Facility location


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Facility location

  2. 2. DIBYAGYAN-H 15 BISWAJIT –H 12 INTRODUCTION Almost every private and public sector faces with the task of locating facilities. For the consideration of this type of work is gaining importance because of the emerging world is going global. Therefore, plants are placed in different countries and different regions. Models developed to analyze facility location decisions for the optimized one or more objectives, subject to physical, structural, and policy constraints, governmental implementations, incentives in variety in a static or deterministic setting. As because of the large capital outlays that are involved, facility location decisions are executed in the long-term. Consequently, there may be considerable uncertainty of the parameters of the location decision. Facility location has an important role because the site selection directly relates with the warehouse systems, inventory control and handling, customers and suppliers. A good location gives a strategic advantage against competitors. To give service to potential customers better by short distances as locating more outlets a company enhances its accessibility and hence improves its overall customer service. The determination of a facility location is a well-known phenomenon in operational research area. The facility location means the placement of a planned facility with regard to other facilities according to some constraints. There are both quantitative and qualitative methods applied for the facility location problems. FACILITY LOCATION FACTORS In real life there exist many factors directly or indirectly affect on the facility
  3. 3. location selection. As global location factors it can be defined as; government stability, governed regulations, political and economic systems, exchange rates, culture, climate, export & import regulations, tariffs and duties, raw material availability, availability of suppliers, transportation & distribution systems, labor force, available technology, technical expertise, cross- border trade regulations and group trade agreements. On the other hand, for the selection of the region, city or country the factors considered are; labor, proximity to customers, number of customers, construction costs, land cost, availability of modes and quality of transportation, transportation costs, local business regulations, business climate, tax regulations financial services, incentive packages applied to that region and labor force education are both critical and important in facility location selection. Therefore it is clear that there is a need in location problem approaches concentrating on the combination of qualitative and quantitative factors. FACILITY LOCATION At the duration of previous two decades facility location science has attracted attention of communities from the academic space as well as from the business space. A lot of big companies make use of science even for smaller importance choices, allowing thus at least a place of full time employment for superior employee that has the suitable knowledge and possibilities. Facility location problems have attracted researchers from a lot of different inquiring sectors as the operational research, the information technology, the mathematics, the applied mechanics, the geography, the finances and the marketing as well as professionals from various sectors of work. At facility location problems each of the above groups gives emphasis in different aspects which is up to the needs, the background and the scientific origin. The humans who research and work in facility location problems have different background and different needs. Accordingly, each one creates different way of resolution for these problems taking into consideration different factors and criteria. Perhaps the most creative task in making a decision for location / allocation –relocation facility is to choose the factors that are important for that decision. Facility location
  4. 4. decision concerns those utilities which want to locate, relocate or they extend their activities. The process of decision covers the determination, the analysis, the evaluation and the choice between the alternative solutions. Plants of industrial units, warehouses, distribution centres, and retail disposal places are characteristic installations among lot of others that concern facility location. The choice of regions for facility location begins usually with the creation of new company while for those which are in use this happens after the ascertainment of need for additional productive faculty. After the need of extra industrial unit installation follows the search of "most optimal" place. FACILITY LOCATION APPLIED FACTORS Facility location factors have not changed or they have changed lightly since the science of operational research continues using them. Labour costs, ground costs, buildings costs, transports costs, operation costs, tax motives and other financing criteria are the more usually used factors. The aim of facility location problem solution is the combination of these factors in order to achieve lower cost per produced product unit. We can observe that while the facility location decisions continue be based on the economic elements that aim in the maximisation of profit or in the minimisation of cost, environmental, aesthetic, ecological and social influences increase and have real importance. The objective of maximisation of profit or minimisation of expenses in the process of facility location is obvious, but there is an unanswerable question if this objective can be achieved when most of the applied solving processes exclude the not quantitative factors, as are the immaterial factors that estimate quality of life and environment. The optimisation models and other operational research techniques like the linear programming can analyze the interdependences between the economic variables, without taking into consideration the fact that the persons the decision concerns are not to be prompted neither to be effective when they are sent to work and to live in a place does not satisfy them.
  5. 5. Factors that really influence the efficiency of utilities which are involved in the facility location decision and do not participate in the location process. The choice of some place for facility location is a characteristic decision-making multicriteria analysis problem in which the administrative preference and the quantification of other potentially invisible factors, between the efficiency ones, play a fundamental role in the final decision. In order to be expressly evaluated the leader’s preference with a model of preference, have been overwhelmed a lot of efforts so as to be developed the theory and the methodology for the assessment of this preference. Recently the quality of life and the environment situation constitute common concern for a lot of persons who are afraid that in our society the environmental and human values are neglected for industrial production, technological and economic growth. The term quality of life as it is used here is an eclectic term that is reported in various potentially independent factors that all together have repercussions in life of somebody. Research in relative bibliography has shown that the following team of factors has the biggest influence in the general quality of life and the worker’s ego: • The personality of himself (the faculty, the effectiveness and the expectations of somebody). • His family (spouse, children and relatives). • His economic resources. • The residence. • The amusement in his life (that it is usually connected with the family). • His friends • The use of free time. It is obvious that the social environment has direct relation with five from these seven groups of factors. Even if the differences in the culture, the social class, the familial nurturing, the education and the personality create diversity in the human preferences, it is realised that the seven factors are in effect globally for the population as well as for important subgroups of population. This research underlines an element that is not always taken into consideration by the administrative teams of enterprises. The enterprise should occupy the repercussions not only from movement of an executive member but also the movement of his spouse, children, and casually his relatives, and it should remember that opinions of all of them and same
  6. 6. the spouse are critical on quality of life issues and this is in accordance with the motives and the productivity of this executive member. The applied facility location criteria are based on the quantitative estimate (measurability), they exist however apart from quantitative and the qualitative categories. In one hand the quantitative ones can be measured with numerical prices, as the cost of ground, operation, transportation, the tax motives etc In the other the qualitative incorporates the not-quantitative determinable factors which are opposite to business transactions facility in a particular region, as are the environment, the operational climate, the social environment the quality of life etc Such factors cannot easily be expressed with numerical prices and be evaluated from the quantitative models. The problems of location become more complex when such qualitative factors are taken into account, because they are under subjective judgement. It is henceforth acceptable that location choice for the installation of some industrial unit has important strategic repercussions in the enterprises in which they are reported, because such a decision regularly includes long-term engagement of capitals and of course is not refundable. Concretely, the location choice for the installation of industrial unit can practise important strategic effect in the competitive place of company from the view of the operation cost, the efficiency of workers, the speed of products delivery and the flexibility of company rival in the market. For example, the location choice for the installation of some industrial unit that will allow the enterprise to achieve the proximity to the suppliers constitutes a critical strategic advantage in the market, since the proximity to the suppliers is important for the time improvement of delivery of products. However the success of enterprises is in the hands of few persons that constitute their administrative team. It is the guidance, the ambition, the initiative and their crisis that determines if the expected results of enterprises will be achieved. The efficiency is always result of possibility and motives when the motive in the work is optimized, the productivity is increased. Consequently, the executives with given possibilities will not achieve the expected results in new installations if their environment creates dissatisfaction that has repercussions in the motives. There is no reason for someone to achieve more rapid time of delivery if the productivity of these persons is decreased.
  7. 7. Consequently, the final location choice for the installation of some industrial unit should contribute in the success of corporate strategic plans that concerns in the financing, in the successful correspondence in the objectives of production and demand as well as in the increased productivity of human potential, however nothing from the above cannot be ignored because the result of studies is based on their harmonious coexistence. Facility location The general facility location problem is: given a set of facility locations and a set of customers who are served from the facilities then: which facilities should be used which customers should be served from which facilities so as to minimise the total cost of serving all the customers. Typically here facilities are regarded as "open" (used to serve at least one customer) or "closed" and there is a fixed cost which is incurred if a facility is open. Which facilities to have open and which closed is our decision. Below we show a graphical representation of the problem.
  8. 8. =[One possible solution is shown below. Other factors often encountered here: customers have an associated demand with capacities (limits) on the total customer demand that can be served from a facility customers being served by more than one facility. Example
  9. 9. The problems of facility size and facility location are very closely linked and should be considered simultaneously. In fact the package used here disregards (for reasons of simplicity) the problem of facility size and deals only with facility location. We shall illustrate the problem of facility location by means of an example. At Gotham City airport terminal there are 10 arrival gates (A to J respectively). A pictorial representation of the terminal is given below with the location of the gates being: Gate x coordinate y coordinate A 0 2 B 2 4 C 5 6 D 5 10 E 7 15 F 10 15 G 12 10 H 12 6 I 15 4 J 20 2 Luggage from arriving flights is unloaded at these gates and moved to a passenger luggage pick-up point.
  10. 10. It is estimated that the number of pieces of luggage arriving per day at each gate (A to J respectively) is: 3600, 2500, 1800, 2200, 1000, 4500, 5600, 1400, 1800 and 3000 respectively. Where should the passenger luggage pick-up point be located in order to minimize movement of luggage? Solution In order to logically locate the passenger luggage pick-up point we need to make use of the amount of luggage flowing from the gates to the pick-up point. Logically a gate from which there is a large flow should be nearer to the pick-up point than a gate with a small flow. Informally therefore we would like to position the pick-up point so as to minimise the sum over all gates g (distance between g and the pick-up point) multiplied by (flow between g and the pick-up point). This approach to choosing the location of the pick-up point is precisely the approach used by the facility location module in the package. Typically in such location problems we are concerned with a load-distance score (the product of load and distance for all points). The initial input to the package for this problem is shown below. Note here the package terminology is somewhat peculiar: existing facilities - are points where we know in advance exactly where they are and they are fixed in position new facilities - are points where we do not know where they are and their location is what we have to determine (using the package)
  11. 11. In order to enter the data relating to the gates we can ignore the columns in the package input that are concerned with flows between existing facilities - here all flows are from the existing facilities to the new facility. Note here that in solving the problem we need to specify the appropriate distance model. This is because as we do not yet know where the new facility (luggage pick-up point) is to be we cannot specify the distance between it and the gates without a general expression for calculating the distance between two locations. If (xi,yi) and (xj,yj) represent the coordinates of two locations i and j then the distance model measures can be: rectilinear - distance between i and j is: |xi-xj| + |yi-yj| Euclidean - distance between i and j is: [(xi-xj)2 + (yi-yj)2]0.5 squared Euclidean - distance between i and j is: (xi-xj)2 + (yi- yj)2 The rectilinear distance measure is often used for factories, American cities, etc which are laid out in the form of a rectangular grid. For this reason it is sometimes called the Manhattan distance measure. The Euclidean distance measure is used where genuine straight line travel is possible. The squared Euclidean distance measure is used where straight line travel is possible but where we wish to discourage excessive distances (squaring a large distance number results in an even larger distance number and recall that we use the distance number in the objective which we are trying to minimise). The output from the package for each of the distance measures is shown below. Rectilinear
  12. 12. Euclidean Squared Euclidean
  13. 13. From the package output we can see that the location for the luggage pick-up point should be: Distance measure x coordinate y coordinate Rectilinear 10 6 Euclidean 10.12 8.98 Squared Euclidean 9.05 7.67 The picture below shows these three possible locations with respect to the terminal (labelled R, E and S for rectilinear, Euclidean and squared Euclidean respectively).
  14. 14. Note here that (in reality) the initial choice of distance measure is often between rectilinear and Euclidean (based upon the technology of how the luggage flows within the terminal). If the luggage flows in an Euclidean (straight-line) manner then choosing to use squared Euclidean, rather than Euclidean, penalises excessively long distances. One point to note about the above picture is that we are not really interested in determining positions down to the nearest millimetre (the data is probably not accurate enough anyway!). Instead we are using the package to get an indication of the approximate region where it would be sensible to site a luggage pick-up point. Note too that the package uses a "centre of gravity" approach to decide where to locate a single pick-up point. Extension Suppose now we are interested in having two luggage pick-up points. We have two types of decisions: location decisions - where to locate luggage pick-up points; and allocation decisions - which gates to allocate to which luggage pick-up points.
  15. 15. Ideally we would like a way of automatically solving both these decision problems simultaneously (since obviously location affects allocation and vice-versa). The package we are using cannot do this. Instead we must ourselves decide the allocation and allow the package to solve to produce appropriate locations. However more sophisticated packages can solve both decisions simultaneously. Suppose therefore that we make an (arbitrary) allocation decision, based upon the map of the terminal, namely that we will have one luggage pick-up point dealing with gates C to H (inclusive) and the other dealing with gates A, B, I and J. With this allocation decision made we can solve the problem using the package, the input being shown below. Note here that in this input we have made new facility number 1 the luggage pick-up point for gates C to H (inclusive) and new facility number 2 the luggage pick-up point for gates A, B, I and J. Note the cells associated with flows between New Facilities. This is for flows between new facilities, whose locations we do not yet know. For example, we could be moving luggage using a concentrator system. Luggage flows to a central point (new facility, a concentrator point) before being passed onward to a collection point (new facility). In such a case the flow from the concentrator point to the collection point would need to be given in this matrix. The output from the package for each of the three distance measures is shown below. Rectilinear
  16. 16. Euclidean Squared Euclidean
  17. 17. From this output we can see that the locations for the luggage pick-up points should be: Distance measure Facility x coordinate y coordinate Rectilinear 1 10.03 10.02 2 2.04 2.06 Euclidean 1 11.00 10.50 2 2.54 3.38 Squared Euclidean 1 9.45 10.89 2 8.44 2.79 The picture below shows all these locations with respect to the terminal (labelled R, E and S for rectilinear, Euclidean and squared Euclidean respectively).
  18. 18. Concentrator Suppose now that in the example we just considered the luggage pick-up point for gates C to H (inclusive) is merely acting as a concentrator, concentrating luggage before passing it to the other pick-up point, which collects luggage from gates A,B, I and J directly. In this system all passengers see is a single pick-up point at which they collect their luggage. To locate this concentrator (and the final pick-up point) we make use of flows between new facilities. Here the total amount of luggage collected from C to H will flow to the final pick-up point from this intermediate concentrator. This will total 1800+2200+1000+4500+5600+140 =16500 pieces of luggage. Hence the input to the package is:
  19. 19. The solutions are: Rectilinear So in this case the final and concentrator locations coincide.
  20. 20. Euclidean So in this case the final and concentrator locations are near to each other. Squared Euclidean
  21. 21. So in this case the final and concentrator locations are not particularly close to each other. Other approaches Technically the approach used above for location, where any point is a potential location for a new facility, is called the infinite set approach. More commonly nowadays location studies are done using a feasible set approach. With this approach there are a finite set of alternatives for the new facilities and the problem is to choose from these alternatives the best subset to service a known set of customers (existing facilities in the terminology of the package used above). The advantage of this approach is that it can take explicit account of items such as fixed costs and capacities associated with facilities (i.e. items connected with facility size), as well as the issue of deciding the allocation of customers to facilities. Location models based upon the feasible set approach typically use integer programming. More about such models can be found here. Example
  22. 22. One example of a facility location problem that I have worked on was to do with church location for Church of England churches. The idea here was to investigate which churches could best be closed. For the purposes of this study a 100 kilometre square to the north-east of London was chosen. An obvious first question is How many churches are there in this area and where are they? Alas the organisation did not seem too sure of the answers to this question. Eventually we consulted maps of the area and came to the conclusion that we thought there were 504 (Church of England) churches in this area. A plot of the location of these churches is shown below (church positions to one- tenth of a kilometre). You can see that they are clustered together in a number of distinct areas. Now if a church (facility) is to be closed then logically we should consider information like cost of operating the church revenue from land sale/disposal if church closed size of the church etc. Unfortunately this was an extremely data-poor environment. The only data (aside from the above location data) we had was the average congregation (attendance) size for each of the 504 churches. This data is
  23. 23. plotted below as a histogram. You can see that the average congregation size for a significant number of churches is very small. We concluded that we had to work with the limited data we had, rather than attempt to discover data for 504 different churches, effectively an impossible task. The approach we decided upon was to say that if a church was closed its congregation was displaced to their nearest open church. This leads naturally to the idea of displacement distance - defined to be congregation size multiplied by distance they are displaced. Our problem therefore is to choose the churches to close so as to minimise total displacement distance. To solve this problem we took a simple interchange heuristic from the literature and coded it. The effect of closing churches in terms displacement distance (measured in people kilometres) is shown below. You can see that as more churches are closed the total displacement distance increases.
  24. 24. One complication to this study was that closer examination of the data revealed a number of churches very close to each other (say within 0.5 of a kilometre of each other) but with relatively large congregations. The algorithm attempted to close one of these churches (displacing the congregation to the other). Now all churches, even within the Church of England, are not the same in terms of the type of church service which they offer. Some are more evangelical, some more traditional, etc. It seemed likely that two churches very close to each other, but both with large congregations, were offering a different type of church service, so closing one and displacing the congregation to the other would not be satisfactory in practice. We therefore modified our algorithm to ensure that no churches with a congregation of 50 or more could be closed (i.e. only "small" churches with a congregation less than 50 could be closed). The effect of this upon total displacement distance can be seen in the diagram below. In that diagram the lower line is as above (all churches available for closure) and the upper line is when only small churches can be closed.
  26. 26. Many applications of the facility location problem such as caching in the Internet inherently apply to distributed settings. In this paper, we have given a classification of the trade-off between the amount of communication and the quality of the obtained global solution. Our solution technique is based on the distributed approximation of a linear program which is not a covering or packing problem. By thus pushing the boundaries of distributed LP approximation, we hope that our paper is a step towards understanding the nature of more general linear programs in a distributed context. Our results give raise to several questions. First, the fact that in the centralized case, the metric facility location problem allows constant approximations raises hope for faster approximations algorithms in distributed settings, too. Moreover, our problem setting is a complete bipartite graph. Interestingly, there are virtually no lower bounds for the bounded message. For instance, all lower bounds for the MST problem apply to graphs with diameter at least 3. Finding lower bounds for this model appears to be an outstanding open problem. We have given strategies for one-dimensional competitive facility location, allowing the second player, Red, to win. We have also shown that the _rst player, Blue, can keep the winning margin as small as he wishes. For all practical purposes. Similarly, if players are allowed to place points in_nitesimally close to their opponent (that is, on the same location, but indicating a side"), then Blue's defense strategy will guarantee a tie. Do our endings have any bearing on the two-dimensional Voronoi Game? The concept of keypoints turned out to be essential to our strategies. We have seen that a player governing all keypoints cannot possibly lose the game. Surprisingly, the situation in two dimensions is quite different: It can be shown that for any given set of n blue points in, say, a unit square, we can understand a set of n red points so that the area dominated by Red is at least for an absolute constant _ > 0 not depending on n.