ON BI-LEVEL LINEAR FRACTIONAL •I PROGRAMMING PROBLEMS
Rcfaat Mohammad Aly Rabie;
Abstract
The d.cccntralizcd planning. has been recognized as an important decision-making problem. Mult-i-level programming models partition control over decision variables among the ordered levels wi\hin a hierarchical planning structure. The decentralized planning seeks to find a simulta eous compromise among the various objective functions of the different divisions.
Te Bi-lcvel linear programming problem is a special case of the multi-level linear programming prpblems and is a nested optimization model i11volving two problems, an upper and lower one. Both problems have to be optimized given a single feasible region. Each decision-maker at both' levels attempts to optimize his individual objective function, and their final decisions are executed sequentially where the upper-level
decisioR-'n.1aker 1i1akes his decision firstly.
Most applications of the hi-level linear programming problems are in the economics realm, particularly central economic planning. The problem can be viewed as a two-person sequential •game of perfect infonnation, Le., a two-person static Stackelberg game, where two players wish to minimize their own cost functions. The first player, the leader, knows the cost function of the second player, the follower, who may or may not know the cost function of the leader, knows the selected strat gy by the leader and takes this into account when computing his own strategy. The leader is assumed to be• able to anticipate the reactions of the follower.
When there is only one level of decision, the optimization problems involving one or more ratios in the objective function are called fractional programming. Ratio functions arise in economic applications when n efficient measure of a system is optimized or in approaching a stochastic p ogramming problem.
In the hi-level linear programming, the linear fractional objectives are sometimes encountered (i.e., ratio objectives that have linear numerators •and denominators). Examples of fractional objectives including return on investment, liquidity, productivity, assets per share, etc; can be found in finance or corporate planning.
Te Bi-lcvel linear programming problem is a special case of the multi-level linear programming prpblems and is a nested optimization model i11volving two problems, an upper and lower one. Both problems have to be optimized given a single feasible region. Each decision-maker at both' levels attempts to optimize his individual objective function, and their final decisions are executed sequentially where the upper-level
decisioR-'n.1aker 1i1akes his decision firstly.
Most applications of the hi-level linear programming problems are in the economics realm, particularly central economic planning. The problem can be viewed as a two-person sequential •game of perfect infonnation, Le., a two-person static Stackelberg game, where two players wish to minimize their own cost functions. The first player, the leader, knows the cost function of the second player, the follower, who may or may not know the cost function of the leader, knows the selected strat gy by the leader and takes this into account when computing his own strategy. The leader is assumed to be• able to anticipate the reactions of the follower.
When there is only one level of decision, the optimization problems involving one or more ratios in the objective function are called fractional programming. Ratio functions arise in economic applications when n efficient measure of a system is optimized or in approaching a stochastic p ogramming problem.
In the hi-level linear programming, the linear fractional objectives are sometimes encountered (i.e., ratio objectives that have linear numerators •and denominators). Examples of fractional objectives including return on investment, liquidity, productivity, assets per share, etc; can be found in finance or corporate planning.
Other data
| Title | ON BI-LEVEL LINEAR FRACTIONAL •I PROGRAMMING PROBLEMS | Other Titles | حول مشكلات البرمجة الخطية الكسرية ذات المستويين | Authors | Rcfaat Mohammad Aly Rabie | Issue Date | 2006 |
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