Linear programming allocation

The linear programming approach outlined in Section IV,B,l,b has also been applied to cyclic networks (Kl), the lack of theoretical validity notwithstanding. On an operational level, linear programming has been used to determine the most efficient means of supplying the water requirements of a major metropolitan area (G3) and to guide the allocation of production and supply of gas for the northwestern counties of England (BIO). In the latter application the results of the grid optimization are used to determine (i) optimal allocation of natural gas supply, (ii) production... 

The problem is to allocate optimally the crudes between the two processes, subject to the supply and demand constraints, so that profits per week are maximized. The objective function and all constraints are linear, yielding a linear programming problem (LP). To set up the LP you must (1) formulate the objective function and (2) formulate the constraints for the refinery operation. You can see from Figure El6.1 that nine variables are involved, namely, the flow rates of each of the crude oils and the four products. 

The general procedure mentioned in the preceding paragraph is designated as linear programming. It is a mathematical technique for determining optimum conditions for allocation of resources and operating capabilities to attain a definite objective. It is also useful for analysis of alternative uses of resources or alternative objectives. 

If the systems and their economic functions are all linear, then in principle the supersystem could be optimized directly by linear programming. This approach would eliminate not only the need for allocation quotas, but also the need for the local managers to plan their own systems. However, when one considers that the time required for the solution of a linear-programming problem on a high-speed computer is approximately proportional to the cube of the number of constraints, it immediately becomes clear that optimization of the entire supersystem at once would not be very efficient. Moreover, supersystems the size of many chemical companies could not be solved in a reasonable time even on the... 

The problem is to determine the optimum biomass allocation policy in order to maximize the profit. A generalized linear program, SIMPLES (10), was used to develop the resource allocation model. 

Abstract. In the present paper the problem of reuse water networks (RWN) have been modeled and optimized by the application of a modified Particle Swarm Optimization (PSO) algorithm. A proposed modified PSO method lead with both discrete and continuous variables in Mixed Integer Non-Linear Programming (MINLP) formulation that represent the water allocation problems. Pinch Analysis concepts are used jointly with the improved PSO method. Two literature problems considering mono and multicomponent problems were solved with the developed systematic and results has shown excellent performance in the optimality of reuse water network synthesis based on the criterion of minimization of annual total cost. 

Tjalling Charles Koopmans (1910-1985), American econometrist of Dutch origin and professor at Yale University, introduced mathematical procedures of linear programming to economics, and received the Nobel Prize in 1975 for work on the theory of optimum allocation of resourcesr... 

Sanayei, A. Mousavi, S. E Abdi, M. R, Mohaghar, A. 2008. An integrated group decision-making process for supplier selection and order allocation using multi-attribute utility theory and linear programming. Journal of the Franklin Institute. 345 (7) 731-747. 

Assume myopic best-response strategies. Formulate a linear program (LP) for the efficient allocation problem. The LP should be integral, such that it computes feasible solutions to the allocation problem, and have appropriate economic content. This economic content requires that the dual formulation computes competitive equilibrium prices that support the efficient allocation, and that there is a solution to the dual problem that provides enough information to compute VCG payments. 

Milind Dawande, R. Chandrasekharan, and Jayant Kalagnanam. On a question in linear programming and its application in decentralized allocation. Technical report, IBM research report, Jul 2002. 

That is, the superadditive dual reduces to the dual of the linear programming relaxation of SPR In this case we can interpret each yi to be the price of object i. Thus an optimal allocation given by a solution to the CAP can be supported by prices on individual objects. 

Formulate as a linear program the problem of finding the efficient allocation. Appropriate variables in the dual can be interpreted as the prices paid by buyers as well the surplus they receive. There can be many different formulations of the same problem but not any formulation will do. The formulation must be sufficiently rich that the Vickrey prices are contained in the set of feasible dual solutions. We believe that with the exception of diminishing marginal utilities, the only formulation rich enough for the job is CAPS. 

Single objective models In Section 6.2, we presented a single objective linear programming model for order allocation using Example 6.3. The model considered supplier capacities, price discounts, buyers demand, quality, and lead-time constraints. The objective was to minimize total cost, which included fixed and variable cost of the suppliers. We shall briefly review here, some of the other single objective models that have been discussed in the literature. 

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