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Vladimir Kats

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Papers by Vladimir Kats

Cyclic scheduling of processes in robotic cells characterized by directed acyclic graphs

Actas del XXX Congreso Nacional de Estadística e Investigación Operativa y de las IV Jornadas de Estadística Pública, 2007, ISBN 978-84-690-7249-3, 2007

We consider a multiple-product, multiple-robot, 1-cyclic scheduling problem in a robotic assembly... more We consider a multiple-product, multiple-robot, 1-cyclic scheduling problem in a robotic assembly/disassembly system. The durations of the processing, setup, and transportation operations are controllable decision variables lying in given time intervals ("time windows"). The precedence relations between assembly/disassembly operations of any job are given in the form of a general directed acyclic graph, rather than a chain. The objective is to maximize the cell performance, or, equivalently, to minimize the cyclic time. The problem generalizes several known polynomial-solvable cyclic scheduling problems. The cyclic problem considered is equivalent to the parametric critical path problem on a network which is a further development of the network constructed by Alcaide et al. (EJOR, vol. 177, pp. 147-162, 2007). In spite of the above generalizations, the problem complexity, even though not as good as that for a single-product case, still remains polynomial.

A parametric critical path problem and an application for cyclic scheduling

Discrete Applied Mathematics, Oct 1, 1998

The paper addresses a problem of finding critical paths in PERT networks (digraphs) with variable... more The paper addresses a problem of finding critical paths in PERT networks (digraphs) with variable arc lengths depending on a parameter. By equipping the Bellman-Ford label-correcting algorithm with variable vectorial labels depending on the parameter, we derive its version that solves the problem in 0(mn2) time, for all possible parameter values (where M stands for the number of arcs, and n is the number of nodes in the digraph). An application related to cyclic scheduling of tasks in a robotic cell is considered.

Minimizing the number of vehicles in periodic scheduling: The non-Euclidean case

European Journal of Operational Research, Jun 1, 1998

In this paper we consider the problem of minimizing the number of vehicles needed to meet a fixed... more In this paper we consider the problem of minimizing the number of vehicles needed to meet a fixed periodically repeating set of tasks where set-up times between tasks do not satisfy the triangle inequality. We reduce this problem to finding the minimal length cycle-cover in a graph. In a special case, where the set-up times satisfy the triangle inequality, we reduce the scheduling problem to the assignment problem.

A note on periodic schedules for linear precedence constraints

Discrete Applied Mathematics, Feb 1, 2013

Hanen and Munier-Kordon [C. Hanen, A. Munier Kordon, Periodic schedules for linear precedence con... more Hanen and Munier-Kordon [C. Hanen, A. Munier Kordon, Periodic schedules for linear precedence constraints, Discrete Applied Mathematics 157 (2) (2009) 280-291] have considered a problem of scheduling periodic tasks each of which has to be repeated with its own period. They have developed a weakly polynomial algorithm for a particular class of linear precedence graphs called unitary graphs, which generalizes the usual not-earlier precedence relations between the tasks. The purpose of this note is twofold. First, we suggest a further generalization of the unitary relations that extends the usual not-later precedence relations; as a result, the arc lengths and heights in the underlying graph may be negative. Second, we show that, as soon as the arc heights in the graph are computed, an optimum periodic schedule can be found in strongly polynomial time.

Cyclic Flowshop Scheduling with Operators and Robots: Vyacheslav Tanaev’s Vision and Lasting Contributions

Journal of Scheduling, Jan 15, 2011

This note discusses the pioneering role and main contributions of V.S. Tanaev in the field of cyc... more This note discusses the pioneering role and main contributions of V.S. Tanaev in the field of cyclic robotic flowshop scheduling. Open questions (either explicitly or implicitly) posed in his papers and kept unsolved up to date are exposed. Keywords Cyclic flowshop • Robotic scheduling • Method of prohibited intervals • Dominance of cyclic schedules, Graph model

A polynomial algorithm for 2-cyclic robotic scheduling: A non-Euclidean case

Discrete Applied Mathematics, 2009

In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an m-mac... more In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an m-machine production line in which a robot is responsible for moving each part from a machine to another. The aim is to find the minimum cycle time for the so-called 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. The earlier known polynomial-time algorithms for this problem are applicable only under the additional assumption that the robot travel times satisfy the triangle inequalities. We lift this assumption on robot travel times and present a polynomial-time algorithm with the same time complexity as in the metric case, O(m 5 log m).

A faster algorithm for 2-cyclic robotic scheduling with a fixed robot route and interval processing times

European Journal of Operational Research, Feb 1, 2011

Consider an m-machine production line for processing identical parts served by a mobile robot. Th... more Consider an m-machine production line for processing identical parts served by a mobile robot. The problem is to find the minimum cycle time for 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. This work treats a special case of the 2-cyclic robot scheduling problem when the robot route is given and the operation durations are to be chosen from prescribed intervals. The problem was previously proved to be polynomially solvable in O(m 8 log m) time. This paper proposes an improved algorithm with reduced complexity O(m 4).

Minimizing the cycle time of multiple-product processing networks with a fixed operation sequence, setups, and time-window constraints

European Journal of Operational Research, Jun 1, 2008

We solve a special case of the single-robot cyclic scheduling problem with a fixed robot operatio... more

A note on a quadratic algorithm for the 2-cyclic robotic scheduling problem

Theoretical Computer Science, Nov 1, 2009

Recently, Pablo Sáez (2009) [1] has developed a quadratic algorithm for a 2-cyclic robotic schedu... more

Cyclic scheduling in a robotic production line

Journal of Scheduling, 2002

The solution of cyclic scheduling problems is part of the classical repertoire on scheduling algo... more

Cyclic routing algorithms in graphs: Performance analysis and applications to robot scheduling

Computers & Industrial Engineering, Sep 1, 2011

In this paper we revisit and extend the algorithm for the cyclic project scheduling problem which... more In this paper we revisit and extend the algorithm for the cyclic project scheduling problem which was originally proposed by Romanovskii (1967). While the algorithm has been derived for fixed numerical data, we show how it can be extended to handle the problems with interval data. We also propose a new algorithm for the cyclic scheduling problem with interval data that extends the parametric method developed by Megiddo (1979) and runs in strongly polynomial time.

A strongly polynomial algorithm for no-wait cyclic robotic flowshop scheduling

Operations Research Letters, Nov 1, 1997

We consider the problem of cyclic scheduling of identical jobs in a re-entrant flowshop. A robot ... more We consider the problem of cyclic scheduling of identical jobs in a re-entrant flowshop. A robot is responsible for moving each job from a machine to another. Our aim is to find a minimum length cycle of the robot's moves such that exactly one new job enters the system and exactly one completed job leaves the system during the cycle. We present a strongly polynomial algorithm for finding such a cycle.

Multiple-part cyclic hoist scheduling using a sieve method

IEEE Transactions on Robotics and Automation, 1999

... Vladimir Kats, Eugene Levner, and Leonid Meyzin Abstract The paper proposes an algorithm for... more

Cyclic scheduling in robotic flowshops with bounded work-in-process levels

Naval Research Logistics, Dec 2, 2010

This study addresses cyclic scheduling in robotic flowshops with bounded work-in-process (WIP) le... more This study addresses cyclic scheduling in robotic flowshops with bounded work-in-process (WIP) levels. The objective is to minimize the cycle time or, equivalently, to maximize the throughput, under the condition that the WIP level is bounded from above by a given integer number. We present several strongly polynomial algorithms for the 2-cyclic robotic flowshop scheduling problems for various WIP levels.

On the existence of dominating 6-cyclic schedules in four-machine robotic cells

European Journal of Operational Research, Jul 1, 2018

Abstract We consider a four-machine robotic cell producing identical parts and served by a single... more Abstract We consider a four-machine robotic cell producing identical parts and served by a single robot. We study the no-wait multi-cyclic scheduling problem. Using the forbidden-intervals method, we show that in such a cell the optimal schedule can be k-cyclic with minimum k ≥ 6. This fact refutes Agnetis’ conjecture (Agnetis, 2000) stating that the minimum k for the optimal k-cyclic m-machine schedules does not exceed m−1. In particular, we construct a counter-example to Agnetis’ conjecture.

A Polynomial Algorithm for 2-Cyclic Robotic Scheduling

Springer eBooks, 2006

We solve a single-robot m-machine cyclic scheduling problem arising in flexible manufacturing sys... more We solve a single-robot m-machine cyclic scheduling problem arising in flexible manufacturing systems served by computer-controlled robots. The problem is to find the minimum cycle time for the so-called 2-cyclic (or "2degree") schedules, in which exactly two parts enter and two parts leave the production line during each cycle. An earlier known polynomial time algorithm for this problem was applicable only to the Euclidean case, where the transportation times must satisfy the "triangle inequality". In this paper we study a general non-Euclidean case. Applying a geometrical approach, we construct a polynomial time algorithm of complexity O(m 5 log m).

Method and apparatus for slope to threshold conversion for process state monitoring and endpoint detection

A method for converting a slope based detection task to a threshold based detection task is provi... more A method for converting a slope based detection task to a threshold based detection task is provided. The above-described method begins by defining 140 the approximation equation for a set of points corresponding to values of a process being monitored. Next, the estimated value at the current point of the process being monitored is predicted (142). Next, the difference between the measured value and the expected value corresponding thereto at the current point of the process being monitored is calculated (144). Next, the difference is monitored for successful point for detecting a deviation value between the measured value and the estimated value (146). Then, the transition point for the process being monitored is identified based on the detection of the deviation value (148). A processing system and a computer-readable medium configured to provide real time data for a slope based transition is also provided. Endpoint, transition

Method and apparatus for slope to threshold conversion for process state monitoring and endpoint detection

A multilevel decision-making system with multiple resources for controlling cotton harvesting

International Journal of Production Economics, 1996

A number of our recent papers have demonstrated the advantage of using multilevel production cont... more A number of our recent papers have demonstrated the advantage of using multilevel production control models, especially for flexible manufacturing systems. The results obtained may be applied to various man-machine systems, e.g., building systems, mining, forestry, agriculture, etc., where control actions are carried out by decision-makers on different levels since the plants are not fully automatic. The best results can be achieved for hierarchical production systems, e.g.. company-section-production units, where each level faces stochastic optimization problems. In this paper, we consider the problem of reallocating multiple resources among production units while all previous models include only one type of interchangeable resource• For control problems with several resources, all the optimization problems become more difficult. The results obtained are used for creating a hierarchical decision-making system for controlling cotton harvesting. Three levels are considered-the team level, the farm level and the district level. Two types of resources are considered: mechanical harvesters and workers. On the team level, the team's foreman periodically reallocates the resources among cotton fields. The farm level is faced with stochastic optimization problems of rcallocating resources among the teams. The district level is faced with similar reallocation problems, including problems of determining minimal additional resource amounts that. on the average, guarantee completion of cotton harvesting by the due date. A numerical example is presented. Various application areas are considered.

An improved algorithm for cyclic flowshop scheduling in a robotic cell

European Journal of Operational Research, 1997

This paper addresses a cyclic robot scheduling problem in an automated manufacturing line in whic... more This paper addresses a cyclic robot scheduling problem in an automated manufacturing line in which a single robot is used to move parts from one workstation to another. The objective is to minimize the cycle length. Previously known algorithms are either heuristic or at best polynomial of the fifth degree in the number of machines, m. We derive an exact scheduling algorithm solving the problem in O(m 3 log m) time.

Cyclic scheduling of processes in robotic cells characterized by directed acyclic graphs

Actas del XXX Congreso Nacional de Estadística e Investigación Operativa y de las IV Jornadas de Estadística Pública, 2007, ISBN 978-84-690-7249-3, 2007

We consider a multiple-product, multiple-robot, 1-cyclic scheduling problem in a robotic assembly... more We consider a multiple-product, multiple-robot, 1-cyclic scheduling problem in a robotic assembly/disassembly system. The durations of the processing, setup, and transportation operations are controllable decision variables lying in given time intervals ("time windows"). The precedence relations between assembly/disassembly operations of any job are given in the form of a general directed acyclic graph, rather than a chain. The objective is to maximize the cell performance, or, equivalently, to minimize the cyclic time. The problem generalizes several known polynomial-solvable cyclic scheduling problems. The cyclic problem considered is equivalent to the parametric critical path problem on a network which is a further development of the network constructed by Alcaide et al. (EJOR, vol. 177, pp. 147-162, 2007). In spite of the above generalizations, the problem complexity, even though not as good as that for a single-product case, still remains polynomial.

A parametric critical path problem and an application for cyclic scheduling

Discrete Applied Mathematics, Oct 1, 1998

The paper addresses a problem of finding critical paths in PERT networks (digraphs) with variable... more The paper addresses a problem of finding critical paths in PERT networks (digraphs) with variable arc lengths depending on a parameter. By equipping the Bellman-Ford label-correcting algorithm with variable vectorial labels depending on the parameter, we derive its version that solves the problem in 0(mn2) time, for all possible parameter values (where M stands for the number of arcs, and n is the number of nodes in the digraph). An application related to cyclic scheduling of tasks in a robotic cell is considered.

Minimizing the number of vehicles in periodic scheduling: The non-Euclidean case

European Journal of Operational Research, Jun 1, 1998

In this paper we consider the problem of minimizing the number of vehicles needed to meet a fixed... more In this paper we consider the problem of minimizing the number of vehicles needed to meet a fixed periodically repeating set of tasks where set-up times between tasks do not satisfy the triangle inequality. We reduce this problem to finding the minimal length cycle-cover in a graph. In a special case, where the set-up times satisfy the triangle inequality, we reduce the scheduling problem to the assignment problem.

A note on periodic schedules for linear precedence constraints

Discrete Applied Mathematics, Feb 1, 2013

Hanen and Munier-Kordon [C. Hanen, A. Munier Kordon, Periodic schedules for linear precedence con... more Hanen and Munier-Kordon [C. Hanen, A. Munier Kordon, Periodic schedules for linear precedence constraints, Discrete Applied Mathematics 157 (2) (2009) 280-291] have considered a problem of scheduling periodic tasks each of which has to be repeated with its own period. They have developed a weakly polynomial algorithm for a particular class of linear precedence graphs called unitary graphs, which generalizes the usual not-earlier precedence relations between the tasks. The purpose of this note is twofold. First, we suggest a further generalization of the unitary relations that extends the usual not-later precedence relations; as a result, the arc lengths and heights in the underlying graph may be negative. Second, we show that, as soon as the arc heights in the graph are computed, an optimum periodic schedule can be found in strongly polynomial time.

Cyclic Flowshop Scheduling with Operators and Robots: Vyacheslav Tanaev’s Vision and Lasting Contributions

Journal of Scheduling, Jan 15, 2011

This note discusses the pioneering role and main contributions of V.S. Tanaev in the field of cyc... more This note discusses the pioneering role and main contributions of V.S. Tanaev in the field of cyclic robotic flowshop scheduling. Open questions (either explicitly or implicitly) posed in his papers and kept unsolved up to date are exposed. Keywords Cyclic flowshop • Robotic scheduling • Method of prohibited intervals • Dominance of cyclic schedules, Graph model

A polynomial algorithm for 2-cyclic robotic scheduling: A non-Euclidean case

Discrete Applied Mathematics, 2009

In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an m-mac... more In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an m-machine production line in which a robot is responsible for moving each part from a machine to another. The aim is to find the minimum cycle time for the so-called 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. The earlier known polynomial-time algorithms for this problem are applicable only under the additional assumption that the robot travel times satisfy the triangle inequalities. We lift this assumption on robot travel times and present a polynomial-time algorithm with the same time complexity as in the metric case, O(m 5 log m).

A faster algorithm for 2-cyclic robotic scheduling with a fixed robot route and interval processing times

European Journal of Operational Research, Feb 1, 2011

Consider an m-machine production line for processing identical parts served by a mobile robot. Th... more Consider an m-machine production line for processing identical parts served by a mobile robot. The problem is to find the minimum cycle time for 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. This work treats a special case of the 2-cyclic robot scheduling problem when the robot route is given and the operation durations are to be chosen from prescribed intervals. The problem was previously proved to be polynomially solvable in O(m 8 log m) time. This paper proposes an improved algorithm with reduced complexity O(m 4).

Minimizing the cycle time of multiple-product processing networks with a fixed operation sequence, setups, and time-window constraints

European Journal of Operational Research, Jun 1, 2008

We solve a special case of the single-robot cyclic scheduling problem with a fixed robot operatio... more

A note on a quadratic algorithm for the 2-cyclic robotic scheduling problem

Theoretical Computer Science, Nov 1, 2009

Recently, Pablo Sáez (2009) [1] has developed a quadratic algorithm for a 2-cyclic robotic schedu... more

Cyclic scheduling in a robotic production line

Journal of Scheduling, 2002

The solution of cyclic scheduling problems is part of the classical repertoire on scheduling algo... more

Cyclic routing algorithms in graphs: Performance analysis and applications to robot scheduling

Computers & Industrial Engineering, Sep 1, 2011

In this paper we revisit and extend the algorithm for the cyclic project scheduling problem which... more In this paper we revisit and extend the algorithm for the cyclic project scheduling problem which was originally proposed by Romanovskii (1967). While the algorithm has been derived for fixed numerical data, we show how it can be extended to handle the problems with interval data. We also propose a new algorithm for the cyclic scheduling problem with interval data that extends the parametric method developed by Megiddo (1979) and runs in strongly polynomial time.

A strongly polynomial algorithm for no-wait cyclic robotic flowshop scheduling

Operations Research Letters, Nov 1, 1997

We consider the problem of cyclic scheduling of identical jobs in a re-entrant flowshop. A robot ... more We consider the problem of cyclic scheduling of identical jobs in a re-entrant flowshop. A robot is responsible for moving each job from a machine to another. Our aim is to find a minimum length cycle of the robot's moves such that exactly one new job enters the system and exactly one completed job leaves the system during the cycle. We present a strongly polynomial algorithm for finding such a cycle.

Multiple-part cyclic hoist scheduling using a sieve method

IEEE Transactions on Robotics and Automation, 1999

... Vladimir Kats, Eugene Levner, and Leonid Meyzin Abstract The paper proposes an algorithm for... more

Cyclic scheduling in robotic flowshops with bounded work-in-process levels

Naval Research Logistics, Dec 2, 2010

This study addresses cyclic scheduling in robotic flowshops with bounded work-in-process (WIP) le... more This study addresses cyclic scheduling in robotic flowshops with bounded work-in-process (WIP) levels. The objective is to minimize the cycle time or, equivalently, to maximize the throughput, under the condition that the WIP level is bounded from above by a given integer number. We present several strongly polynomial algorithms for the 2-cyclic robotic flowshop scheduling problems for various WIP levels.

On the existence of dominating 6-cyclic schedules in four-machine robotic cells

European Journal of Operational Research, Jul 1, 2018

Abstract We consider a four-machine robotic cell producing identical parts and served by a single... more Abstract We consider a four-machine robotic cell producing identical parts and served by a single robot. We study the no-wait multi-cyclic scheduling problem. Using the forbidden-intervals method, we show that in such a cell the optimal schedule can be k-cyclic with minimum k ≥ 6. This fact refutes Agnetis’ conjecture (Agnetis, 2000) stating that the minimum k for the optimal k-cyclic m-machine schedules does not exceed m−1. In particular, we construct a counter-example to Agnetis’ conjecture.

A Polynomial Algorithm for 2-Cyclic Robotic Scheduling

Springer eBooks, 2006

We solve a single-robot m-machine cyclic scheduling problem arising in flexible manufacturing sys... more We solve a single-robot m-machine cyclic scheduling problem arising in flexible manufacturing systems served by computer-controlled robots. The problem is to find the minimum cycle time for the so-called 2-cyclic (or "2degree") schedules, in which exactly two parts enter and two parts leave the production line during each cycle. An earlier known polynomial time algorithm for this problem was applicable only to the Euclidean case, where the transportation times must satisfy the "triangle inequality". In this paper we study a general non-Euclidean case. Applying a geometrical approach, we construct a polynomial time algorithm of complexity O(m 5 log m).

Method and apparatus for slope to threshold conversion for process state monitoring and endpoint detection

A method for converting a slope based detection task to a threshold based detection task is provi... more A method for converting a slope based detection task to a threshold based detection task is provided. The above-described method begins by defining 140 the approximation equation for a set of points corresponding to values of a process being monitored. Next, the estimated value at the current point of the process being monitored is predicted (142). Next, the difference between the measured value and the expected value corresponding thereto at the current point of the process being monitored is calculated (144). Next, the difference is monitored for successful point for detecting a deviation value between the measured value and the estimated value (146). Then, the transition point for the process being monitored is identified based on the detection of the deviation value (148). A processing system and a computer-readable medium configured to provide real time data for a slope based transition is also provided. Endpoint, transition

Method and apparatus for slope to threshold conversion for process state monitoring and endpoint detection

A multilevel decision-making system with multiple resources for controlling cotton harvesting

International Journal of Production Economics, 1996

A number of our recent papers have demonstrated the advantage of using multilevel production cont... more A number of our recent papers have demonstrated the advantage of using multilevel production control models, especially for flexible manufacturing systems. The results obtained may be applied to various man-machine systems, e.g., building systems, mining, forestry, agriculture, etc., where control actions are carried out by decision-makers on different levels since the plants are not fully automatic. The best results can be achieved for hierarchical production systems, e.g.. company-section-production units, where each level faces stochastic optimization problems. In this paper, we consider the problem of reallocating multiple resources among production units while all previous models include only one type of interchangeable resource• For control problems with several resources, all the optimization problems become more difficult. The results obtained are used for creating a hierarchical decision-making system for controlling cotton harvesting. Three levels are considered-the team level, the farm level and the district level. Two types of resources are considered: mechanical harvesters and workers. On the team level, the team's foreman periodically reallocates the resources among cotton fields. The farm level is faced with stochastic optimization problems of rcallocating resources among the teams. The district level is faced with similar reallocation problems, including problems of determining minimal additional resource amounts that. on the average, guarantee completion of cotton harvesting by the due date. A numerical example is presented. Various application areas are considered.

An improved algorithm for cyclic flowshop scheduling in a robotic cell

European Journal of Operational Research, 1997

This paper addresses a cyclic robot scheduling problem in an automated manufacturing line in whic... more This paper addresses a cyclic robot scheduling problem in an automated manufacturing line in which a single robot is used to move parts from one workstation to another. The objective is to minimize the cycle length. Previously known algorithms are either heuristic or at best polynomial of the fifth degree in the number of machines, m. We derive an exact scheduling algorithm solving the problem in O(m 3 log m) time.