1 / 14

140 likes | 431 Vues

Linear Programming Models in Services. Learning Objectives. Describe the features of constrained optimization models. Formulate LP models for computer solution. Solve two-variable models using graphics. Explain the nature of sensitivity analysis.

Télécharger la présentation
## Linear Programming Models in Services

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Learning Objectives**• Describe the features of constrained optimization models. • Formulate LP models for computer solution. • Solve two-variable models using graphics. • Explain the nature of sensitivity analysis. • Solve LP models with Excel Add-in Solver and interpret the results. • Formulate a goal programming model.**Stereo Warehouse**Let x = number of receivers to stock y = number of speakers to stock Maximize 50x + 20y gross profit Subject to 2x + 4y 400 floor space 100x + 50y 8000 budget x 60 sales limit x, y 0**Diet ProblemLakeview Hospital**Let E = units of egg custard base in the shake C = units of ice cream in the shake S = units of butterscotch syrup in the shake Minimize Subject to cholesterol fat protein calories**Shift-Scheduling ProblemGotham City Police Patrol**Let xi= number of officers reporting at period i for i =1, 2, 3, 4, 5, 6 Minimize x1 + x6 6 period 1 x1 + x2 4 period 2 x2+ x3 14 period 3 x3 + x4 8 period 4 x4+ x5 12 period 5 x5 + x616 period 6**Workforce-Planning ProblemLast National Drive-in Bank**Let Tt= number of trainees hired at the beginning of period t for t = 1,2,3,4,5,6 At = number of tellers available at the beginning of period t for t = 1,2,3,4,5,6 Minimize subject to A1= 12 for t = 2,3,4,5,6 At , Tt 0 and integer for t = 1,2,3,4,5,6**Transportation ProblemLease-a-Lemon Car Rental**Let xij= number of cars sent from city i to city j for i = 1,2,3 and j = 1,2,3,4 Minimize 439x11 + 396 x12 + . . . +479x33 + 0x34 subject to x11 + x12 + x13 + x14 = 26 x21 + x22 + x23 + x24 = 43 x31 + x32 + x33 + x34 = 31 x11 + x21 + x31 = 32 x12 + x22 + x32 = 28 x13 + x23 + x33 = 26 x14 + x24 + x34 = 14 xij 0 for all i , j**Graphical SolutionStereo Warehouse**Z=3800 Z=3600 Z=3000 Z=2000 E Optimal solution ( x = 60, y = 40) D C A B**Model in Standard Form**Let s1 = square feet of floor space not used s2 = dollars of budget not allocated s3 = number of receivers that could have been sold Maximize Z = 50x + 20y subject to 2x + 4y + s1 = 400 (constraint 1) 100x + 50y + s2 = 8000 (constraint 2) x + s3 = 60 ( constraint 3) x, y, s1, s2, s3 0**Stereo WarehouseExtreme-Point Solutions**Extreme Nonbasic Basic Variable Objective-function point variables variables value value Z A x, y s1 400 0 s2 8000 s3 60 B s3, y s1 280 3000 s2 2000 x 60 C s3, s2 s1 120 3800 y 40 x 60 D s1, s2 s3 20 3600 y 80 x 40 E s1, x s3 60 2000 y 100 s2 3000**Sensitivity AnalysisObjective-Function Coefficients**z = 50x + 20y (constraint 3 ) D (constraint 1) (constraint 2) C A B**Sensitivity AnalysisRight-Hand-Side Ranging**(constraint 3 ) D H (constraint 2) C A B I**Goal ProgrammingStereo Warehouse Example**Let x = number of receivers to stock y = number of speakers to stock = amount by which profit falls short of $99,999 = amount by which profit exceeds $99,999 = amount by which floor space used falls short of 400 square feet = amount by which floor space used exceeds 400 square feet = amount by which budget falls short of $8000 = amount by which budget exceeds $8000 = amount by which sales of receivers fall short of 60 = amount by which sales of receivers exceed 60 = priority level with rank k Minimize subject to profit goal floor-space goal budget goal sales-limit goal**Topics for Discussion**• How can the validity of LP models be evaluated? • Interpret the meaning of the opportunity cost for a nonbasic decision variable that did not appear in the LP solution. • Explain graphically what has happened when a degenerate solution occurs in an LP problem. • Is LP a special case of goal programming? Explain. • What are some limitations to the use of LP?

More Related