No abstract

This paper deals with flowshop/sum of completion times scheduling problems, working under a "no-idle'' or a "no-wait'' constraint, the former prescribes for the machines to work continuously without idle intervals and the latter for the jobs to be processed continuously without waiting times between consecutive machines. Under either of the constraints the problem is unary NPComplete for two machines. We prove some properties of the optimal schedule for n/2/F, no-idle/ZC,. For n / m / P , no-idle/ZC, and n / m / P , nowait/ZC, with an increasing or decreasing series of dominating machines, we prove theorems that are the basis for polynomial bounded algorithms. All theorems are demonstrated numerically.

An M/M/1 service station (computer center) consists of M separate queues. The ith (i= 1, 2, * * *, M) queue has priority over the jth iff i

Jobs with known processing times and due dates have to be processed on a machine which is subject to a single breakdown. The moment of breakdown and the repair time are independent random variables. Two cases are distinguished with reference to the processing time preempted by the breakdown (no other preemptions are allowed): (i) resumption without time losses and (ii) restart from the beginning. Under certain compatible conditions, we find the policies which minimize stochastically the number of tardy jobs.

The problem of scheduling a two-machine unit-operation-time jobshop to complete all jobs as rapidly as possible is shown to be solved by the following rule. Select for service from available jobs at each stage one with longest remaining processing time. The running time and storage space of the rule are both linear functions of the total number of operations, thereby establishing that the problem belongs to P.