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- Evgeny R. Gafarov, Alexander A. Lazarev, Frank Werner
- Mathematical Social Sciences
- 2011

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)

- T. C. Edwin Cheng, Alexander A. Lazarev, Evgeny R. Gafarov
- Computers & OR
- 2009

We propose a hybrid algorithm based on the Ant Colony Optimization (ACO) meta-heuristic, in conjunction with four well-known elimination rules, to tackle the NP -hard single-machine scheduling problem to minimize the total job tardiness. The hybrid algorithm has the same running time as that of ACO. We conducted extensive computational experiments to test… (More)

- Evgeny R. Gafarov, Alexander A. Lazarev, Frank Werner
- Annals OR
- 2014

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)

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 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… (More)

We consider some special cases of the NP -hard resource-constrained project scheduling problem (RCPSP ) to minimize the makespan. We conjecture that the ratio of the optimal makespan of RCPSP to that of the preemptive version of the problem is less than 2. We show that a well-known lower bounds for the problem may yield bad approximation ratios or its… (More)

- Evgeny R. Gafarov, Alexander A. Lazarev, Frank Werner
- Mathematical Social Sciences
- 2013

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 approximable in polynomial time with an approximation ratio bounded by a constant. We prove that there exist instances for which the optimal makespan values… (More)

- Evgeny R. Gafarov, Alexandre Dolgui, Alexander A. Lazarev
- Computers & Industrial Engineering
- 2015

In this paper, the single-track railway scheduling problem with two stations and several segments of the track is considered. Two subsets of trains are given, where trains from the first subset go from the first station to the second station, and trains from the second subset go in the opposite direction. The speed of trains over each segment is the same. A… (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.