Transportation model (Business problem analysis and Decision making)

Case Problem THE GRAPHIC PALETTE poster for an upcoming arts festival. The poster is more complex than anything Kathleen and Lindsey have previ- The Graphic Palette is a firm in Charleston, South stages , and the processing must proces rapidity to produce Carolina, that does graphic artwork and produces color the desired color effect. and black-and-white posters, lithographs, and banners. The By suspending all their other jobs, they can devote firm's owners, Kathleen and Lindsey Taylor, have been ap- three machines to the first stage, four to the second stage, proached by a client to produce a spectacularly colored and two to the last stage of the process. Posters that come 284 CHAPTER 6 TRANSPORTATION, TRANSSHIPMENT, AND ASSIGNMENT PROBLEMS off the machines at each stage can be processed on any of the machines at the next stage. However, all the machines are of different models and of varying ages, so they cannot process the same number of posters in the specified time frame necessary to complete the job. The different ma- chine capacities at each stage are as follows: Machine Machine (cost) 8 9 S36 $41 40 52 42 46 33 49 5 6 7 Stage 1 Machine 1 = 750 Machine 2 = 900 Machine 3 = 670 Stage 2 Machine 4 = 530 Machine 5 = 320 Machine 6 = 450 Machine 7 = 250 Stage 3 Machine 8 = 620 Machine 9 = 750 Kathleen and Lindsey are unsure how to route the posters from one stage to the next to make as many posters as they possibly can at the lowest cost. Determine how to route the posters through the various stages for Graphic Palette to minimize costs. Because the machines are of different ages and types, the costs of producing posters on them differ. For example, a poster that starts on machine 1 and then proceeds to machine 4 costs $18. If this poster at machine 4 is then processed on machine 8, it costs an additional $36. The processing costs for each combination of machines for stages 1, 2, and 3 are as follows: Machine (cost) 5 6 Machine 4 7 1 2 3 $18 20 24 $23 26 24 S25 24 22 $21 19 23