Supplement E Notes

# Supplement E Notes - Supplement E Notes Linear Programming:...

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Supplement E Notes Linear Programming: a technique that is useful for allocating scarce resources among competing demands; it is an optimization process Linear Programming Models and mathematical assumptions that apply to them have several characteristics: 1) Objective Function - An expression in linear programming modes that states mathematically what is being maximized or minimized - Provides the "scorecard" on which the attractiveness of different solutions is judged 2) Decision Variables - Variables that represent choices the decision maker can control - Solving the problem yields their optimal values - Linear Programming is based on the assumption these variables are continuous (can be fractional quantities and not whole numbers) - When the decision variables represent non-divisible units, we can usually simply round the solution up or down to get a reasonable solution that isn't in violation of any constraints - Integer Programming - more advanced technique to deal with non-divisible units 3) Constraints - Limitations that restrict the permissible choices for the decision variables - Each limitation can be expressed mathematically in one of three ways: 1) A less-than-or-equal-to (< ) - Puts an upper limit on some function of decision variables and most often is used with maximization problems 2) An equal-to (=) - The function must equal some value, often used for certain mandatory relationships 3) A greater-than-or-equal-to (> ) - Puts a lower limit on some function of decision variables and may specify that production of a product must exceed or equal demand 4) Feasible Region - Taken together, the constraints define a feasible region - this represents the permissible combinations of decision variables - In some unusual situations, the problem is so tightly constrained there is only one possible solution, or none - Usually, feasibility region contains infinitely many possible solutions, assuming that the feasible combinations of the decision variables can be fractional values - The goal of the decision maker is to find the best possible solution

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## This note was uploaded on 06/08/2011 for the course MGSC 395 taught by Professor Zimmer during the Spring '10 term at South Carolina.

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Supplement E Notes - Supplement E Notes Linear Programming:...

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