Management decision-making for transportation problems through goal programming.ABSTRACT This paper presents a lexicographic lex·i·cog·ra·phy n. The process or work of writing, editing, or compiling a dictionary. [lexico(n) + -graphy. goal programming (LGP LGP Linux Game Publishing LGP Low Ground Pressure LGP Local Governance Program (Iraq) LGP LG.Philips LGP Lysosomal Membrane Glycoprotein LGP Linux Global Partners LGP Left-Green Alliance (Iceland) ) model for management decision-making in petroleum refinery industry for distribution of oil to the various depots. The model presented in the paper is designed to illustrate how LGP can be used as an aid for solving transportation problems with multiple objectives. The data for the study has been used from a petroleum refinery industry in India. 1. INTRODUCTION The classical single objective transportation problems are a special type of linear programming (LP) problems. The sources may include plants and warehouses and destinations may include sales outlets and customers. The coefficients of the objective function represent transportation cost, delivery time, number of goods transported, unfulfilled demand, and many others. In operations research operations research Application of scientific methods to management and administration of military, government, commercial, and industrial systems. It began during World War II in Britain when teams of scientists worked with the Royal Air Force to improve radar detection of , several quantitative techniques have been used for solving transportation problems. The most commonly used techniques are linear programming (LP) and generalized gen·er·al·ized adj. 1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain. 2. Not specifically adapted to a particular environment or function; not specialized. 3. minimum cost network (Hadley 1972, Hemaida & Kwak 1994). The decision-maker, public or private, may not have a utility function with a single argument (usually profits). The single objective optimization optimization Field of applied mathematics whose principles and methods are used to solve quantitative problems in disciplines including physics, biology, engineering, and economics. techniques presented by Romero in his article are examples (Romero, 1991). Businesses and industries are practically faced with both economic optimization such as cost minimization and non-economic items that are vital to the existence of their firms (Lee, 1972). Transportation problems involve multiple and conflicting goals such as the cost minimization, balancing work among the plants, transportation fleets, and many others. These multiple and conflicting goals can be achieved by using goal programming (GP) technique. The goal programming (GP) technique has become a widely used approach in Operations Research (OR). GP model and its variants have been applied to solve large-scale multi-criteria decision-making problems. The GP technique was first used by Charnes and Cooper in 1960s. This solution approach has been extended by Ijiri (1965), Lee (1972), and others. For detailed research survey on GP, see Lee (1972), Ignizio (1976), Romero (1991), Romero (1986), Tamiz and Jones (1995), and Sharma, Alade and Vasishta (1999). Lee and Moore (1973) used GP model for solving transportation problem with multiple and conflicting objectives. Arthur and Lawrence (1982) designed a GP model for production and shipping patterns in chemical and pharmaceutical industries. Kwak and Schniederjans (1985) applied GP to transportation problem with variable supply and demand requirements. Several other researchers (Sharma et al., 1999) have also used the GP model for solving the transportation problem. In this paper, we present a lexicographic goal programming (LGP) model for management decision-making in petroleum refinery industry, involving the distribution of oil to the various depots. The model is designed to illustrate how LGP can be used as an aid for solving transportation problems with multiple objectives. The results of the study have utilized in decision making process at a petroleum refinery industry in India. 2. MODEL FORMULATION formulation /for·mu·la·tion/ (for?mu-la´shun) the act or product of formulating. American Law Institute Formulation The LGP model has been described in detail by Lee (1972), Ignizio (1976) and Olson (1984). The general model of the LGP can be written as follows: Find [bar.X] ([X.sub.11],[X.sub.12],[X.sub.13], ..., [X.sub.mn]) so as to Minimize [P.sub.1]([w.sub.i1.sup.+] [d.sub.ij.sup.+] + [w.sub.i1.sup.-][d.sub.i2.sup.-]), Minimize [P.sub.2]([w.sub.i2.sup.+][d.sub.i2.sup.+] + [w.sub.i2.sup.-][d.sub.i2.sup.-]), Minimize [P.sub.k]([w.sub.ik.sup.+] [d.sub.ik.sup.+] + [w.sub.ik.sup.-][d.sub.ik.sup.-]), Minimize [P.sub.K]([w.sub.iK.sup.+] [d.sub.iK.sup.+] + [w.sub.iK.sup.-][d.sub.iK.sup.-]), where i = 1,2,3, ..., m Subject to, [f.sub.i]([bar.X]) + [d.sup.-.sub.i] - [d.sup.+.sub.i] = [b.sub.i], [d.sup.-.sub.i], [d.sup.+.sub.i], X [greater than or equal to] 0 and [d.sup.-.sub.i] x [d.sup.+.sub.i] = 0 for i = 1,2,3, ..., K where X = vector of [m.sup.*]n decision variables. [P.sub.k] = [k.sup.th] priority factor as assigned as·sign tr.v. as·signed, as·sign·ing, as·signs 1. To set apart for a particular purpose; designate: assigned a day for the inspection. 2. to the set of goals, 1 [less than or equal to] k [less than or equal to] K [less than or equal to] m. Also P, >>[P.sub.i+1]; 1 [less than or equal to] i [less than or equal to] K [f.sub.i]([bar.X]) = linear function for [i.sup.th] goal [d.sub.ik.sup.-] = under-achievement from the [i.sup.th] goal level [b.sub.i]. at the priority level [P.sub.k] [d.sub.ik.sup.+] = under-achievement from the [i.sup.th] goal level [b.sub.i]. at the priority level [P.sub.k] [w.sub.ik.sup.+] and [w.sub.ik.sup.-] ([greater than or equal to] 0) are numerical numerical expressed in numbers, i.e. Arabic numerals of 0 to 9 inclusive. numerical nomenclature a numerical code is used to indicate the words, or other alphabetical signals, intended. weights associated with the deviational variables [d.sub.ik.sup.-] and [d.sub.ik.sup.+] respectively where [d.sub.ik.sup.-] and [d.sub.ik.sup.+] are the renamed for the convenience of actual deviational variables [d.sup.-.sub.j] and [d.sup.+.sub.j] respectively. Variables and Constants The decision variables, deviational variables, and constants for model formulation are defined as below: Decision Variables [X.sub.ij] = the amount of oil to be transported from the i-th refinery to the [j.sup.th] depot, i = 1, ..., m, j = 1 ..., n Constants and Co-efficient [S.sub.i] = the production capacity of the refinery i [R.sub.i] = minimum amount of oil to be supplied by the refinery i, at the crisis period [D.sub.j] = the demand at the depot j [L.sub.j] = minimum amount of oil to be transported to depot j [C.sub.ij] = the unit transportation cost from the [i.sup.th] refinery to the [j.sup.th] depot TC = total transportation cost. Constraints CONSTRAINTS - A language for solving constraints using value inference. ["CONSTRAINTS: A Language for Expressing Almost-Hierarchical Descriptions", G.J. Sussman et al, Artif Intell 14(1):1-39 (Aug 1980)]. (i) a) Refineries have installed production capacity. The refineries can not supply more than the production capacity. The LGP constraints for supply are in the form: (1) [MATHEMATICAL EXPRESSION A group of characters or symbols representing a quantity or an operation. See arithmetic expression. NOT REPRODUCIBLE re·pro·duce v. re·pro·duced, re·pro·duc·ing, re·pro·duc·es v.tr. 1. To produce a counterpart, image, or copy of. 2. Biology To generate (offspring) by sexual or asexual means. IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. .] b) In crisis period, to ensure the minimum supply from the refineries the goal constraints can be developed as follows: (2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (ii) The oil transported from refineries to the depots should not exceed the demand of individual depots. The goal constraints for demand are (3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (iii) There should be a minimum amount of oil to be transported from refinery i to depot j. The goal constraints are (4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (iv) The budgetary constraint Constraint A restriction on the natural degrees of freedom of a system. If n and m are the numbers of the natural and actual degrees of freedom, the difference n - m is the number of constraints. of total transportation cost is: (5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 3. APPLICATION The oil company (name withheld for security reasons) used in this study uses crude oil to produce petroleum products in the northern India. The company has two oil refineries This is a list of oil refineries. The Oil and Gas Journal also publishes a worldwide list of refineries annually in a country-by-country tabulation that includes for each refinery: location, crude oil daily processing capacity, and the size of each process unit in the refinery. and fifteen depots in the northern region. The supply chain begins with the refineries. The crude oil is refined to obtain petroleum as finished products. The petroleum is then transported to different depot locations by rail, road & pipelines. Since all three modes of transportation are not available for all the depots, the minimum transportation cost for the available modes is taken into consideration in the model formulation. The monthly production capacities of oil product and the monthly demand of each depot and cost per Metric Ton at the two refineries are given in Table 1. The Goals The following goals are set by the management in order of their importance: [P.sub.1] Achieve the minimum amount to be supplied by refineries and the minimum demand of depots. [P.sub.2] Achieve the installed production capacity of the refinery and maximum demand of depots. [P.sub.3] Minimize the total transportation cost. Goal Constraints The LGP model constraints for the transportation problem are formulated for·mu·late tr.v. for·mu·lat·ed, for·mu·lat·ing, for·mu·lates 1. a. To state as or reduce to a formula. b. To express in systematic terms or concepts. c. as follows: Supply Constraints a) The refineries have installed production capacities. The refineries can not supply more than their capacities. The LGP constraints for supply can be given as follows: (6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] b) In crisis period, to ensure the minimum supply from the refineries the goal constraints can be presented as follows: (8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] Demand Constraints a) The refined oil, shipped to the depots from the refineries, should not exceed the depots-demand individually. The LGP constrains for demand can be given as follows: (10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (15) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (16) [[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (18) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (19) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (20) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (23) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (24) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] b) The refined oil, shipped to the depots from the refineries, should not below the depots' minimum demand. The LGP constrains for demand can be given as follows: (25) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (26) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (27) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (28) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (29) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (30) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (31) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (32) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (33) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (34) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (35) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (36) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (37) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (38) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (39) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] c) The total transportation cost should not be greater than the budgeted amount, Rs. 19,254,710. (40) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] The Objective Function The priority structure of the problem is as follows: Minimize [P.sub.1] [[2d.sub.3.sup.-] + [2d.sub.4.sup.-] + [d.sub.20.sup.-] + [d.sub.21.sup.-] + [d.sub.22.sup.-] + [d.sub.23.sup.-] + [2d.sub.24.sup.-] + [d.sub.25.sup.-] + [d.sub.26.sup.-] + [2d.sub.27.sup.-] + [d.sub.28.sup.-] + [d.sub.29.sup.-] + [d.sub.30.sup.-] + [d.sub.31.sup.-] + [d.sub.32.sup.-] + [d.sub.33.sup.-] + [d.sub.34.sup.-]] Minimize [P.sub.2] [[d.sub.1.sup.+] + [d.sub.2.sup.+] + [d.sub.5.sup.+] + [d.sub.6.sup.+] + [d.sub.7.sup.+] + [d.sub.8.sup.+] + [d.sub.9.sup.+] + [d.sub.10.sup.+] + [d.sub.11.sup.+] + [d.sub.12.sup.+] + [d.sub.13.sup.+] + [d.sub.14.sup.+] + [d.sub.15.sup.+] + [d.sub.16.sup.+] + [d.sub.17.sup.+] + [d.sub.18.sup.+] + [d.sub.19.sup.+]] Minimize [P.sub.3] [[d.sub.35.sup.+]] 4. RESULTS The LGP transportation problem contains 30 variables, 35 constraints, 3 priorities, and an objective function. A summary of results is as follows: TABLE 2: DECISION VARIABLE ANALYSIS Decision Value Variable [X.sub.1,1] 2267 [X.sub.1,2] 103.25 [X.sub.1,3] 3199.6 [X.sub.1,4] 3139.5 [X.sub.1,5] 6805 [X.sub.1,6] 4110 [X.sub.1,7] 16724 [X.sub.1,8] 5650 [X.sub.1,9] 2088 [X.sub.1,10] 2413 [X.sub.1,11] 4503 [X.sub.1,12] 10634 [X.sub.1,13] 0 [X.sub.1,14] 0 [X.sub.1,15] 0 [X.sub.2,1] 0 [X.sub.2,2] 166.75 [X.sub.2,3] 2152.4 [X.sub.2,4] 3393.5 [X.sub.2,5] 5090 [X.sub.2,6] 2030 [X.sub.2,7] 0 [X.sub.2,8] 2055 [X.sub.2,9] 0 [X.sub.2,10] 0 [X.sub.2,11] 0 [X.sub.2,12] 14200 [X.sub.2,13] 1113 [X.sub.2,14] 2129 [X.sub.2,15] 2005 TABLE 3: ANALYSIS OF OBJECTIVE FUNCTION Priority Achievements Deviational Values [P.sub.1] Achieved All associated deviational variables are zero. [P.sub.2] Achieved All associated deviational variables are zero. [P.sub.3] Achieved All associated deviational variables are zero. The solution of the problem indicates that all three priorities are fully achieved. 5. CONCLUSION In this study, we have been able to demonstrate that LGP approach is a better technique than the single objective criterion when multiple conflicting objectives are involved. There are several practical applications of the technique proposed in this paper in the petroleum industry. Other constraints may be included in the model based on the situation surrounding sur·round tr.v. sur·round·ed, sur·round·ing, sur·rounds 1. To extend on all sides of simultaneously; encircle. 2. To enclose or confine on all sides so as to bar escape or outside communication. n. the decision processes on the business. The model is general enough to incorporate many of the incommensurable in·com·men·su·ra·ble adj. 1. a. Impossible to measure or compare. b. Lacking a common quality on which to make a comparison. 2. Mathematics a. and incompatible incompatible adj. 1) inconsistent. 2) unmatching. 3) unable to live together as husband and wife due to irreconcilable differences. In no-fault divorce states, if one of the spouses desires to end the marriage, that fact proves incompatibility, and a divorce economic and operational goals of industries. Some of the practical aspects of the case study have not been studied thoroughly.
TABLE 1: MONTHLY DEMAND OF EACH DEPOT AND COST
PER TON FROM EACH REFINERY
To Depots
1 2 3 4 5
From
Refineries
1 41 14 14 12 272.
5.1 7.1 4 3
2 398.2 58.8 247.3 140.9 276.4
Min 1260 165 3052 4220 8600
Demand
Max 226 27 53 65 118
Demand 7 0 52 33 95
To Depots
6 7 8 9 10
From
Refineries
1 19 255. 15 46. 10
6.4 8 3.8 1 7.6
2 276.4 410.4 175.1 310.5 390
Min 4030 10720 5605 2015 2240
Demand
Max 61 167 77 65 66
Demand 40 24 05 88 43
To Depots
11 12 13 14 15 Capacity
From
Refineries
1 119. 72.8 40 37 41 100000
8 8.6 0.6 4.5
2 415.9 53.2 200.6 158.2 119.8 85000
Min 4500 15600 1050 2018 1998
Demand
Max 125 248 36 61 52
Demand 43 34 63 49 44
REFERENCES Arthur, J.L & Lawrence, K.D., "Multiple goal production and logistics planning in a chemical and pharmaceutical company," Computers & Operations Research, 9(2), 1982, 127-137. Charnes, A. and Cooper, W. W., Management Models and Industrial Applications of Linear Programming, 1, John Wiley John Wiley may refer to:
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of , 1961. Hadley, G., Linear Programming, Addition-Wesley Publishing Company, Massachusetts, 1972. Hemaida, R. & Kwak, N. K., "A linear goal programming model for transshipment Transshipment The passing goods from one ocean vessel to another. problems with flexible supply and demand constraints," Journal of Operational Research Society, 45(2), 1994, 215-224. Ijiri, Y., Management Goals and Accounting for Control, Amsterdam, North-Holland, 1965. Ignizio, J.P., Goal Programming and Extensions, Lexington Books, Massachusetts, 1976. Kvanli, A., "Financial planning Financial planning Evaluating the investing and financing options available to a firm. Planning includes attempting to make optimal decisions, projecting the consequences of these decisions for the firm in the form of a financial plan, and then comparing future performance against using goal programming," Omega, 8, 1980, 207-218. Kwak, N.K. and Schniederjans, M.J., "A goal programming model for improved transportation problem solutions," Omega, 12, 1979, 367-370. Kwak N.K. and Schniederjans, M.J., "Goal programming solutions to transportation problems with variable supply and demand requirements," Socio-Econ. Planning Science, 19(2), 1985, 95-100. Lee, S.M., Goal Programming for Decision Analysis, Auerbach, Philadelphia, 1972. Moore, L.J., Taylor III, B.W. & Lee, S.M., "Analysis of a transshipment problem with multiple conflicting objectives," Computers & Operations Research, 5, 1978, 39-46. Olson, D.L., "Comparison for four Goal Programming Algorithm algorithm (ăl`gərĭth'əm) or algorism (–rĭz'əm) [for Al-Khowarizmi], a clearly defined procedure for obtaining the solution to a general type of problem, often numerical. ", Journal of Operational Research Society, 35(4), 1984, 347-354. Romero, C., Handbook of Critical Issues in Goal Programming, Pergamon Press, Oxford, 1991. Romero, C., "A survey of generalized goal programming (1970-1982)," European Journal European Journal is a weekly Deutsche Welle (DW) news program produced in English. It is broadcast from Brussels, Belgium and primarily covers political and economic developments across the European Union and the rest of Europe, as well as issues of particular concern to of Operational Research, 25, 1986, 188-191. Sharma, Dinesh K., Alade, J. A. and Vasishta, "Applications of Multiobjective Programming in MS/OR MS/OR Management Science and Operations Research ," Acta Ciencia Indica, XXV M(2), 1999, 225-228. Tamiz, M. and Jones, D.F., "A Review of Goal Programming and its Applications," Annals an·nals pl.n. 1. A chronological record of the events of successive years. 2. A descriptive account or record; a history: "the short and simple annals of the poor" of Operations Research, 58, 1995, 39-53. Author Profiles: Mr. Rakesh K. Sharma is a lecturer in the Department of Mathematics and Computer Science at the University of Maryland Eastern Shore University of Maryland Eastern Shore, located on 776 acres (2.5 km²) in Princess Anne, Maryland, is part of the University System of Maryland. The school was founded in 1886 by through the offices of the Delaware Conference of the Methodist Episcopal Church and was known as . He received his Master in Information Sciences (MIS) degree from the North Carolina Central University History NCCU was chartered in 1909 and opened in 1910 as the National Religious Training School and Chautauqua under the leadership of President James E. Shepard. . He has worked for Electronic Data Systems (EDS (Electronic Data Systems, Plano, TX, www.eds.com) Founded in 1962 by H. Ross Perot (independent candidate for the President of the U.S. in 1992), EDS is the largest outsourcing and data processing services organization in the country. ) and held consulting positions in the IT department of Department of Defense, American Airlines American Airlines Major U.S. airline. American was created through a merger of several smaller U.S. airlines and incorporated in 1934. It continued to buy the routes of other airlines, becoming an international carrier in the 1970s; its routes include South America, the , and United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. Postal Service postal service, arrangements made by a government for the transmission of letters, packages, and periodicals, and for related services. Early courier systems for government use were organized in the Persian Empire under Cyrus, in the Roman Empire, and in medieval . He has presented several papers in International conferences. His area of research includes Mathematical programming mathematical programming Application of mathematical and computer programming techniques to the construction of deterministic models, principally for business and economics. and information system design. Mr. Avinash Gaur Gaur, ruined city, India Gaur (gour), ruined city, West Bengal state, India. Known also as Lakhnauti, the city was an ancient Hindu capital of Bengal. It was captured (c. earned his M.S. from the Chaudhary Charan Singh University About Chaudhary Charan Singh University also called Meerut University is located in Meerut, Uttar Pradesh. The Meerut university was established in 1966. It was later renamed to its current name after Chaudhary Charan Singh, former Prime minister of India. in 1996. He is a lecturer in the department of applied mathematics at RKGIT Engineering College, Ghaziabad and Ph.D. student in the department of Mathematics at Meerut College, Meerut, U.P. (India). His research has focused on mathematical programming and applied business studies. Dr. Daniel Okunbor is an associate professor in the Department of Mathematics and Computer Science at the University of Maryland Eastern Shore. He received Ph.D. in Computer Science from the University of Illinois at Urbana-Champaign Early years: 1867-1880 The Morrill Act of 1862 granted each state in the United States a portion of land on which to establish a major public state university, one which could teach agriculture, mechanic arts, and military training, "without excluding other scientific . His research interests are in mathematical modeling
http://computer.org/. , American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards to mathematicians. and Association of Computing Machinery. He received National Science Foundation Research Initiation Award and has given many invited research presentations worldwide. Rakesh K. Sharma, University of Maryland Eastern Shore, Princess Anne, Maryland Princess Anne is a town in Somerset County, Maryland, United States. The population was 2,313 at the 2000 census. It is the county seat of Somerset CountyGR6. , USA Avinash Gaur, RKGIT Engineering College, Ghaziabad, INDIA Daniel Okunbor, University of Maryland Eastern Shore, Princess Anne, Maryland, USA 
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