Sequencing and performance

Which job should go first? It sounds like a small choice, but the answer depends on what we want to improve. Northstar can do a short job first to clear work fast. It can do the job with the first due date to protect a promise. We will test both ideas with the same data. There is one machine, all jobs are ready at zero, and there are no setups. Each job must run to its end once it starts. A takes sixty minutes and is due at seventy. B takes twenty and is due at one hundred twenty. C takes forty and is due at one hundred. The short job rule, SPT, gives B, C, A. B ends at twenty, C at sixty, and A at one hundred twenty. Add those ends and divide by three. Mean completion is about sixty seven minutes. The last finish is one hundred twenty. Keep both numbers, since they tell us different things. The due date rule, EDD, gives A, C, B. A ends at sixty, C at one hundred, and B at one hundred twenty. Mean completion is about ninety three minutes. The last finish is still one hundred twenty. All three jobs now meet their due dates. In the short job plan, A was fifty minutes late. One plan has a lower mean and the other has better due date results. A rule name alone does not settle that choice. We need clear words for the scorecard. Completion is the point when a job ends. Lateness is that point less the due time. It can be below zero. If a job ends at eighty and is due at one hundred, its lateness is minus twenty. Tardiness counts only the late part, so it is zero for that job. Do not let an early job cancel a late job when the measure you report is total tardiness. Flow time asks how long the job spent in the system after it was ready. If it is released at ten and ends at eighty, its flow time is seventy. Makespan asks when the last job ends from our zero clock. In our first case, all run times add to one hundred twenty, with no gaps. So both rules have that makespan. A lower mean completion does not imply that the team can go home sooner. Now look at a second scorecard. A runs from zero to fifty, B from fifty to eighty, and C from eighty to one hundred. Their due times are forty, one hundred, and ninety. Their lateness values are ten, minus twenty, and ten. Total tardiness is twenty, not zero. Two jobs are late. If A has weight three and C weight two, their late work earns fifty weighted minute points. The weights express a choice about priority, not extra machine time. Under the narrow all ready, one machine conditions, SPT has a result for total completion time. EDD has a result for maximum lateness. Neither claim says it wins every goal or stays best after we add releases and setups. The small lab lets you check all six orders by hand or in a table. That makes it possible to see each result rather than trust a label. Keep ties visible and use the tie rule given in the task. When you write your decision, show the job rows as well as the totals. Name who waits and how long. Then change one due date and test the rules again. A due date change can alter EDD while leaving SPT in place. This is a clue to what each rule sees. Finish with a plain claim: this plan wins this measure under these facts. A careful limited claim is far more useful than calling one rule the best way to schedule all work. Keep the units on the scorecard too. Mean completion is in minutes from the chosen origin. The count of late jobs is a count, not a duration. A weighted score is a policy score, not elapsed time. These may all be useful, but we should not add them without a stated rule. In your memo, use one short sentence for each measure that matters. Then say which measure has first claim on the choice and which loss you are willing to accept in this case.

1. Two queue rules

   Original static calculation card for two queue rules, using the Northstar numbers stated in the narration; show labeled units and no decorative charts.

   • SPT sorts run time
   • EDD sorts due time
   • All jobs ready at0
2. Build completions

   Original static timeline for build completions, using the Northstar numbers stated in the narration; show labeled units and no decorative charts.

   • SPT B-C-A
   • Ends20,60,120
   • Mean66.67
3. Read due performance

   Original static calculation card for read due performance, using the Northstar numbers stated in the narration; show labeled units and no decorative charts.

   • EDD A-C-B
   • Ends60,100,120
   • No tardy jobs
4. Separate measures

   Original static timeline for separate measures, using the Northstar numbers stated in the narration; show labeled units and no decorative charts.

   • Lateness can be negative
   • Tardiness is at least0
   • Flow subtracts release
5. Compare weights

   Original static timeline for compare weights, using the Northstar numbers stated in the narration; show labeled units and no decorative charts.

   • Weights are policy
   • 3 times10 gives30
   • Show raw measures too
6. Name the objective

   Original static calculation card for name the objective, using the Northstar numbers stated in the narration; show labeled units and no decorative charts.

   • Makespan120 in both
   • Name the first priority
   • State narrow assumptions