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We consider single machine scheduling problems with a non-renewable resource. This type of problems has not been intensively investigated in the literature so far. For several problems of this type with standard objective functions (namely the minimization of makespan, total tardiness, number of tardy jobs, total completion time and maximum lateness), we… (More)

In this paper, we consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed. We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time.

In this paper, we consider the well-known resource-constrained project scheduling problem. We propose some arguments that already a special case of this problem with a single type of resources is not ap-proximable in polynomial time with an approximation ratio bounded by a constant. We prove that there exist instances for which the optimal makespan values… (More)

For five single machine total tardiness problems a fully polynomial-time approximation scheme (FPTAS) based on a graphical algorithm is presented. The FPTAS has the best running time among the known approximation schemes for these problems.

In this paper, a graphical algorithm (GrA) is presented for an investment optimization problem. This algorithm is based on the same Bellman equations as the best known dynamic programming algorithm (DPA) for the problem but the GrA has several advantages in comparison with the DPA. Based on this GrA, a fully-polynomial time approximation scheme is proposed… (More)

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may… (More)

In this paper, we consider the well-known resource-constrained project scheduling problem. We give some arguments that already a special case of this problem with a single type of resources is not approximable in polynomial time with an approximation ratio bounded by a constant. We prove that there exist instances for which the optimal makespan values for… (More)

We consider a Project Investment problem, where a set of projects and an overall budget are given. For each project, a profit function is known which describes the profit obtained if a specific amount is invested in this project. The objective is to determine the amount invested in each project such that the overall budget is not exceeded and the total… (More)