Beaver Creek Pottery Example Sensitivity Analysis (1 of 4)海狸溪陶器的例子的敏感性分析（1的4）.pptVIP

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Beaver Creek Pottery Example Sensitivity Analysis (1 of 4)海狸溪陶器的例子的敏感性分析（1的4）.ppt

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Beaver Creek Pottery Example Sensitivity Analysis (1 of 4)海狸溪陶器的例子的敏感性分析（1的4）

Chapter 3 - Linear Programming: Computer Solution and Sensitivity Analysis by Asst. Prof. Sami Fethi Chapter Topics Sensitivity analysis determines the effect on the optimal solution of changes in parameter values of the objective function and constraint equations. Changes may be reactions to anticipated uncertainties in the parameters or to new or changed information concerning the model. The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point will remain optimal. The sensitivity range for the xi coefficient is designated as ci. Changing individual constraint parameters Adding new constraints Adding new variables Defined as the marginal value of one additional unit of resource. The sensitivity range for a constraint quantity value is also the range over which the shadow price is valid. The Dual Problem and Shadow prices Every linear programming problem, called the primal problem, has a corresponding or symmetrical problem called the dual problem. A profit-maximization primal problem has a cost-minimization dual problem, and vice versa. The solution of a dual problem yields the shadow prices. They give the change in the value of the objective function per unit change in each constraint in the primal problem. According to the duality theorem, the optimal value of the objective function is the same in the primal and in the corresponding dual problems. Dual of the Profit Maximization Problem Dual of the Profit Maximization Problem In the dual problem we seek to minimize the shadow prices of inputs A, B, and C used by the firm. Defining VA, VB, as the shadow prices of inputs and C as the total imputed values of the fixed quantities of inputs available to the firm, we can write the dual objective function as minimize C=7 VA+5 VB+2 VC Thus the constraints of the dual problem can be written as follow: 1VA + 0.5VB ? $30 1VA + 1VB + 0.5VC ? $40 so VC=0 due to slack variable. 1VA + 0