Earliness and Tardiness Penalties. Chapter 5 Elements of Sequencing and Scheduling by Kenneth R. Baker Byung-Hyun Ha. Outline. Introduction Minimizing deviations from a common due date Four basic results Due date as decisions The restricted version
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Elements of Sequencing and Schedulingby Kenneth R. Baker
= 0pB1 + 1pB2 + ... + (b – 2)pB(b–1) + (b – 1)pBb.
1. Assign the longest job to set B.
2. Find the next two longest jobs. Assign one to B and one to A.
3. Repeat Step 2 until there are no jobs left, or until there is one job left, in which case assign this job to either A or B. Finally, order the jobs in B by LPT and the jobs in A by SPT.
1. Let L = d and R = i=1npi – d. Let k = 1.
2. If L R, assign job k to the first available position in sequence and decrease L by pk.
Otherwise, assign job k to the last available position in sequence and decrease R by pk.
3. If k n, increase k by 1 and go to Step 2. Otherwise, stop.
1. Initially, sets B and A are empty, and jobs are in LPT order.
2. If |B| (1 + |A|), then assign the next job to B; otherwise, assign the next job to A.
3. Repeat Step 2 until all jobs have been scheduled.
1. There is no inserted idle time.
2. Jobs that complete on or before the due date can be sequenced in non-increasing order of the ratio pj /j, and jobs that start late can be sequenced in non-decreasing order of the ratio pj /j .
3. One job completes at time d.
4. In an optimal schedule the bth job in sequence completes at time d, where b is the smallest integer satisfying the inequality
iB (j + j) j=1nj