Use the Range command to generate a range report for the model in the active window. A range report shows over what ranges you can: 1 change a coefficient in the objective without causing any of the optimal values of the decision variables to change, or 2 change a row's constant term also referred to as the right-hand side coefficient without causing any of the optimal values of the dual prices or reduced costs to change.
Ranges in which the basis is unchanged:. Objective Coefficient Ranges. Current Allowable Allowable. Variable Coefficient Increase Decrease. Righthand Side Ranges. Row Current Allowable Allowable. RHS Increase Decrease. ALIM CLIM JOINT The first section of the report is titled Objective Coefficient Ranges. In the first column, titled Variable, all the optimizable variables are listed by name.
The next column, titled Current Coefficient , lists the current coefficient of the variable in the objective row. The next column, Allowable Increase , tells us the amount that we could increase the objective coefficient without changing the optimal values for the variables. The final column, Allowable Decrease , lists the amount that the objective coefficient of the variable could decrease before the optimal values of the variables would change.
Information on the allowable increases and decreases on objective coefficients can be useful when you need answers to questions like, "How much more less profitable must this activity be before we should be willing to do more less of it? Referring to the Objective Coefficient Ranges report for our example, we can say, as long as the objective coefficient of A is greater-than-or-equal-to 15, the optimal values of the variables will not change.
The same may be said for the objective coefficient of variable C , as long as it falls within the range of [0,40]. Now the processing plant can get 50 barrels of milk a day, and the total working hours of formal workers are hours per day, and equipment A can process up to kilograms of A 1 per day, and the processing capacity of equipment B is unlimited. Try to develop a production plan for the plant to maximize daily profit, and further discuss the following 3 additional issues:.
If investing, how many barrels of milk can I buy every day? Should the production plan be changed? Mathematical model: Suppose x 1 barrel of milk is used to produce A1 every day , and x 2 barrels of milk are used to produce A2. Objective function: Set daily profit as z yuan. Raw material supply: The total amount of raw materials milk for the production of A 1 and A 2 does not exceed the daily supply of 50 barrels, namely.
Working time: The total processing time for the production of A 1 and A 2 does not exceed the total working time of formal workers hours per day, namely. Equipment capacity: The output of A 1 shall not exceed the daily processing capacity of equipment A by hours, namely. Obviously, the objective function and constraint conditions are linear.
This is a linear programming LP. The optimal solution obtained will give the production plan that maximizes the net profit. Obviously, if the constraint just takes the equal sign at the optimal solution ie, "tight constraint", also called effective constraint or active constraint , the dual price value may not be zero.
The same goes for row 4. For non-compact constraints for example, lines 2 and 5 in this example are non-compact constraints , the value of DUAL PRICE is 0, which means that the slight disturbance of the right term of the inequality in the corresponding constraint does not affect the objective function. The result of the sensitivity analysis is Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease There is a dual price corresponding to each constraint in the result.
If its value is p, it means the right end of the inequality in the corresponding constraint DESKS Lines 3, 4, and 5 can be interpreted similarly. However, because the constraints change at this time , even if the optimal basis remains unchanged, the optimal solution and optimal value will also change.
The sensitivity analysis result represents the coefficient range within which the optimal basis remains unchanged. From this, it can be further determined how the optimal basis, optimal solution, and optimal value change when the cost coefficient of the objective function and the right term of the constraint change slightly. Below we illustrate by solving a practical problem. Since the constraints have not changed at this time just.
According to market demand, all A1 and A2 produced can be sold, and a profit of 24 yuan per kilogram of A1 and a profit of 16 yuan per kilogram of A2. Now the processing plant can get 50 barrels of milk a day, the total working hours of formal workers are hours per day, and workshop A can process up to kg of A1 per day, and the processing capacity of workshop B is unlimited. Try to develop a production plan for the factory to maximize daily profit, and further discuss the following three additional questions: 1 If you can buy a barrel of milk for 35 yuan, should you make this investment?
If investing, how many barrels of milk can be purchased per day? Global optimal solution found at iteration: 0 Objective value: In addition to telling us the optimal solution of the problem In addition to the optimal value, there is a lot of useful information for the analysis results. The following combined with the three additional questions raised in the title to give the output Slack or Surplus whether these three resources are surplus under the optimal solution: raw materials, labor The remaining time is zero, and workshop A has a remaining 40 kg processing capacity.
0コメント