Soo Y. Chang

Parallel machine scheduling under a grade of service provision

Abstract We consider the problem of scheduling parallel machines that process service requests from various customers who are entitled to many different grade of service (GoS) levels. We propose and analyze one simple way to ensure such differentiated service. In particular, we investigate how the longest processing time first algorithm (LPT) would perform in the worst case and show that a slight modification of LPT could significantly improve its worst-case performance.

Online and semi-online scheduling of two machines under a grade of service provision

We consider the online scheduling of two machines under a grade of service (GoS) provision and its semi-online variant where the total processing time is known. Respectively for the online and semi-online problems, we develop algorithms with competitive ratios of 53 and 32 which are shown to be optimal.

Optimal production run length and inspection schedules in a deteriorating production process

This paper presents an economic manufacturing quantity model which determines an optimal production run length and inspection schedules simultaneously in a deteriorating production process. It is assumed that a production process is subject to a random deterioration from the in-control state to the out-of-control state and, thus, produces some proportion of defective items. An optimal production run length and an optimal number of inspections are derived, and unique properties of the proposed model are discussed. A numerical experiment is carried out to examine the behavior of the proposed model and compare the proposed model to an existing model.

Optimal Weighting of Bias and Variance in Dual Response Surface Optimization

Dual response surface optimization simultaneously considers the mean and the standard deviation of a response. The minimization of the mean squared error (MSE) is a simple, yet effective, approach in dual response surface optimization. The bias and variance components of MSE need to be weighted properly if they are not of the same importance in the given problem situation. To date, the relative weights of bias and variance have been equally set or determined only by the data. However, the weights should be determined in accordance with the tradeoffs on various factors in quality and costs. In this paper, we propose a systematic method to determine the weights of bias and variance in accordance with a decision makers preference structure regarding the tradeoffs.

The effect of machine availability on the worst-case performance of LPT

We consider the makespan minimization parallel machine scheduling problem where each machine may be unavailable for a known time interval. For this problem, we investigate how the worst-case behavior of the longest processing time first algorithm (LPT) is affected by the availability of machines. In particular, for given m machines, we analyze the cases where arbitrary number, λ, ranging from one to m - 1, machines are unavailable simultaneously. Then, we show that the makespan of the schedule generated by LPT is never more than the tight worst-case bound of 1 + ½ ⌊m/(m - λ)⌋ times the optimum makespan.

The steepest descent gravitational method for linear programming

We present a version of the gravitational method for linear programming, based on steepest descent gravitational directions. Finding the direction involves a special small “nearest point problem” that we solve using an efficient geometric approach. The method requires no expensive initialization, and operates only with a small subset of locally active constraints at each step. Redundant constraints are automatically excluded in the main computation. Computational results are provided.

The worst-case analysis of the MULTIFIT algorithm for scheduling nonsimultaneous parallel machines

Abstract In this paper we consider the nonsimultaneous multiprocessor scheduling problem, or NMSP for short. The NMSP is a makespan minimization scheduling problem which involves the nonpreemptive assignment of independent jobs on m parallel machines with different starting times. It is well known that the longest processing time (LPT) algorithm and the modified LPT(MLPT) algorithm yield schedules with makespans bounded by 3 2 − 1 2m and 4/3 times the optimum makespan, respectively. In this paper, we show that the best known worst-case performance bound, 4/3 of the MLPT, is tight by constructing a worst-case example. Then, we employ the bin-packing heuristic algorithm called the MULTIFIT to solve the NMSP and show that the makespan of the schedule generated by the MULTIFIT algorithm is bounded by 9/7+2−k times the optimum makespan, where k is the selected number of the major iterations in the MULTIFIT. This worst-case bound of the MULTIFIT algorithm is, so far, the best bound for the NMSP and the tightness of the bound is still an open question.

Heuristics for automated knowledge source integration and service composition

The NP-hard component set identification problem is a combinatorial problem arising in the context of knowledge discovery, information integration, and knowledge source/service composition. Considering a granular knowledge domain consisting of a large number of individual bits and pieces of domain knowledge (properties) and a large number of knowledge sources and services that provide mappings between sets of properties, the objective of the component set identification problem is to select a minimum cost combination of knowledge sources that can provide a joint mapping from a given set of initially available properties (initial knowledge) to a set of initially unknown properties (target knowledge). We provide a general framework for heuristics and consider construction heuristics that are followed by local improvement heuristics. Computational results are reported on randomly generated problem instances.

Continuous slab caster scheduling and interval graphs

We define and solve a scheduling problem for operating the continuous steel slab caster which converts molten steel into slabs. The nature of our problem has an interesting connection to a special class of graphs known as interval graphs. We show that our problem can be seen as a variant of the clique partitioning problem defined on interval graphs and develop an optimal algorithm for it.

A POSTERIOR COMPETITIVENESS FOR LIST SCHEDULING ALGORITHM ON MACHINES WITH ELIGIBILITY CONSTRAINTS

We consider the on-line problem of scheduling n independent jobs on m identical machines under the machine eligibility constraints, where each job has its own specified subset of machines which are eligible for processing it. We investigate a greedy algorithm LS and prove its posterior competitiveness ratio is , where λ is the number of machines eligible for processing the job with the latest completion time.