Showing papers on "Single-machine scheduling published in 1984"
TL;DR: A dynamic programming solution to the problem of partially ordered tasks, when the constraining partial order has a dimension ≤2, is presented by definining a “compact” labeling scheme and an efficient enumerative procedure for all the feasible subsets.
Abstract: Consider the set of tasks that are partially ordered by precedence constraints. The tasks are to be sequenced so that a given objective function will assume its optimal value over the set of feasible solutions. A subset of tasks is called feasible, if for every task in the subset, all of its predecessors are also in the subset. We present a dynamic programming solution to the problem, when the constraining partial order has a dimension ≤2. This is done by definining a “compact” labeling scheme and an efficient enumerative procedure for all the feasible subsets. In this process a new characterization is given for 2-dimensional partial orders.
43 citations
TL;DR: In this paper, the authors give optimality conditions to obtain a priori precedence relationships among some of the jobs in a single machine scheduling problem so as to curtail the enumeration while using branch-based methods.
Abstract: This paper gives optimality conditions to obtain a priori precedence relationships among some of the jobs in a single machine scheduling problem so as to curtail the enumeration while using branch-...
30 citations
TL;DR: This work considers the problem of schedulingn jobs without preemption on a single machine to maximize total profit, where profit is given by a nonincreasing, concave separable function of job starting times and gives a heuristic in which jobs are sequenced optimally relative to a specific linear approximation of the profit, function.
Abstract: We consider the problem of schedulingn jobs without preemption on a single machine to maximize total profit, where profit is given by a nonincreasing, concave separable function of job starting times. A heuristic is given in which jobs are sequenced optimally relative to a specific linear approximation of the profit, function. This heuristic always obtains at least 2/3 of the optimal profit, and examples exist where the heuristic obtains only 2/3 of the optimal profit. A large class of alternative linearizations is considrred and shown to give arbitrarily bad results.
23 citations
TL;DR: In this paper, the optimization of a function f defined on feasible permutations assuming that the function f induces certain job interchange relations is considered. The interchange relations include job insertion, interchange of symbol chains, and the mutually complementary properties of interchange and embedding.
Abstract: The article focuses on effective single-machine scheduling algorithms. We consider the optimization of a functionf defined on feasible permutations assuming that the functionf induces certain job interchange relations. The interchange relations include “job insertion,” interchange of symbol chains, and the mutually complementary properties of interchange and embedding. Some new nontraditional problem formulations are considered together with the corresponding methods of solution.
2 citations