Vladimir Kats

Cyclic scheduling in robotic flowshops

Fully automated production cells consisting of flexible machines and a material handling robot have become commonplace in contemporary manufacturing systems. Much research on scheduling problems arising in such cells, in particular in flowshop-like production cells, has been reported recently. Although there are many differences between the models, they all explicitly incorporate the interaction between the materials handling and the classical job processing decisions, since this interaction determines the efficiency of the cell. This paper surveys cyclic scheduling problems in robotic flowshops, models for such problems, and the complexity of solving these problems, thereby bringing together several streams of research that have by and large ignored one another, and describing and establishing links with other scheduling problems and combinatorial topics.

Survey: Complexity of cyclic scheduling problems: A state-of-the-art survey

In this survey we review the current complexity status of basic cyclic scheduling models. We start with the formulations of three fundamental cyclic scheduling problems, namely the cyclic jobshop, cyclic flowshop, and cyclic project scheduling problems. We present state-of-the-art results on the computational complexity of the problems, paying special attention to recent results on the unsolvability (NP-hardness) of various cyclic problems arising from the scheduling of robotic cells.

An improved algorithm for cyclic flowshop scheduling in a robotic cell

Abstract 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.

Multiple-part cyclic hoist scheduling using a sieve method

The paper proposes an algorithm for generating optimal cyclic schedules of hoist moves in a printed circuit board electroplating facility where transportation of parts between workstations is performed by a computer-controlled hoist. The objective of the scheduling problem is to maximize the throughput rate. Unlike many previous algorithms which consider 1-part cyclic schedules, the proposed algorithm provides an exact solution for the more complicated case of r-part cyclic schedules where r>1. The algorithm is illustrated with numerical examples comparing 1-part and multiple-part optimal schedules.

A parametric critical path problem and an application for cyclic scheduling

Abstract 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 O(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.

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

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 robots 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.

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

Abstract We solve a special case of the single-robot cyclic scheduling problem with a fixed robot operation sequence and time window constraints on processing times. It generalizes the known single-part fixed-sequence problems into the one to cover a processing network with multiple part types and setup time requirements between the processing steps for different parts at the shared stations. The objective is to minimize the cycle time. We prove that this problem is equivalent to the parametric critical path problem, and propose a strongly polynomial time solution algorithm which uses a new labeling procedure to identify all feasible parameter values. The proposed algorithm is based on an extension to the known Bellman–Ford algorithm. The occurrence of time windows together with multiple products and a network-type process makes our problem much more complex than that of the single-product single processing-line case. One key observation from this study is that in spite of this generalization, the problem is proved to be solvable by the proposed parametric critical path algorithm. Its complexity, though not as good as that for the single-product problem, still remains strongly polynomial and, as such, dominates the complexity of general linear programming methods in this case. This observation makes our result a candidate optimization subroutine to be used in heuristic algorithms that solve general cyclic scheduling problems with time windows and setup time constraints and that allow different robot operation sequences in a cycle to be evaluated.

Minimizing the number of robots to meet a given cyclic schedule

We study a problem of cyclic no-wait scheduling of identical parts on m sequential machines. A number of robots are used to transport the parts from one machine to another. We consider the problem that has two performance measures: one is the number of robots to be used, the other is the period of a cyclic schedule. We find the minimal number of robots needed to meet a given cyclic schedule, for all possible cycle lengths, the complex-ity of the suggested algorithm being O(m 5 ), independently of the range within which the cycle length value may vary.

Cyclic multiple-robot scheduling with time-window constraints using a critical path approach

Abstract An automated production system is considered in which several robots are used for transporting parts between workstations following a given route in a carousel mode. The problem is to maximize the throughput rate. Extending previous works treating scheduling problems for a single robot, we consider a more realistic case in which workstations are served by multiple robots. A graph model of the production process is developed, making it possible to apply PERT–CPM solution techniques. The problem is proved to be solvable in polynomial time.

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

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(m8log m) time. This paper proposes an improved algorithm with reduced complexity O(m4).