Inna G. Drobouchevitch

Scheduling dual gripper robotic cell: One-unit cycles

We consider the scheduling problem of cyclic production in a bufferless dual-gripper robot cell processing a family of identical parts. The objective is to find an optimal sequence of robot moves so as to maximize the long-run average throughput rate of the cell. While there has been a considerable amount of research dealing with single-gripper robot cells, there are only a few papers devoted to scheduling in dual-gripper robotic cells. From the practical point of view, the use of a dual gripper offers the attractive prospect of an increase in the cell productivity. At the same time, the increase in the combinatorial possibilities associated with a dual-gripper robot severely complicates its theoretical analysis. The purpose of this paper is to extend the existing conceptual framework to the dual-gripper situation, and to provide some insight into the problem. We provide a notational and modelling framework for cyclic production in a dual-gripper robotic cell. Focusing on the so-called active cycles, we discuss the issues of feasibility and explore the combinatorial aspects of the problem. The main attention is on 1-unit cycles, i.e., those that restore the cell to the same initial state after the production of each unit. For an m-machine robotic cell served by a dual-gripper robot, we describe a complete family of 1-unit cycles, and derive an analytical formula to estimate their total number for a given m. In the case when the gripper switching time is sufficiently small, we identify an optimal 1-unit cycle. This special case is of particular interest as it reflects the most frequently encountered situation in real-life robotic systems. Finally, we establish the connection between a dual-gripper cell and a single-gripper cell with machine output buffers of one-unit capacity and compare the cell productivity for these two models.

Scheduling Multiple Parts in a Robotic Cell Served by a Dual-Gripper Robot

A robotic cell-a manufacturing system widely used in industry-contains two or more robot-served machines, repetitively producing a number of part types. In this paper, we consider scheduling of operations in a bufferless dual-gripper robotic cell processing multiple part types. The processing constraints specify the cell to be a flowshop. The objective is to determine the robot move sequence and the sequence in which parts are to be processed so as to maximize the long-run average throughput rate for repetitive production of parts. We provide a framework to study the problem, and address the issues of problem complexity and solvability. Focusing on a particular class of robot move sequences, we identify all potentially optimal robot move sequences for the part-sequencing problem in a two-machine dual-gripper robot cell. In the case when the gripper switching time is sufficiently small, we specify the best robot move sequence in the class. We prove the problem of finding an optimal part sequence to be strongly NP-hard, even when the robot move sequence is specified. We provide a heuristic approach to solve the general two-machine problem and evaluate its performance on the set of randomly generated problem instances. We perform computations to estimate the productivity gain of using a dual-gripper robot in place of a single-gripper robot. Finally, we extend our results for the two-machine cell to solve an m -machine problem.

A heuristic algorithm for two‐machine re‐entrant shop scheduling

This paper considers the problem of sequencing n jobs in a two‐machine re‐entrant shopwith the objective of minimizing the maximum completion time. The shop consists of twomachines, M1 and M2 , and each job has the processing route (M1 , M2 , M1 ). An O(n log n)time heuristic is presented which generates a schedule with length at most 4/3 times that ofan optimal schedule, thereby improving the best previously available worst‐case performanceratio of 3/2.

Heuristics for the two-stage job shop scheduling problem with a bottleneck machine

The paper considers the job shop scheduling problem to minimize the makespan. It is assumed that each job consists of at most two operations, one of which is to be processed on one of m⩾2 machines, while the other operation must be performed on a single bottleneck machine, the same for all jobs. For this strongly NP-hard problem we present two heuristics with improved worst-case performance. One of them guarantees a worst-case performance ratio of 3/2. The other algorithm creates a schedule with the makespan that exceeds the largest machine workload by at most the length of the largest operation.

Throughput optimization in robotic cells with input and output machine buffers: A comparative study of two key models

We consider the problem of scheduling operations in a robotic cell processing a single part type. Each machine in the cell has a one-unit input buffer and a one-unit output buffer. The machines and buffers are served by one single gripper robot. The domain considered is free-pickup cells with additive inter-machine travel time. The processing constraints specify the cell to be a flow shop. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes throughput. Bufferless robotic cells have been studied extensively in the literature. However, the few studies of robotic cells with output buffers at each machine have shown that the throughput can be improved by such a configuration. We show that there is no throughput advantage in providing machine input buffers in addition to output buffers. The equivalence in throughput between the two models has significant practical implications, since the cost of providing additional buffers at each machine is substantial.

Minimization of earliness, tardiness and due date penalties on uniform parallel machines with identical jobs

We consider a problem of scheduling n identical nonpreemptive jobs with a common due date on m uniform parallel machines. The objective is to determine an optimal value of the due date and an optimal allocation of jobs onto machines so as to minimize a total cost function, which is the function of earliness, tardiness and due date values. For the problem under study, we establish a set of properties of an optimal solution and suggest a two-phase algorithm to tackle the problem. First, we limit the number of due dates one needs to consider in pursuit of optimality. Next, we provide a polynomial-time algorithm to build an optimal schedule for a fixed due date. The key result is an O(m^2logm) algorithm that solves the main problem to optimality. Scope and purpose: To extend the existing research on cost minimization with earliness, tardiness and due date penalties to the case of uniform parallel machines.

Two-stage open shop scheduling with a bottleneck machine

Abstract It is known that for the open shop scheduling problem to minimize the makespan there exists no polynomial-time heuristic algorithm that guarantees a worst-case performance ratio better than 5/4, unless P ≠NP. However, this result holds only if the instance of the problem contains jobs consisting of at least three operations. This paper considers the open shop scheduling problem, provided that each job consists of at most two operations, one of which is to be processed on one of the m ⩾2 machines, while the other operation must be performed on the bottleneck machine, the same for all jobs. For this NP-hard problem we present a heuristic algorithm and show that its worst-case performance ratio is 5/4.

A polynomial algorithm for the three‐machineopen shop with a bottleneck machine

The paper considers the three‐machine open shop scheduling problem to minimize themakespan. It is assumed that each job consists of at most two operations, one of which is tobe processed on the bottleneck machine, the same for all jobs. A new lower bound on theoptimal makespan is derived, and a linear‐time algorithm for finding an optimalnon‐preemptive schedule is presented.

Heuristics for short route job shop scheduling problems

Abstract. We consider two “minimum”NP-hard job shop scheduling problems to minimize the makespan. In one of the problems every job has to be processed on at most two out of three available machines. In the other problem there are two machines, and a job may visit one of the machines twice. For each problem, we define a class of heuristic schedules in which certain subsets of operations are kept as blocks on the corresponding machines. We show that for each problem the value of the makespan of the best schedule in that class cannot be less than 3/2 times the optimal value, and present algorithms that guarantee a worst-case ratio of 3/2.