Linear Programming Transportation Research Articles

APPLICATION OF TRANSPORTATION MODEL TO SOLVE TANKERS’ – ROUTING PROBLEM

The problem of selecting minimum cost routes for tankers in distributing petroleum products and satisfying customers’ requirement without scarcity in Nigeria remains a huge challenge to major marketers in the oil industries. The cost of transporting petroleum products from sources to destinations matters a lot to oil marketers because of the direct impact it has on their profits. The means of distributing petroleum products from refineries to depots or filling stations are tankers’ routing and pipelines. In this research, we extended some existing tankers’-routing models in literature which use a discrete integer programming approach to determine efficient and effective distribution of petroleum products. Consequently, we developed a new transportation linear programming algorithm to determine minimum cost routes in the delivery of petroleum product from their supply centers (refinery) to demand centers (filling stations). The significance of the application we adopted in this research lies in the modified distribution approach to tackle the complexity involved when transportation problems are formulated as linear programming problem having several variables and constraints. In this research, we formulate a new version of transportation model of tankers’ routing with the aim of reducing the cost of petroleum products delivery. The proposed transportation linear programming model was applied to a numerical example alongside other existing transportation algorithms. It is observed that, the new algorithm produced approximately the same total cost obtained by using other existing algorithms

SOLVING STOCHASTIC TRANSPORTATION ELECTRICITY PROBLEM WITH FUZZY INFORMATION ON PROBABILITY DISTRIBUTION USING MATLAB PROGRAM

This study focuses on MATLAB code programs of the entire stages of solving Stochastic Transportation Linear Programming Problems with Fuzzy Uncertainty Information on Probability Distribution Space (STLPPFI) with its algorithm outlines. A MATLAB code program of STLPPFI problem solver with algorithm outlines are proposed to solve STLPPFI model problems, and it utilizes many concepts as Alpha-Cut technique, Truth Degrees technique, Linear Fuzzy Membership Function (LFMF), Trapezoidal Fuzzy Number , Triangular Fuzzy Number , Linear Fuzzy Ranking Function (LFRF), Expectation Weighted Summation technique (EWS) and analyzing cases via second condition test of alpha-cut technique. The STLPPFI problem solver is utlized to convert STLPPFI into its corresponding equivalent Deterministic Transportation Linear Programming Problem (DTLPP) via defuzzifying from fuzziness on probability distribution space and derandomization randomness of problem formulation respectively. In addition, Dual-Simplex algorithm method with Vogel Approximation Algorithm Method (VAM) are used to obtain optimal solution from DTLPP. All MATLAB code programs with their proposed algorithm outlines are new except Dual-Simplex and VAM. The MATLAB code program of STLPPFI problem solver are more efficient along with a numerical example on electricity field illustrating practicability of this proposed MATLAB code program with its algorithm. Finally, the solution procedure illustrates the MATLAB code program of the proposed method is practical and applicable in the fields of energy and industry as it facilitates the method of transforming the energy at the lowest cost, least time running and is commercially applicable. Comparative comments are provided between Dual-Simplex and VAM in solution process.

Quantum Walk on the Generalized Birkhoff Polytope Graph.

We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and bounded-degree graphs. In contrast, our numerical results show that it is possible to achieve a greater than quadratic quantum speedup for the mixing time on a subclass of GBPG (TLP with two consumers and m suppliers). We analyze two types of initial states. If the walker starts on a single node, the quantum mixing time does not depend on m, even though the graph diameter increases with it. To the best of our knowledge, this is the first example of its kind. If the walker is initially spread over a maximal clique, the quantum mixing time is , where ϵ is the threshold used in the mixing times. This result is better than the classical mixing time, which is .

Solving the Multiobjective Transportation Decision-Making Problem Based on Improved S-Type Membership Function

Aiming at the problem of multiobjective transportation decision-making, a fuzzy compromise method with an improved S-type membership function is proposed. This method not only considers a single objective and evaluates it marginally but also evaluates the overall objective as a whole. First of all, a multiobjective transportation decision-making model is established. Then, each objective function is mapped to a function on the interval [0,1] through the S-type membership function, thereby transforming the multiobjective transportation linear programming model into a multiobjective transportation fuzzy compromise programming model, and its satisfaction is expressed by the global utility function. Finally, through two examples, the results of the example algorithm are compared with the results in the literature, highlighting the superiority of the method. The experimental results show that in the multiobjective transportation decision-making problem, the fuzzy compromise method of the S-type membership function has better flexibility and effectiveness.

Why do the poor travel less? Urban structure, commuting and economic informality in Mexico City

While in Mexico City formal jobs are concentrated in the city centre, affordable housing is generally only available in its outer rings. This reduced accessibility to formal employment would suggest that the poor have longer commutes. However, observed travel times show that low-income workers actually have the shortest commutes. Using two linear programming transportation models we found that this is due to the location of informal work activities, which seems to be a function of the residential location of workers involved in the informal sector as a response to the disadvantages of the formal urban structure of jobs and housing that affect the poor.

William W. Cooper: Innovator, Fighter, and Scholar

W illiam Wager Cooper was born on July 23, 1914 in Birmingham, Alabama, where his father was a bookkeeper and later a distributor for Anheuser-Busch. Bill’s family moved to Chicago when he was three years old. His father owned a chain of gasoline stations, but lost them during the Great Depression. With his father in ill health and no family revenue, Bill left high school after his sophomore year to work at whatever jobs he could find. These included spotting pins in bowling alleys, caddying at golf courses, and even professional boxing, where his record was 58 wins, 3 losses, and 2 draws. While hitchhiking to the golf course one day, Bill met Eric L. Kohler, a principal with Arthur Andersen & Co., who became his life-long mentor. Kohler loaned him money to enroll as a non-degree student at The University of Chicago. Bill liked the academic atmosphere and took the college entrance examinations, intending to become a physical chemist. During his studies, Kohler asked him to review the mathematics used in a patent infringement suit. After Cooper found errors in the mathematics used by the plaintiff’s engineers, Andersen hired him part time during the school year and full time in the summer. This awakened Cooper’s interest in accounting, and he switched his major to economics. While at Chicago, Bill became good friends with a political science student, Herbert A. Simon. Cooper graduated Phi Beta Kappa with his A.B. in 1938.

Contribution of Decision Support System in Enhancing Productivity and Profitability of the Firm

The business paradigms are changing amidst changing business environment. There are newer technologies at disposal, rising customer awareness and their expectations from the need to attain efficiency and effectiveness in business processes for survival and competitive advantage. This paper provides insights on the significance of business decision making and present state of organizations that are striving to achieve optimal utilization of limited business resources. The paper highlights the nature of linear programming model and its importance in effective business decision making. The business impact of model is illustrated in the case using the linear programming model and transportation method through excel solver in computer manufacturing firms to help in deciding optimum quantity to produce within limited resources and how the computers manufactured can be distributed to market places at minimal cost. The paper elicits the effectiveness of the linear programming model to realize good decision making in business by meeting the business objectives through optimal utilization of resources. It concludes that model driven decision support system enhances the productivity and profitability of the firm in a constrained environment and is a highly effective model for solving business problems.

Fuzzy Transportation Linear Programming Models based on L-R Fuzzy Numbers

Transportation models play an important role in logistics and supply chain management for reducing cost and improving service. In this paper two new fuzzy transportation linear programming models are developed: one with equality constraints and other with inequality constraints using L-R fuzzy numbers. The membership functions of L-R fuzzy numbers of fuzzy transportation cost are consider being linear and exponential. This paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem, in that the cost coefficients and the supply and demand are L-R fuzzy numbers. The two models are illustrated with an example. The optimal fuzzy transportation cost for the two models slightly varies when linear membership functions are equal and the optimal fuzzy transportation cost is same in case of different membership functions i.e., either linear or exponential membership functions defined on L-R fuzzy numbers. Most of the fuzzy transportation problems reviewed in literature have the negative optimal fuzzy transportation cost but in our proposed method we obtain positive optimal fuzzy transportation cost in all most all cases.

The logistics of supplying single vs. multi-crop cellulosic feedstocks to a biorefinery in southeast North Dakota

This study investigates the economics of supplying cellulosic crop residue feedstocks within 100mile (or 161km) radius of a potential new biorefinery in southeast North Dakota. We utilize linear programming transportation models and GIS (Geographic Information System) maps to identify optimal cellulosic feedstock supply sites for the biorefinery. Our evidence indicates that future crop residue removal policy will be important in assessing economic viability of harvesting crop residues for biofuel production. An increase in residue removal rate would narrow the size of supply areas required to provide total feedstock need for the biorefinery and consequently result in reducing transportation costs. There is an economic tradeoff between residue collection density and distance from the biorefinery. When multiple residue feedstocks are considered, this analysis is complicated further because greatest densities for each crop are not in similar regions. Overall, our findings show that higher costs savings can be achieved if multiple feedstocks are employed to produce cellulosic biofuels. In addition, feedstock supply risks can be lower with the use of multiple feedstocks.

A note on asymptotic formulae for one-dimensional network flow problems

This note develops asymptotic formulae for single-commodity network flow problems with random inputs. The transportation linear programming problem (TLP) where N points lie in a region of R1 is one example. It is found that the average distance traveled by an item in the TLP increases with N1/2; i.e., the unit cost is unbounded when N and the length of the region are increased in a fixed ratio. Further, the optimum distance does not converge in probability to the average value. These one-dimensional results are a useful stepping stone toward a network theory for two and higher dimensions.

Bounds and Approximations for the Transportation Problem of Linear Programming and Other Scalable Network Problems

Bounds and approximate formulae are developed for the average optimum distance of the transportation linear programming (TLP) problem with homogeneously, but randomly distributed points and demands in a region of arbitrary shape. It is shown that if the region size grows with a fixed density of points, then the cost per item is bounded from above in 3+ dimensions (3+-D), but not in 1-D and 2-D. Lower bounds are also developed, based on a mild monotonicity conjecture. Computer simulations confirm the conjecture and yield approximate formulae. These formulae turn out to have the same functional form as the upper bounds. Curiously, the monotonicity conjecture implies that the cost per item does not depend on zone shape asymptotically, as problem size increases, for 2+-D problems but it does in 1-D. Therefore, the 2-D case can be viewed as a transition case that shares some of the properties of 1-D (unbounded cost) and some of the properties of 3-D (shape independence). The results are then extended to more general network models with subadditive link costs. It is found that if the cost functions have economies of scale, then the cost per item is bounded in 2-D. This explains the prevalence of the “last mile” effect in many logistics applications. The paper also discusses how the results were used to estimate costs under uncertainty for a vehicle repositioning problem.

SPATIAL PRICE EQUILIBRIUM AS A FOUNDATION TO UNIFIED SPATIAL COMMODITY MODELING

ABSTRACT Various approaches to modeling spatial commodity flows are critically examined. Starting with the linear programming transportation problem, it is found that the properties of the spatial equilibrium model tan be served as a foundation to a host of other models. The convergence of some key characteristics embedded in these models indicates that the spatial price equilibrium model is indeed an important cornerstone upon which the entropy formulations, imperfect competition and spatial econometric models are built.

A linear-programming-based price negotiation procedure for contracting shipping companies

A procedure for a shipper contracting with ocean container shipping companies is described. The procedure incorporates the solution to a linear programming transportation model with results from sensitivity analysis. The procedure described enables shippers to evaluate all possible means of obtaining the lowest adjusted price for a given shipping route in a short period of time. Snippers that spend a minimum amount of time on price negotiation are generally able to accept or reject a pending offer prior to expiration of a shipping company's imposed time limit. A case study illustrates the negotiation procedure.

A graphical interface for production and transportation system modeling: PTS

PTS is a graphical interface for production and transportation system modeling. It provides a means of creating an economic model of production and transportation activities in a system of plants and markets. The model created by PTS is translated into the GAMS language and is solved using that system. The results are then returned to PTS and are displayed graphically. PTS runs under Windows on IBM PCs and compatibles. PTS is used to (1) provide a graphical interface for knowledge-based model development systems, (2) provide a test-bed for studies of parallel model representations and (3) analyze methods of production and transportation model development which are simpler than the knowledge-based methods. The system is currently implemented for linear programming production and transportation problems. Also, the current implementation provides graphical and GAMS representations of the model.

Characteristics of the fuzzy LP transportation problem for civil engineering application

Abstract The fuzzy linear programming (FLP) transportation problem is a useful tool for some civil engineering problems. It can deal with problems whose objective and constraints are not well-defined, or information on them is not precise. It considers that the objective and constraints are fuzzy sets in the space of alternatives and defines the decision set as the intersection of the two sets. The solution is the element of the decision set which has the maximum membership grade. This paper addresses the type of problems which are suited for fuzzy LP transportation modeling; examines the formulation of the model and characteristics of the solution; and presents an example of FLP transportation formulation for the earth moving problem during highway construction. The solution's sensitivity to the fuzziness of objective and information on the quantities of supply and demand is also analysed.

An Evaluation of the Maxwell-Boltzmann Entropy Model of the Appalachian Steam Coal Market

Since the early 1950’s, there has been much effort expended in modeling interregional commodity flows. Among them are linear programming transportation models (e.g., Henderson); the Enke-Samuelson-Takayama-Judge models; the Leontief-Strout gravity models; and other econometric models. However, the entropy model has so far eluded description especially when implemented empirically. In this paper, we implement the Maxwell-Boltzmann entropy maximization model to the Appalachian steam coal market. We then compare the solution of optimum coal shipments with that of the corresponding linear programming transportation and spatial equilibrium models. It is found that (1) the performance of the Maxwell- Boltzmann entropy model is comparable to that of the spatial equilibrium model and (2) the entropy has outperformed the linear programming transportation model in its simplest form in terms of predicting actual coal shipments.

A sensitivity analysis of the linear complementarity programming model: Appalachian steam coal and the natural gas market

There have been extensive attempts in recent years to perform spatial equilibrium analysis of commodity markets, particularly that of energy. Most of these attempts have been based on linear programming transportation models, and more recently quadratic programming models. Unfortunately, neither of these modelling approaches can deal with the case of multi-commodity analysis with non-symmetric regression coefficients. In this paper, we overcome this problem by employing the linear complementarity programming model. In addition, we show how the model can be applied to coal and gas energy flows within a single region. Future potential applications of the model are also implied.

Empty freight car dispatching model under freight car pool concept

In the last few years, growing attention has been given to the cost savings potential of the specialized freight car pool concept. Under this concept, a fleet of single-purpose freight cars are pooled at many loading points, and the cars emptied at unloading terminals can be sent back to any loading point in order to reduce empty car miles and time. As part of a continuing effort to improve the car dispatching method for this concept, this paper offers an improvement to the traditional linear programming transportation problem approach, incorporating daily variations of empty car supply and demand characteristics in the model. The proposed method, therefore, allocates cars between supply and demand points with the dispatching date specified, enabling the dispatcher to make daily car disposition decisions. It can incorporate both the travel distance cost and inventory cost of empty cars at terminals in the objective. If the holding of empty vehicles at the terminals for future dispatch is allowed, the problem is structured as a transshipment problem in which the overnight storage is the transshipment point.

Scheduling of Demand‐Responsive Transit Vehicles

This paper presents a vehicle dispatching procedure designed to minimize empty vehicle travel and idle time for a demand-responsive transportation system. The method schedules the empty vehicle assignment between passenger drop-off points and passenger pick-up points by examining the times of drop-offs and pick-ups, and the travel times and distance between them. The minimization of empty vehicle travel and idle time is accomplished through the use of a linear programming transportation problem in which supply and demand vectors contain both location and time elements. The service area is divided into zones and the operating hours into time periods; the vehicle movements (loaded and empty) are processed as the movements between zones, and between time periods. The outputs of the model include scheduling instructions for each vehicle (both loaded and empty trips), estimates of vehicle miles and time, fleet size requirements to satisfy the passenger trip requests, and the identification of passenger trips which cannot be met due to fleet size limitation.

A Mathematical-Computer Language for Linear Programming Problems

This paper describes the development of a compiler which permits the translation of linear programming problems from a mathematical statement of the problem to a GAMS statement. The GAMS statement can then be read by the computer and the linear programming problem can be solved. Thus it is demonstrated that it is feasible to develop a computer language which will permit one to use mathematical symbols to direct the computer to solve a class of linear programming problems.The paper provides a small example linear programming transportation problem and shows how the problem may be input to the computer in a mathematical formatting language and then translated (i) into a mathematical statement and (ii) into a GAMS statement. Then a description is given of the lexical analyzer generator and the parser generator that were used to develop the math to GAMS translator.The present version of the translator can handle only a very restricted set of problems. Thus the paper closes with a description of the work which will be required to enable the translator to handle a much wider class of programming problems.