Requirements of a Linear 
                                     Requirements of a Linear 
                                           Programming Problem
                                           Programming Problem
                1 Must seek to maximize or minimize some 
                        quantity (the objective function)
                2 Presence of restrictions or constraints - limits 
                        ability to achieve objective
                3 Must be alternative courses of action from 
                        which to choose
                4 Objectives and constraints must be 
                        expressible as linear equations or inequalities
                PowerPoint presentation to accompany Operations                            B-2                              © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 
                Management, 6E (Heizer & Render)                                                                            07458
                                                              Metode Grafik
                                                              Metode Grafik
                          Langkah penyelesaian :
                          1.         Gambarkan fungsi kendala dalam bentuk persamaan 
                                     pada sumbu Cartesius
                          2.         Tentukan daerah solusi layak (feasible solution) 
                                     dengan memperhatikan tanda ketidaksamaan  fungsi 
                                     kendala.
                          3.         Gambarkan fungsi tujuan,  geser garis tsb ke lokasi 
                                     titik solusi yang optimal 
                          4.         Selesaikan persamaan-persamaan pada titik solusi 
                                     untuk menentukan solusi optimal 
                PowerPoint presentation to accompany Operations                            B-3                              © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 
                Management, 6E (Heizer & Render)                                                                            07458
                                Examples of Successful LP 
                                 Examples of Successful LP 
                                                                 Applications
                                                                  Applications
                 Scheduling school busses to minimize total 
                        distance traveled when carrying students
                 Allocating police patrol units to high crime 
                        areas in order to minimize response time to 
                        911 calls
                 Scheduling tellers at banks to that needs are 
                        met during each hour of the day while 
                        minimizing the total cost of labor
                PowerPoint presentation to accompany Operations                            B-4                              © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 
                Management, 6E (Heizer & Render)                                                                            07458
                                Examples of Successful LP 
                                 Examples of Successful LP 
                                      Applications - continued
                                       Applications - continued
                 Picking blends of raw materials in feed mills 
                        to produce finished feed combinations at 
                        minimum costs
                 Selecting the product mix in a factory to 
                        make best use of machine- and labor-hours 
                        available while maximizing the firm’s profit
                 Allocating space for a tenant mix in a new 
                        shopping mall so as to maximize revenues 
                        to the leasing company
                PowerPoint presentation to accompany Operations                            B-5                              © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 
                Management, 6E (Heizer & Render)                                                                            07458
                   Formulating Linear Programming 
                   Formulating Linear Programming 
                                                                        Problems
                                                                        Problems
                Assume:
                          You wish to produce two products (1) Walkman 
                              AM/FM/Cassette and (2) Watch-TV
                          Walkman takes 4 hours of electronic work and 2 hours 
                              assembly
                          Watch-TV takes 3 hours electronic work and 1 hour 
                              assembly
                          There are 240 hours of electronic work time and 100 
                              hours of assembly time available
                          Profit on a Walkman is $7; profit on a Watch-TV $5
                PowerPoint presentation to accompany Operations                            B-6                              © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 
                Management, 6E (Heizer & Render)                                                                            07458