Sequencing with Series-Parallel Precedence Constraints

Abstract

One of the most important ideas in the theory of sequencing and scheduling is the method of adjacent pairwise job interchange. This method compares the costs of two sequences which differ only by interchanging a pair of adjacent jobs. In 1956, W. E. Smith defined a class of problems for which a total preference ordering of the jobs exists with the property that in any sequence, whenever two adjacentjobs are not in preference order, they may be interchanged with no resultant cost increase. In such a case the unconstrained sequencing problem is easily solved by sequencing thejobs in preference order. In this paper, a natural subclass of these problems is considered for which such a total. preference ordering exists for all subsequences ofjobs. The main result is an efficient general algorirhm for these sequencing problems with series-parallel precedence constraints. These probleris include the least cost fault detcction problem, the one-machine total weighted complction time problem; the two-machine maximum completion time flow-shop problem and the maldmum cumulativi cost problem.

R&D project scheduling when activities may fail

“…This corollary settles what is said to be an open problem in Monma andSidney (1979) andinÜnlüyurt (2004). In order to further examine the complexity status of LCT, we start with the problem 1|pr ec| w j (1 − e −rC j ), the single-machine scheduling problem with discounted weighted-completiontime objective and general precedence constraints, with objective function to be minimized (see for instance Pinedo (2002)).…”

“…We define problem LCT as problem RDPSP whose solution space is restricted to schedules that impose a complete order on N; Monma and Sidney (1979) refer to this setting as the "least-cost fault-detection problem." We note that LCT is not a subproblem of RDPSP since we restrict the set of solutions and not the input parameters.…”

“…A polynomial-time algorithm for LCT also exists when G(N, A) consists of a number of parallel chains (see Chiu et al (1999)). Based on Monma and Sidney (1979) it can be shown that the problem is also solvable in polynomial time when G(N, A) is series parallel.…”

Fifty years of scheduling: a survey of milestones

“…Chapter 3 of the book by Tanaev et al (1984) is based on the research conducted by Yakov Shafransky in the 1970s on the theory of minimizing of so-called priority-generating functions over partially ordered sets of jobs. This is related to the contributions of Monma and Sidney (1979) in this area of scheduling with precedence constraints.…”

A concise survey of efficiently solvable special cases of the permutation flow-shop problem

“…The two machine flow-shop problem has also been solved efficiently subject to precedence constraints on the jobs of a certain type [14,15,24,25,26,34]. This approach capitalizes on the f act that Johnson's Rule can be viewed as the outcome of a simple interchange argument that can be adapted to account for these precedence constraints.…”