Presentation is made of a computer implementation of an effective approach for the solution of nonlinear, nonconvex ratio goals problems. The approach employs Charnes and Cooper's (1977) linearization method of s...
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Presentation is made of a computer implementation of an effective approach for the solution of nonlinear, nonconvex ratio goals problems. The approach employs Charnes and Cooper's (1977) linearization method of solution of ratio goals problems with a sequence of perturbed linearprogramming (LP) problems. For efficient solution, it incorporates the Opposite Sign Algorithm and the Negative Image Method, both of which employ the available information from the most recently solved problem. The efficiency of these algorithms against a new start every time a new LP problem is set up for solution has been confirmed by computational testing on randomly generated problems.
Test computations using a proposed procedure for solving general multidimensional knapsack problems with a few contraints have positive results. The solution procedure assumes that the problem has a few resource cons...
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Test computations using a proposed procedure for solving general multidimensional knapsack problems with a few contraints have positive results. The solution procedure assumes that the problem has a few resource constraints and that the parameters are all positive integers. It uses a state generation scheme, but the generated state sets are revised regularly using the dominance principle rather than the strict principle of optimality. Nonpromising state vectors are pruned by considering the highest return that can be obtained with the remaining decision variables and resources. If the size of a state set exceeds a threshold value, the problem will be partitioned into subproblems, which are combined optimally at the last stage. The test results indicate that computation times are very good and that the preprocessing procedure of eliminating dominated variables is a cost-effective technique, especially for small dimensional problems with uncorrelated data.
This note presents a simple and intuitive graphical method for finding the shortest route between two specified nodes in a network. The approach is similar to the Hungarian Method for solving assignment problems.E. A....
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This note presents a simple and intuitive graphical method for finding the shortest route between two specified nodes in a network. The approach is similar to the Hungarian Method for solving assignment problems.E. A. Silver
This paper shows how to generalize the Dantzig-Wolfe decomposition principle to integer programming. It does this in a unified way, regardless of the choice between the two main solution methods: ‘Branch and bound’ ...
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This paper shows how to generalize the Dantzig-Wolfe decomposition principle to integer programming. It does this in a unified way, regardless of the choice between the two main solution methods: ‘Branch and bound’ or ‘cutting plane’. In both instances the authority at the central level issues price directives in the form of a polyhedral, concave price function, where the purpose is to charge the sublevels for the use of central resources including a penalty for any attempts to violate the integrality of the result. The sublevels then respond with their optimal activities given this price function. Finite convergence of the procedure is established.
The computational results of a new zero-one goal programming algorithm are compared with those obtained using the algorithm developed by Lee and Morris (1977). The proposed constraint aggregation and partitioning alg...
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The computational results of a new zero-one goal programming algorithm are compared with those obtained using the algorithm developed by Lee and Morris (1977). The proposed constraint aggregation and partitioning algorithm is based on an aggregation scheme that allows all constraints under consideration to be combined in one operation. The upper and lower bounds for the number of nonzero variables needed to satisfy each constraint and each priority level are determined by the algorithm, which then searches for the subprogram consisting of the first priority levels that can be achieved completely. By this process, the problem is partitioned according to priority level. The algorithm also derives the conditions needed to determine the range of nonzero variables that may provide complete achievement for a subprogram and also generate the optimal solution. The new algorithm is more accurate and more reliable and requires about 10% of the central processing unit time of the Lee and Morris algorithm.
A constructive parameterization procedure for a class of operational stochastic linearprogramming problems is proposed which is based on predicting the base set of LLP solutions. The problem of predicting the composi...
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A constructive parameterization procedure for a class of operational stochastic linearprogramming problems is proposed which is based on predicting the base set of LLP solutions. The problem of predicting the composition of the base set is formally stated and methods of its solution are proposed.
A common warehouse/distribution problem is the unitization of pallet loads. A linearprogramming model has been developed to determine optimal stacking patterns on the basis of the dimensions of the boxes that constit...
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A common warehouse/distribution problem is the unitization of pallet loads. A linearprogramming model has been developed to determine optimal stacking patterns on the basis of the dimensions of the boxes that constitute the load. The desired dimensions of the finished load may be user specified. No restriction is placed on the number of boxes of various types that may be loaded. The developed model is two-dimensional and assumes that all boxes have the same height.
A steepest edge active set algorithm is described which is suitable for solving linearprogramming problems where the constraint matrix is sparse and has more rows than columns. The algorithm uses a steepest edge crit...
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A steepest edge active set algorithm is described which is suitable for solving linearprogramming problems where the constraint matrix is sparse and has more rows than columns. The algorithm uses a steepest edge criterion for selecting the search direction at each iteration and recurrence relations are derived which enable it to execute efficiently. The canonical form for the active set method is convenient for many applications and may be exploited to devise a simple crash procedure which is employed prior to phase one. A complete two-phase algorithm which incorporates the crash procedure is outlined. Only one artificial variable is needed to determine if the linearprogramming problem has a feasible solution in phase one. Some computational results are given to illustrate the effectiveness of the algorithm for a range of sparse linearprogramming problems. Comparisons between the steepest edge criterion and the traditional Dantzig criterion suggest that the former usually requires fewer iterations and often leads to substantial savings for large problems.
We improve the standard transformation of the symmetric, single-depot, multiple traveling salesman problem (MTSP) to one on a sparser edge configuration. The improvement tends to suppress, to a large extent, the degen...
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We improve the standard transformation of the symmetric, single-depot, multiple traveling salesman problem (MTSP) to one on a sparser edge configuration. The improvement tends to suppress, to a large extent, the degeneracy of the resulting symmetric traveling salesman problem (TSP). As a result, a 1-tree based TSP algorithm solves large MTSPs of the type we consider as easily as it solves standard TSPs. We demonstrate the improvement by presenting computational results that are currently the best available. [ABSTRACT FROM AUTHOR]
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