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We consider a variant of the resource constrained scheduling problem, which originated from a machine scheduling problem. A number of jobs are to be processed on a single machine with a prespecified capacity. Each job has a size and a processing time, and the machine can process a set of jobs simultaneously as long as the total size of the jobs being processed does not exceed the capacity of the machine. The objective is to find a schedule to minimize the total time (i.e., the makespan) to complete all jobs, subject to the machine capacity constraint. For the problem where the machine is completely available at the starting time, we analyze a previously published algorithm and prove that the worst-case ratio of this algorithm is no more than 7/4, which significantly improves the previous result and thus answers an open question about this algorithm. For the problem where the machine is partially available at the beginning, an algorithm is shown to have a worst-case ratio of no more than two. An on-line algorithm is also presented., 1. Introduction In the past four decades, many papers have been published in the literature on scheduling. Most scheduling literature assumes that a machine can handle exactly one job and [...]

We study a scheduling problem in a multipurpose machine environment where every job can be processed by a subset of the machines operated in parallel, with the objective of minimizing makespan. We develop lower bounds, heuristic algorithms, and a branch-and-bound procedure. We perform an extensive computational experiment to assess how much flexibility is enough to render the multipurpose machine system equally efficient to an equivalent system of parallel identical machines. We find that very small amounts of flexibility appropriately distributed across processors provide nearly the same makespan performance as a system of fully flexible parallel machines., 1. Introduction Consider a system of m parallel identical machines each of which is capable of executing any job and takes the same processing time as any other machine. Minimizing [...]

We consider the problem of scheduling jobs on-line on parallel batch processing machines with dynamic job arrivals to minimize makespan. We are given m identical batch processing machines, each of [...]

Most scheduling literature considers a 'one-job-on-one-processor' pattern, which assumes that a processor processes exactly one job at a time. In this paper we consider a new scheduling problem with a 'multiple-job-on-one-processor' pattern, where several jobs can be processed by a single processor simultaneously, provided that the total size of the jobs being processed does not exceed the capacity of the processor at any point in time. This problem is motivated by the operation of berth allocation, which is to allocate vessels (jobs) to a berth (processor), where the vessels, if small in dimension, may share the berth with some other vessels for loading/unloading the goods. We consider the problem to minimize the makespan of the schedule. The well-known First-Fit Decreasing heuristic is generalized and applied to several variations of the problem, and the worst-case behavior of the generalized heuristics is studied. Worst-case error bounds are obtained for those models. Computational experiments are conducted to test the heuristics. The results suggest that the heuristics are effective in producing near-optimal solutions., 1. Introduction Scheduling models concern how to optimally allocate the limited resource (processors) to tasks (jobs) over time. It is a decision making process that exists in most production systems, [...]

This paper provides a new portfolio selection rule. The objective is to minimize the maximum individual risk and we use an [l.sub.[infinity]] function as the risk measure. We provide an explicit analytical solution for the model and are thus able to plot the entire efficient frontier. Our selection rule is very conservative. One of the features of the solution is that it does not explicitly involve the covariance of the asset returns., 1. Introduction The portfolio selection problem is of both theoretical and practical interest. Markowitz (1952) laid the foundations for this line of research with his mean--variance (M--V) model. While Markowitz [...]

CHUNG-YEE LEE [1] XIAOQIANG CAI [2] In this paper we study a two-processor scheduling problem where some tasks need to be processed by one processor, while the others have to [...]

Synchronous production systems are examined with regard to workforce planning, and heuristic algorithms are developed to solve the problem for arbitrary number of work centers.