Unit 2

Management of Conversion System Chapter 6: Facility location

Lesson 19 – Location selection models

Learning Objectives After reading this lesson you would be able to understand Decision regarding site selection Load distance model Center of gravity model Facility location within a network of locations

In this lesson, we are continuing on different factors affecting location choices and how to apply load distance and center of gravity method for selecting single-site location problem.

Decisions regarding site selection

Management must first decide whether to expand on site, build another facility, or relocate to another site. The advantages of building a new plant or moving to a new retail or office space are that the firm does not have to rely on production from a single plant, can hire new and possibly more productive labour, can modernize with new technology, and can reduce transportation costs. Most firms that choose to relocate are small. They tend to be single-location companies overcrowded for space and needing to redesign their production processes and layouts.

Before selecting a site, several issues must be examined from different angles and their relative merits and de-merits should be properly examined. Dear friends, let us now turn our attention to:- Comparing several sites The process of selecting a new facility location involves a series of steps.

1. Identify the important location factors and categorize them as dominant or secondary

2. Consider alternative regions; then narrow the choices to alternative communities and finally to specific sites

3. Collect data on the alternatives from location consultants, state development agencies, city planning departments, chambers of commerce, land developers, electric power companies, banks, and on-site visits.

4. Analyze the data collected, beginning with the quantitative factors- factors that can be measured in rupees, such as annual transportation costs or taxes. These rupees values may be broken into separate cost categories (e.g., inbound and outbound transportation, labour, construction, and utilities) and separate revenue sources (e.g., sales, stock or bond issues, and interest income). These financial factors can then be converted to a single measure of financial merit and used to compare two or more sites.

5. Consider qualitative factors pertaining to each site into the evaluation. A qualitative factor is one that cannot be evaluated in rupees terms, such as quality of life or community attitudes. To merge quantitative and qualitative factors, some managers review the expected performance of each factor, while others assign each factor a weight of relative importance and calculate a weighted score for each site, using a preference matrix. What is important in one situation may be unimportant or less important in another. The site with the highest weighted score is best.

Let us look at an example on calculation of weighted scores in a preference matrix. Let us assume that a new medical facility, Health-Care, is to be located in Delhi. The location factors, weights, and scores (1 = poor, 5 = excellent) for one potential site is shown in the following table. The weights in this case add up to 100 percent. A weighted score will be calculated for each site. What is the weighted score for this site? Location factor weight score Total patient km per month 25 4 Facility utilization 25 3 Average time per emergency trip 25 3 Land and construction costs 15 1 Employee preferences 10 1 Solution The weighted score for this particular site is calculated by multiplying each factor’s weight by its score and adding the results:

510115325325425 ×+×+×+×+×=oreweightedsc = 100 + 75+ 75+ 15+50 = 315 The total weighted score of 315 can be compared with the total weighted scores for other sites being evaluated. Based on it, proper decisions could be made. Now, we examine the concept of what is known as, the load-distance model. Load-distance method The load-distance method is a mathematical model used to evaluate locations based on proximity factors. The objective is to select a location that minimizes the total weighted loads moving into and out of the facility. The distance between two points is

expressed by assigning the points to grid coordinates on a map. An alternative approach is to use time rather than distance. Distance measures Suppose that a new warehouse is to be located to serve Delhi. It will receive inbound shipments from several suppliers, including one in Ghaziabad. If the new warehouse were located at Gurgaon, what would be the distance between the two facilities? If shipments travel by truck, the distance depends on the highway system and the specific route taken. Computer software is available for calculating the actual mileage between any two locations in the same county. However, for load-distance method, a rough calculation that is either Euclidean or rectilinear distance measure may be used. Euclidean distance is the straight-line distance, or shortest possible path, between two points.

A(50,185 y B(175, 100) x

Figure 6.1 Distance between point A and point B The point A on the grid represents the supplier’s location in Ghaziabad, and the point B represents the possible warehouse

location at Gurgaon. The distance between points A and B is the length of the hypotenuse of a right triangle, or dAB = ( ) ( )22 ybyaxbxa −+−

where dAB = distance between points A and B Xa = x-coordinate of point A Ya = y-coordinate of point A Xb = x-coordinate of point B Yb = y-coordinate of point B Rectilinear distance measures distance between two points with a series of 900 turns as city blocks. Essentially, this distance is the sum of the two dashed lines representing the base and side of the triangle in figure . The distance traveled in the x-direction is the absolute value of the difference in x-coordinates. Adding this result to the absolute value of the difference in the y-coordinates gives DAB = |xA – xB| + |yA – yB| Calculating a load-distance score Suppose that a firm planning a new location wants to select a site that minimizes the distances that loads, particularly the larger ones, must travel to and from the site. Depending on the industry, a load may be shipments from suppliers, between plants, or to customers, or it may be customers or employees traveling to or from the facility. The firm seeks to minimize its load-distance, generally by choosing a location so that large loads go short distances. To calculate a load-distance for any potential location, we use either of the distance measures and simply multiply the loads

flowing to and from the facility by the distances traveled. These loads may be expressed as tones or number of trips per week. This calls for a practical example to appreciate the relevance of the concept. Let us visit a new Health-Care facility, once again. Example- calculating load-distance scores The new Health-Care facility is targeted to serve seven census tracts in Delhi Figure shows the coordinates for the center of each census tract, along with the projected populations, measured in thousands. Customers will travel from the seven census tract centers to the new facility when they need health care. Two locations being considered for the new facility are at (5.5, 4.5) and (7, 2), which are the centers of census tracts C and F. If we use the population as the loads and use rectilinear distance, which location is better in terms of its total load-distance score? Solution We want to calculate the load-distance score for each location. Using the coordinates from figure. , we calculate the load-distance score for each tract.

Locate at (5.5, 4.5)

Locate at (7,2) Census Tract (x, y) Population (l)

Distance(d) load- distance

Distance (d) load distance

A (2.5, 4.5)

2 3 + 0 = 3 6 4.5 + 2.5 = 7

14

B (2.5, 2.5)

5 3 + 3 = 5 25 4.5 + 0.5 = 5

25

C (5.5, 4.5)

10 0 + 0 = 0 0 1.5 + 2.5 = 4

40

D (5, 2) 7 .5 + 2.5 = 3

21 2 + 0 = 2 14

E (8, 5) 10 2.5 + .5 = 3

30 1 + 3 = 4 40

F (7, 2) 20 1.5 + 2.5 = 4

80 0 + 0 = 0 0

G (9, 2.5) 14 3.5 + 2 = 5.5

77 2 + 0.5 = 2.5

35

Total 239

Total 168

Summing the scores for all tracts gives a total load-distance score of 239 when the facility is located at (5.5, 4.5) versus a load-distance score of 168 at location (7, 2). Therefore, the location in census tract F is a better location. Dear students, we now start with the Center of gravity method for selecting location. Center of gravity Center of gravity is based primarily on cost considerations. This method can be used to assist managers in balancing cost and service objectives. The center of gravity method takes into account the locations of plants and markets, the volume of goods moved, and transportation costs in arriving at the best location for a single intermediate warehouse. The center of gravity is defined to be the location that minimizes the weighted distance between the warehouse and its supply and distribution points, where the distance is weighted by the number of tones supplied or consumed. The first step in this procedure is to place the locations on a coordinate system. The origin of the coordinate system and scale used are arbitrary, just as long as the relative distances are correctly represented. This can be easily done by placing a grid over an ordinary map. The center of gravity is determined by formulae

Cx = ∑∑

i

i

Wi

dixWi

Cy = ∑∑

i

i

Wi

diyWi

Where Cx = x-coordinate of the center of gravity Cy = y-coordinate of the center of gravity Dix = x-coordinate of location i Diy = y-coordinate of location I An Example Activity: Finding the center of gravity Remember the example we discussed in the previous class. Can you find the target area’s center of gravity for the Health-Care medical facility. Try using your understanding of the concept. Once you are through, tally your solution with that given below. Solution To calculate the center of gravity, we start with the following information, where population is given in thousands Census Tract (x, y) population (l) lx ly A (2.5, 4.5) 2 5 9 B (2.5, 2.5) 5 12.5 12.5 C (5.5, 4.5) 10 55 45 D (5, 2) 7 35 14 E (8, 5) 10 80 50 F (7, 2) 20 140 40

G (9, 2.5) 14 126 35 Totals 68 453.5 205.5 Next we find Cx and Cy. Cx = 453.5 / 68 = 6.67 Cy = 205.5 / 68 = 3.02 The center of gravity is (6.67, 3.02), which is not necessarily optimal. It is in the general vicinity of location (7, 2), which was found best from the load-distance score. Using the center of gravity as starting point, managers can now search in its vicinity for the optimal location. It’s that time of the lecture again. You got it. Good. So, here is a case study . POM in practice 6.3 – An application of warehouse location to bloodmobile operations* Bloodmobile staging areas are warehouses or garages where bloodmobiles are provisioned, repaired, and maintained between blood collections. The American Red Cross wanted to examine the effects of proposed site changes for their operations. The total distance traveled each year to collect blood was determined to be a useful criterion function for assessing proposed sites. The proposals considered were either a single central site or a combined of a central site with subsites having limited facilities. In the course of the study, several questions were considered-

1. What is the present collection pattern for the existing site? 2. If each collection point were assigned to the nearest staging area, what

would be the effect on distance traveled? 3. How does distance change if a new configuration of staging areas is

used? 4. What is the minimum possible distance that must be traveled?

This problem was attacked by using facility-location techniques that have proven to be useful in locating warehouses. The objective function to be minimized was

Min ∑−+− 2/1]2)(2)[( ypyixpxiwi

Where Wi is the fraction of the total number of trips made to collection site I; xi, yi are the coordinates of collection sit I; and xp, yp are the coordinates of the proposed bloodmobile staging area. The term in brackets represents the straight-line distance between the collection site and the staging area. Thus the objective is to minimize the sum of distances from collection sites weighted by the number of trips made to the collection sites. A computer program was written to solve this problem and permit rapid comparison of potential sites. The analysis revealed an improved location in one region studied and also helped to determine how many collection units should be used. It was noted that the “method used to assist in the location of bloodmobile staging areas provides useful insight into blood collection patterns and sheds light on a problem that has traditionally been performed by a seat-of-the pants approach.” *Source – Applied Production and Operations management ( J. R. Evans et al) West Publishing Company Locating a facility within a network of facilities When a firm with a network of existing facilities plans a new facility, one of two conditions exists- either the facilities operate independently (e.g., a chain of restaurants, health clinics, banks, or retail establishments) or the facilities interact (e.g., component manufacturing plants, assembly plants, and warehouses). Independently operating units can be located by treating each as a separate single facility, as described. Locating interacting facilities introduces new issues, such as how to allocate work between the facilities and how to determine the best capacity for each. In many cases a workable solution can be identified merely by looking for patterns in the cost, demand, and capacity data. In other cases, more formal approaches are needed. To answer the questions like, what is the best way to partition work among various facilities- transportation method, linear programming can be used. Locating retail, public service, and emergency facilities There are some significant differences between manufacturing locations and those involving retail, public service, and emergency facilities. For a manufacturer, location decisions involve analysis of the costs of distribution and service delivery times. Service facilities, on the other hand, are the terminal points in the system at which demand takes place. Goods are not moved to and from the service location; customers are. Thus the location of

facilities such as fast food franchises, gasoline stations, and banks depend on the concentration of demand and the location of competition. Retail facility location. The major criterion used in locating a retail facility is the volume of demand. For a grocery store or restaurant, this might be measured by rupees sales revenue, whereas for an amusement park, this might be the number of visitors each year. In any case, estimates of demand must be obtained for potential locations. Public service facility location. Public service facilities include post offices, schools, highways, parks, and so on. One of the major problems in locating such facilities is the lack of easily quantifiable data. How does one define “social cost” or “social benefit”? Some of the typical criteria used in public service location problems include the average distance or time traveled by the users of the facilities and the maximum distance or travel time between the facility and its intended population. Another factor not present in individual location problems is that public facilities create demand; one would like to locate facilities to serve the largest segment of the population. In this sense, the problem is similar to locating a bank or grocery store, except that profit is not a motivating factor. Cost-benefit analysis is often used to determine public facility location. Emergency facility location. The problem of locating emergency facilities such as fire stations, ambulance stations, and police substations has the objective of minimizing response time from the notification of an emergency to the delivery of service. Usually, the goal is to locate the facility so that the maximum response time to any point of demand is minimized. The center of gravity method can often be used to locate service facilities. Retail outlets, power-generating stations, sewage-treatment plants, and waste-disposal facilities are some examples. With that, we have come to the end of today’s discussions. I hope it has

been an enriching and satisfying experience.

Points to ponder