Production-transportation problems

A typical production-transportation problem can be described as follows. There are m production plants and n customers. A single product is produced at the plants and shipped from the plants to the customers. Each plant ihas a capacity limit Si, and the production cost is a concave function /(xi, X2, Xm) of the amounts produced at these plants x, X2,Xm- The transportation costs from the plants to the customers are linear the unit transportation cost from plant i to customer j is Cij. The problem involves a single time period only, and the demand of each customer j is known as dj which must be satisfied. The problem seeks a production and distribution plan that minimizes total production and transportation cost. The problem can be formulated as the following mathematical program ... 

There are also topics that require further research within each individual problem class. For production-transportation problems, all the results reviewed consider one product and linear transportation costs. A more general model should address multiple products (which compete for limited production capacity) and a nonlinear (e.g. fixed charge plus variable) transportation cost structure. Note that in practice transportation cost is normally nonlinear. 

Hochbaum, D.S. and S.-P. Hong, On the Complexity of the Production-Transportation Problem , SIAM Journal on Optimization, 6 (1996), 250-264. 

Holmberg, K. and H. Tuy, A Production-Transportation Problem with Stochastic Demand and Concave Production Costs , Mathematical Programming, 85(1999), 157-179. 

Kuno, T. and T. Utsunomiya, A Lagrangian Based Branch-and-Bound Algorithm for Production-Transportation Problems , Journal of Global Optimization, 18 (2000), 59-73. 

Tuy, H., S. Ghannadan, A. Migdalas, and P. Varbrand, A Strongly Polynomial Algorithm for a Concave Production-Transportation Problem with a Fixed Number of Nonlinear Variables , Mathematical Programming, 72 (1996), 229-258. 

Production was initially limited by product transportation problems and the limited number of refineries. The railroad attempted to offset the transportation problem by laying track down to a point within five miles of the oil fields however, wagons were still used to transport the product from the derricks to the railroad. The transport bottleneck was not relieved until 1865, when the first oil pipeline was built between the oil fields and the railroad station. 

In oil bearing formations, the presence of polar chemical functions of asphaltenes probably makes the rock wettable to hydrocarbons and limits their production. It also happens that during production, asphaltenes precipitate, blocking the tubing. The asphaltenes are partly responsible for the high viscosity and specific gravity of heavy crudes, leading to transport problems. 

Laborelec is the Belgian laboratory for the electricity industry. It deals with measuring and studying problems arising with the production, transport and distribution of electricity to industrial and private customers. It has developed very diverse domains of expertise, such as acoustics, material characteristics, technical audits to telecommunications, vibrations monitoring, etc... 

Transformations in Hilbert space, 433 Transition probabilities of negatons in, external fields, 626 Transport theory, 1 Transportation problems, 261,296 Transversal amplitude, 552 Transversal vector, 554 Transverse gauge, 643 Triangular factorization, 65 Tridiagonal form, 73 Triple product ensemble, 218 Truncation error, 52 Truncation of differential equations/ 388... 

Corrosion and scale deposition are the two most costly problems in oil industries. Corrodible surfaces are found throughout production, transport, and refining equipment. The Corrosion and Scale Handbook gives an overview of corrosion problems and methods of corrosion prevention [159]. 

Relaxation of hard constraints is critical for optimization-based planning models used in industry practice with more than even 100,000 constraints and specifically for hard integer programming problems (Fisher 2004). Hard constraints set hard minimum and maximum boundaries for decision variables that have to be fulfilled. It may occur that no solution exists fitting all constraints at the same time. Planners have difficulties to identify manually constraints leading to infeasibility. Value chain planning model infeasibility is mainly caused by volume-related constraints of material flows e.g. by bounding sales quantities, inventories, transportation quantities, production and procurement quantities. Examples in literature for relaxation methods to e.g. transportation problems is presented by Klose/Lidke (2005)... 

In view of the domestic estimates, imports are almost redundant, It appears likely, however, that by 1985-1990 Canada will have about one million additional short tons of acid available for export. At least some would be available in PAD districts I and II, Furthermore, sulfur production from sour natural gas and tar sands is likely to increase. As transport problems are mitigated and formed sulfur gains acceptance, Canadian output will become available to districts I, II, and IV. Excluding the existing stockpile, the estimate for tar sands and heavy oil is... 

Rhizopus oryzae was immobilized in polyurethane foam cubes by Sun et al. -" The effects of the cube size on cell immobilization, cell growth and L(-i-)-lactic acid production were studied, limnobilization was accomplished by simple adsorption. The use of small cubes for R. oiyzae immobilization was very effective in increasing the productivity of L(-t-)-lactic acid by the immobilized cells. The inoculum size was effective for increasing the immobilization ratio (ratio of the number of cubes containing cells to the total number of cubes). We discussed mass transport problems of polyurethane foam and how the application of certain composite technologies mitigates this difficulty earlier in this chapter. 

Just as engineering is sometimes considered to be an applied science, the concepts of this chapter should provide for applications—to hydrates in the earth (Chapter 7) and to hydrate problems in production, transportation, and processing of oil and natural gas (Chapter 8). As an introduction to the chapter, consider an example of some typical hydrate calculations. 

Chapter 8 presents problems of natural gas production, transportation, and processing which are related to hydrates. Because a standard kinetic treatment method has progressed past the fledgling state in the second edition (1998), the state-of-the-art in flow assurance is turning away from thermodynamic properties which encourage hydrate avoidance, to kinetic properties which encourage a new philosophy in flow assurance—that of risk management. 

This involves the engineering of food powder ingredient particles that can maintain ingredient stability and functionality, that do not present dust formation problems, that do not present difficult handling and transport problems, and can be readily rehydrated to deliver their required functional performance in a wet formulation. The major limitation to this type of approach is the low value of food powders and the low cost driven nature of food powder product that stunts this type of innovation. On the other hand, particle engineering is the key to the higher added value of food powders, e g. by producing products with excellent instant properties. 

Wine is a widely consumed beverage worldwide, with thousands of years of tradition and a remarkable commercial and social value. The evaluation of the quality of wine is a permanent concern for manufactures, merchants, and consumers. The presence of potentially toxic elements in wines is associated with soil contamination and also related to atmospheric precipitation, pesticides, and materials used in production, transportation, and storage. Although at the end of alcoholic fermentation there is a significant reduction of the mineral content, this may not be enough to prevent some problems related to wine stability, namely,... 

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