Homework 5

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Chapter 5 • Network Design in the Supply Chain 113

LOCATING TO SPLIT THE MARKET When there are no positive externalities, firms locate to be able to capture the largest possible share of the market. A simple model first proposed by Hotelling explains the issues behind this decision.1

When firms do not control price but compete on distance from the customer, they can maximize market share by locating close to each other and splitting the market. Consider a situation in which customers are uniformly located along the line segment between 0 and 1 and two firms compete based on their distance from the customer as shown in Figure 5-1. A customer goes to the closer firm and customers who are equidistant from the two firms are evenly split between them.

If total demand is 1, Firm 1 locates at point a, and Firm 2 locates at point 1! b, the demand at the two firms, d1 and d2, is given by

Both firms maximize their market share if they move closer to each other and locate at a " b " 1/2.

Observe that when both firms locate in the middle of the line segment (a " b " 1/2), the average distance that customers have to travel is 1/4. If one firm locates at 1/4 and the other at 3/4, the average distance customers have to travel drops to 1/8 (customers between 0 and 1/2 come to Firm 1 located at 1/4 while customers between 1/2 and 1 come to Firm 2 located at 3/4). This set of locations, however, is not an equilibrium because it gives both firms an incentive to try to increase market share by moving to the middle (closer to 1/2). The result of competition is for both firms to locate close together even though doing so increases the average distance to the customer.

If the firms compete on price and the customer incurs the transportation cost, it may be optimal for the two firms to locate as far apart as possible,2 with Firm 1 locating at 0 and Firm 2 locating at 1. Locating far from each other minimizes price competition and helps the firms split the market and maximize profits.

Customer Response Time and Local Presence

Firms that target customers who value a short response time must locate close to them. Customers are unlikely to come to a convenience store if they have to travel a long distance to get there. It is thus best for a convenience store chain to have many stores distributed in an area so that most people have a convenience store close to them. In contrast, customers shop for larger quantity of goods at supermarkets and are willing to travel longer distances to get to one. Thus, supermarket chains tend to have stores that are larger than convenience stores and not as densely distributed. Most towns have fewer supermarkets than convenience stores. Discounters such as Sam’s Club target customers who are even less time sensitive. These stores are even larger than supermarkets and there are fewer of them in an area. W.W. Grainger uses about 400 facilities all over the United States to provide same-day delivery of maintenance and repair supplies to many of its customers. McMaster-Carr, a competitor, targets customers who are willing to wait for

d1 = a + 1 - b - a

2 and d2 =

1 + b - a 2

1 Jean Tirole, The Theory of Industrial Organization (Cambridge, MA: The MIT Press, 1997), 279. 2 Ibid.

a 1 ! b

0 1

FIGURE 5-1 Two Firms Locating on a Line

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Chapter 5 • Network Design in the Supply Chain 115

COMPETITIVE STRATEGY

INTERNAL CONSTRAINTS Capital, growth strategy,

existing network

PRODUCTION METHODS Skill needs, response time

FACTOR COSTS Labor, materials, site specific

PHASE I Supply Chain

Strategy

PHASE II Regional Facility

Configuration

PHASE III Desirable Sites

PHASE IV Location Choices

GLOBAL COMPETITION

TARIFFS AND TAX INCENTIVES

REGIONAL DEMAND Size, growth, homogeneity,

local specifications

POLITICAL, EXCHANGE RATE,

AND DEMAND RISK

AVAILABLE INFRASTRUCTURE

LOGISTICS COSTS Transport, inventory,

coordination

PRODUCTION TECHNOLOGIES

Cost, scale/scope impact, support required, flexibility

COMPETITIVE ENVIRONMENT

AGGREGATE FACTOR AND LOGISTICS COSTS

FIGURE 5-2 Framework for Network Design Decisions

Based on the competitive strategy of the firm, its resulting supply chain strategy, an analysis of the competition, any economies of scale or scope, and any constraints, managers must deter- mine the broad supply chain design for the firm.

Phase II: Define the Regional Facility Configuration

The objective of the second phase of network design is to identify regions where facilities will be located, their potential roles, and their approximate capacity.

An analysis of Phase II starts with a forecast of the demand by country or region. Such a forecast must include a measure of the size of the demand and a determination of the homogene- ity or variability of customer requirements across different regions. Homogeneous requirements favor large consolidated facilities, whereas requirements that vary across countries favor smaller, localized facilities.

The next step is for managers to identify whether economies of scale or scope can play a significant role in reducing costs, given available production technologies. If economies of scale or scope are significant, it may be better to have a few facilities serving many markets. For example, semiconductor manufacturers such as Advanced Micro Devices have few plants for their global markets, given the economies of scale in production. If economies of scale or scope is not significant, it may be better for each market to have its own facility.

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the profit while satisfying customer needs. The following information ideally is available in making the design decision:

Given this information, either gravity models or network optimization models may be used to design the network. We organize the models according to the phase of the network design framework at which each model is likely to be useful.

Phase II: Network Optimization Models

During Phase II of the network design framework (see Figure 5-2), a manager considers regional demand, tariffs, economies of scale, and aggregate factor costs to decide the regions where facil- ities are to be located. As an example, consider SunOil, a manufacturer of petrochemical prod- ucts with worldwide sales. The vice president of supply chain is considering several options to meet demand. One possibility is to set up a facility in each region. The advantage of such an approach is that it lowers transportation cost and also helps avoid duties that may be imposed if product is imported from other regions. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. An alternative approach is to consolidate plants in just a few regions. This improves economies of scale but increases transpor- tation cost and duties. During Phase II, the manager must consider these quantifiable trade-offs along with nonquantifiable factors such as the competitive environment and political risk.

Network optimization models are useful for managers considering regional configuration during Phase II. The first step is to collect the data in a form that can be used for a quantitative model. For SunOil, the vice president of supply chain decides to view the worldwide demand in terms of five regions—North America, South America, Europe, Africa, and Asia. The data col- lected are shown in Figure 5-3.

Annual demand for each of the five regions is shown in cells B9:F9. Cells B4:F8 contain the variable production, inventory, and transportation cost (including tariffs and duties) of pro- ducing in one region to meet demand in each individual region. All costs are in thousands of dollars. For example, as shown in cell C4, it costs $92,000 (including duties) to produce 1 mil- lion units in North America and sell them in South America. As shown in cell G4, it costs $6!million in annualized fixed cost to build a low-capacity plant in North America. Observe that the data collected at this stage are at a fairly aggregate level.

FIGURE 5-3 Cost Data (in Thousands of Dollars) and Demand Data (in Millions of Units) for SunOil

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Consider, for example, Steel Appliances (SA), a manufacturer of high-quality refrigerators and cooking ranges. SA has one assembly factory located near Denver, from which it has supplied the entire United States. Demand has grown rapidly and the CEO of SA has decided to set up another factory to serve its eastern markets. The supply chain manager is asked to find a suitable location for the new factory. Three parts plants, located in Buffalo, Memphis, and St. Louis, will supply parts to the new factory, which will serve markets in Atlanta, Boston, Jacksonville, Philadel- phia, and New York. The coordinate location, the demand in each market, the required supply from each parts plant, and the shipping cost for each supply source or market are shown in Table 5-1.

Gravity models assume that both the markets and the supply sources can be located as grid points on a plane. All distances are calculated as the geometric distance between two points on the plane. These models also assume that the transportation cost grows linearly with the quantity shipped. We discuss a gravity model for locating a single facility that receives raw material from supply sources and ships finished product to markets. The basic inputs to the model are as follows:

xn, yn: coordinate location of either a market or supply source n

Fn: cost of shipping one unit (a unit could be a piece, pallet, truckload or ton) for one mile between the facility and either market or supply source n

Dn: quantity to be shipped between facility and market or supply source n

If (x, y) is the location selected for the facility, the distance dn between the facility at loca- tion (x, y) and the supply source or market n is given by

dn = 21x - xn22 + 1y - yn22 (5.4)

FIGURE 5-6 Using Solver to Set Regional Configuration for SunOil

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and the total transportation cost (TC) is given by

TC = a k

n = 1 dnDnFn (5.5)

The optimal location is one that minimizes the total TC in Equation 5.5. The optimal solution for SA is obtained using the Solver tool in Excel (see spreadsheet Figure 5-8), as shown in Figure 5-8.

FIGURE 5-7 Optimal Regional Network Configuration for SunOil

TABLE 5-1 Locations of Supply Sources and Markets for Steel Appliances

Sources/Markets Transportation

Cost $/Ton Mile (Fn) Quantity in Tons (Dn)

Coordinates xn yn

Supply Sources

Buffalo 0.90 500 700 1,200

Memphis 0.95 300 250 600

St. Louis 0.85 700 225 825

Markets

Atlanta 1.50 225 600 500

Boston 1.50 150 1,050 1,200

Jacksonville 1.50 250 800 300

Philadelphia 1.50 175 925 975

New York 1.50 300 1,000 1,080

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The first step is to enter the problem data as shown in cells B5:F12. Next, we set the decision variables (x, y) corresponding to the location of the new facility in cells B16 and B17, respectively. In cells G5:G12, we then calculate the distance dn from the facility location (x, y) to each source or market, using Equation 5.4. The total TC is then calculated in cell B19 using Equation 5.5.

The next step is to to invoke Solver (Data | Solver). Within the Solver Parameters dialog box (see Figure 5-8), the following information is entered to represent the problem:

Set Cell: B19

Equal To: Select Min

By Changing Variable Cells: B16:B17

Select GRG Nonlinear and click on the Solve button. The optimal solution is returned in cells B16 and B17 to be 681 and 882, respectively.

The manager thus identifies the coordinates (x, y) = (681, 882) as the location of the fac- tory that minimizes total cost TC. From a map, these coordinates are close to the border between North Carolina and Virginia. The precise coordinates provided by the gravity model may not correspond to a feasible location, though. The manager should look for desirable sites close to

—5.2=SUMPRODUCT(G5:G12,D5:D12,C5: C12)

B19

G6:G125.1=SQRT(($B$16-E5)^2+($B$17-F5)^2)G5

Copied toEquationCell FormulaCell

FIGURE 5-8 Using Solver to Optimize Location for Steel Appliances

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Chapter 5 ◆ Network Design in the Supply Chain 123

Figure 5-9 Spreadsheet Area for Decision Variables for TelecomOptic

—Objective function

= SUMPRODUCT(B4:G8, B14:G18) + SUMPRODUCT(H4:H8, H14:H18)

B32

C29:G295.2= B9 - SUM(B14:B18)B29

B23:B265.1= I4*H14 - SUM(B14:G14)B22

Copied toEquationFormulaCell

Figure 5-10 Spreadsheet Area for Constraints for TelecomOptic

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Chapter 5 ◆ Network Design in the Supply Chain 123

Figure 5-9 Spreadsheet Area for Decision Variables for TelecomOptic

—Objective function

= SUMPRODUCT(B4:G8, B14:G18) + SUMPRODUCT(H4:H8, H14:H18)

B32

C29:G295.2= B9 - SUM(B14:B18)B29

B23:B265.1= I4*H14 - SUM(B14:G14)B22

Copied toEquationFormulaCell

Figure 5-10 Spreadsheet Area for Constraints for TelecomOptic

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124 Chapter 5 ◆ Network Design in the Supply Chain

Figure 5-11 Solver Dialog Box for TelecomOptic

Figure 5-12 Optimal Network Design for TelecomOptic

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124 Chapter 5 ◆ Network Design in the Supply Chain

Figure 5-11 Solver Dialog Box for TelecomOptic

Figure 5-12 Optimal Network Design for TelecomOptic

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Chapter 5 ◆ Network Design in the Supply Chain 127

LOCATING PLANTS AND WAREHOUSES SIMULTANEOUSLY A much more general form of the plant location model needs to be considered if the entire supply chain network from the sup- plier to the customer is to be designed. We consider a supply chain in which suppliers send mate- rial to factories that supply warehouses that supply markets, as shown in Figure 5-13. Location and capacity allocation decisions must be made simultaneously for both factories and ware- houses. Multiple warehouses may be used to satisfy demand at a market, and multiple factories may be used to replenish warehouses. It is also assumed that units have been appropriately adjusted such that one unit of input from a supply source produces one unit of the finished prod- uct. The model requires the following inputs:

m = number of markets or demand points n = number of potential factory locations l = number of suppliers t = number of potential warehouse locations

Dj = annual demand from market j Ki = potential capacity of factory at location i Sh = supply capacity at supplier h We = potential warehouse capacity at location e Fi = fixed cost of locating a plant at location i fe = fixed cost of locating a warehouse at location e

chi = cost of shipping one unit from supply source h to factory i cie = cost of producing and shipping one unit from factory i to warehouse e cej = cost of shipping one unit from warehouse e to market j

Open/Closed Atlanta Boston Chicago Denver Omaha Portland

Baltimore Closed 0 0 0 0 0 0

Cheyenne Closed 0 0 0 0 0 0

Salt Lake Open 0 0 0 6 0 11

Memphis Open 10 8 0 0 0 0

Wichita Open 0 0 14 0 7 0

TABLE 5-3 Optimal Network Configuration for TelecomOptic with Single Sourcing

Suppliers Plants Warehouses Markets

Figure 5-13 Stages in a Supply Network

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