Min-Sum Scheduling Under Precedence Constraints

In many scheduling situations, it is important to consider non-linear functions of job completions times in the objective. This was already recognized by Smith (1956). Recently, the theory community has begun a thorough study of the resulting problems, mostly on single-machine instances for which all permutations of jobs are feasible. However, a typical feature of many scheduling problems is that some jobs can only be processed after others. In this paper, we give the first approximation algorithms for min-sum scheduling with (nonnegative, non-decreasing) non-linear functions and general precedence constraints. In particular, for 1|prec|sum w_j f(C_j), we propose a polynomial-time universal algorithm that performs well for all functions f simultaneously. Its approximation guarantee is 2 for all concave functions, at worst. We also provide a (non-universal) polynomial-time algorithm for the more general case 1|prec|sum f_j(C_j). The performance guarantee is no worse than 2+epsilon for all concave functions. Our results match the best bounds known for the case of linear functions, a widely studied problem, and considerably extend the results for minimizing sum w_jf(C_j) without precedence constraints

Parallel machine scheduling with precedence constraints and setup times

This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. Limited discrepancy search methods mixed with local search principles, dominance conditions and specific lower bounds are proposed. The proposed methods are evaluated on a set of randomly generated instances and compared with previous results from the literature and those obtained with an efficient commercial solver. We conclude that our propositions are quite competitive and our results even outperform other approaches in most cases

An Approximately Optimal Algorithm for Scheduling Phasor Data Transmissions in Smart Grid Networks

In this paper, we devise a scheduling algorithm for ordering transmission of synchrophasor data from the substation to the control center in as short a time frame as possible, within the realtime hierarchical communications infrastructure in the electric grid. The problem is cast in the framework of the classic job scheduling with precedence constraints. The optimization setup comprises the number of phasor measurement units (PMUs) to be installed on the grid, a weight associated with each PMU, processing time at the control center for the PMUs, and precedence constraints between the PMUs. The solution to the PMU placement problem yields the optimum number of PMUs to be installed on the grid, while the processing times are picked uniformly at random from a predefined set. The weight associated with each PMU and the precedence constraints are both assumed known. The scheduling problem is provably NP-hard, so we resort to approximation algorithms which provide solutions that are suboptimal yet possessing polynomial time complexity. A lower bound on the optimal schedule is derived using branch and bound techniques, and its performance evaluated using standard IEEE test bus systems. The scheduling policy is power grid-centric, since it takes into account the electrical properties of the network under consideration.Comment: 8 pages, published in IEEE Transactions on Smart Grid, October 201

Single machine scheduling problems with uncertain parameters and the OWA criterion

In this paper a class of single machine scheduling problems is discussed. It is assumed that job parameters, such as processing times, due dates, or weights are uncertain and their values are specified in the form of a discrete scenario set. The Ordered Weighted Averaging (OWA) aggregation operator is used to choose an optimal schedule. The OWA operator generalizes traditional criteria in decision making under uncertainty, such as the maximum, average, median or Hurwicz criterion. It also allows us to extend the robust approach to scheduling by taking into account various attitudes of decision makers towards the risk. In this paper a general framework for solving single machine scheduling problems with the OWA criterion is proposed and some positive and negative computational results for two basic single machine scheduling problems are provided

Flexible resources allocation techniques: characteristics and modelling

At the interface between engineering, economics, social sciences and humanities, industrial engineering aims to provide answers to various sectors of business problems. One of these problems is the adjustment between the workload needed by the work to be realised and the availability of the company resources. The objective of this work is to help to find a methodology for the allocation of flexible human resources in industrial activities planning and scheduling. This model takes into account two levers of flexibility, one related to the working time modulation, and the other to the varieties of tasks that can be performed by a given resource (multi–skilled actor). On the one hand, multi–skilled actors will help to guide the various choices of the allocation to appreciate the impact of these choices on the tasks durations. On the other hand, the working time modulation that allows actors to have a work planning varying according to the workload which the company has to face

Approximate Deadline-Scheduling with Precedence Constraints

We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result is an O(log k)-approximation algorithm for instances with k distinct job deadlines

Scheduling to Minimize Total Weighted Completion Time via Time-Indexed Linear Programming Relaxations

We study approximation algorithms for scheduling problems with the objective of minimizing total weighted completion time, under identical and related machine models with job precedence constraints. We give algorithms that improve upon many previous 15 to 20-year-old state-of-art results. A major theme in these results is the use of time-indexed linear programming relaxations. These are natural relaxations for their respective problems, but surprisingly are not studied in the literature. We also consider the scheduling problem of minimizing total weighted completion time on unrelated machines. The recent breakthrough result of [Bansal-Srinivasan-Svensson, STOC 2016] gave a $(1.5-c)$-approximation for the problem, based on some lift-and-project SDP relaxation. Our main result is that a $(1.5 - c)$-approximation can also be achieved using a natural and considerably simpler time-indexed LP relaxation for the problem. We hope this relaxation can provide new insights into the problem