lingo例题讲解1!10.ppt

* 例题讲解 Model: title Assignment Problem; sets: worker/w1,w2,w3,w4,w5/:capacity; job/j1,j2,j3,j4,j5/:demend; routes(worker,job):cost,volume; endsets min=@sum(routes:cost*volume); @for(job(j):@sum(worker(i):volume(i,j))=demend(j)); @for(worker(i):@sum(job(j):volume(i,j))=capacity(i)); data: capacity=1,1,1,1,1; demend=1,1,1,1,1; cost=8 6 10 9 12 9 12 7 11 9 7 4 3 5 8 9 5 8 11 8 4 6 7 5 11; Enddata end 练习 For our example, we have eleven tasks (A through K) to assign to four workstations (1 through 4). The task precedence diagram looks like this: The times to complete the various tasks are given in the table below: Task: A B C D E F G H I J K Minutes: 45 11 9 50 15 12 12 12 12 8 9 We need to find an assignment of tasks to workstations that minimize the assembly line抯 cycle time. MODEL: ! Assembly line balancing model; ! This model involves assigning tasks to stations in an assembly line so bottlenecks are avoided. Ideally, each station would be assigned an equal amount of work.; SETS: ! The set of tasks to be assigned are A through K, and each task has a time to complete, T; TASK/ A B C D E F G H I J K/: T; ! Some predecessor,successor pairings must be observed(e.g. A must be done before B, B before C, etc.); PRED( TASK, TASK)/ A,B B,C C,F C,G F,J G,J J,K D,E E,H E,I H,J I,J /; ! There are 4 workstations; STATION/1..4/; TXS( TASK, STATION): X; ! X is the attribute from the derived set TXS that represents the assignment. X(I,K) = 1 if task I is assigned to station K; ENDSETS DATA: ! Data taken from Chase and Aquilano, POM; ! There is an estimated time required for each task: A B C D E F G H I J K; T = 45 11 9 50 15 12 12 12 12 8 9; ENDDATA ! The model; ! *Warning* may be slow for more than 15 tasks; ! For each task, there must be one assigned station; *