An Efficient Optimal Algorithm for the Two-Machines Unit-Time Jobshop Schedule-Length Problem

Abstract

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.

Minimizing maximum lateness in a two-machine unit-time job shop

“…This algorithm generalizes recent results by Hefetz and Adiri (1979) who gave an algorithm for the corresponding makespan-problem. Such a problem is derived from P by setting d (i) = 0 for i= 1,..., r. In section 2 we will formulate the algorithm.…”

“…In a second step the tasks are to be scheduled according to this order. An algorithm proposed by Hefetz and Adiri (1979) proceeds exactly in this way. However, due to the special structure of the problem an O (n)-implementation is possible.…”

Job Shop Scheduling by Local Search

“…(4a) length < 3 (4b)* length < 4 (la) [Jackson, 1956); (lb) [Lenstra, Rinnooy Kau & Brucker, 1977); (2a) [Hefetz & Adiri, 1982); (2b) [Leustra & Riuuooy Kau, 1979); (3a) [Akers, 1956;Brucker, 1988); (3b) [Sotskov, 1091); (4a,b) [Williamson, Hall, Hoogeveen, Hurkens, Lenstra & Shmoys, 1994).…”

Scheduling Partially Ordered Jobs Faster than 2 n

“…For example, the aforementioned jobshop problem is NP-complete on at least three machines [17], but polynomial on two machines with unitary processing times [14].…”