sum {d}_{ix}{V}_{i}}{\sum {V}_{i}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{C}_{y}=\frac{\sum {d}_{iy}\text{\hspace{0.17em}}{V}_{i}}{\sum {V}_{i}}$

[15.1]

where

Cx = X coordinate of the centroid

Cy = Y coordinate of the centroid

dix = X coordinate of the ith location

diy = Y coordinate of the ith location

Vi = Volume of goods moved to or from the ith location

384

 exhibit 15.4 Grid Map for Centroid Example

For the Excel template, visit www.mhhe.com/jacobs14e.

EXAMPLE 15.2: HiOctane Refining Company

HiOctane Refining Company needs to locate an intermediate holding facility between its refining plant in Long Beach and its major distributors. Exhibit 15.4 shows the coordinate map and the amount of gasoline shipped to or from the plant and distributors.

In this example, for the Long Beach location (the first location), dix = 325, diy = 75, and Vi = 1,500.

For a step-by-step walkthrough of this example, visit www.mhhe.com/jacobsl4e_sbs_ch15.

SOLUTION

Using the information in Exhibit 15.4, we can calculate the coordinates of the centroid:

Cx=(325×1,500)+(400×250)+(450×450)+(350×350)+(25×450)1,500+250+450+350+450=923,7503,000=307.9

$\begin{array}{c}{C}_{x}=\frac{\left(325×1,500\right)\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\left(400×250\right)+\left(450×450\right)+\left(350×350\right)+\left(25×450\right)}{1,500+250+450+350+450}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{923,750}{3,000}=307.9\end{array}$

Cy=(75×1,500)+(150×250)+(350×450)+(400×350)+(450×450)1,500+250+450+350+450=650,0003,000=216.7

$\begin{array}{c}{C}_{y}=\frac{\left(75×1,500\right)+\left(150×250\right)+\left(350×450\right)+\left(400×350\right)+\left(450×450\right)}{1,500+250+450+350+450}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{650,000}{3,000}=216.7\end{array}$

This gives management the X and Y coordinates of approximately 308 and 217, respectively, and provides an initial starting point to search for a new site. By examining the location of the calculated centroid on the grid map, we can see that it might be more cost-efficient to ship directly between the Long Beach plant and the Anaheim distributor than to ship via a warehouse near the centroid. Before a location decision is made, management would probably recalculate the centroid, changing the data to reflect this (that is, decrease the gallons shipped from Long Beach by the amount Anaheim needs and remove Anaheim from the formula).

385

#### Locating Service Facilities

Because of the variety of service firms and the relatively low cost of establishing a service facility compared to one for manufacturing, new service facilities are far more common than new factories and warehouses. Indeed, there are few communities in which rapid population growth has not been paralleled by concurrent rapid growth in retail outlets, restaurants, municipal services, and entertainment facilities.

Services typically have multiple sites to maintain close contact with customers. The location decision is closely tied to the market selection decision. If the target market is college-age groups, locations in retirement communities—despite desirability in terms of cost, resource availability, and so forth—are not viable alternatives. Market needs also affect the number of sites to be built and the size and characteristics of the sites. Whereas manufacturing location decisions are often made by minimizing costs, many service location decision techniques maximize the profit potential of various sites. Next we present a multiple regression model that can be used to help select good sites.

EXAMPLE 15.3: Screening Hotel Location Sites

Selecting good sites is crucial to a hotel chain’s success. Of the four major marketing considerations (price, product, promotion, and location), location and product have been shown to be most important for multisite firms. As a result, hotel chain owners who can pick good sites quickly have a distinct competitive advantage.

Exhibit 15.5 shows the initial list of variables included in a study to help a hotel chain screen potential locations for its new hotels. Data were collected on 57 existing sites. Analysis of the data identified the variables that correlated with operating profit in two years. (See Exhibit 15.6.)

SOLUTION

An introduction into how regression models are constructed is included in Chapter 18. The details of how variables are selected for inclusion in the model are beyond the scope of this book. Basically the variables that are the most strongly correlated (as shown in Exhibit 15.6) are used in a linear mathematical model to maximize the fit between profitability and characteristics of each potential site. The correlations are a relative measure of the amount of statistical variation explained by each variable. Variables with values closer to 1 or −1 explain more variation than those closer to zero.

The analysis done by the hotel chain indicated that the best variables to include in the model were the following:

• State population per inn (STATE)

• Room rate for the inn (PRICE)

• Square root of the income of the area (INCOME)

• College enrollment within four miles (COLLEGE)

The final form for this model is as follows:

Profitability = 39.05 − 5.41 × State population per inn (1,000)

+ 5.86 × Room rate for the inn

− 3.91 × Square root of the income of the area (1,000)

+ 1.75 × College enrollment within 4 miles

For a step-by-step walkthrough of this example, visit www.mhhe.com/jacobs14e_sbs_ch15.

386

 exhibit 15.5 Independent Variables Collected for the Initial Model-Building Stage

 exhibit 15.6 A Summary of the Variables That Correlated with Operating Margin

387

The model shows that profitability is negatively affected by the state population per inn, positively affected by room rate, negatively affected by area income (the inns do better in lower-income areas), and positively affected by colleges nearby.

The hotel chain implemented the model on a spreadsheet and routinely uses the spreadsheet to screen potential real estate acquisitions. The founder and president of the hotel chain has accepted the model’s validity and no longer feels obligated to personally select the sites.

This example shows that a specific model can be obtained from the requirements of service organizations and used to identify the most important features in site selection.