Nadia Brauner

Cycles and permutations in robotic cells

We consider a robotic cell, consisting of a flow-shop in which the machines are served by a single central robot. We concentrate on the case where only one part type is produced and analyze the validity of the so-called one-cycle conjecture by Sethi, Sriskandarajah, Sorger, Blazewicz and Kubiak. This conjecture claims that the repetition of the best one-unit production cycle will yield the maximum throughput rate in the set of all possible cyclic robot moves. We present a new algebraic approach, unifying the former rather tedious proofs for the known results on pyramidal one-cycles and two- and three-machine cells. In this framework, counterexamples will be constructed, showing that the conjecture is not valid for four and more machines. We first present examples for a general four-machine cell, for which the two-unit production cycles dominate the one-unit cycles. Then we consider in particular the so-called regular cells, where all machines are equidistant, since the one-cycle conjecture has originally been formulated for this case. Here, we prove that for four-machine cells, two-unit production cycles are still dominated by one-unit production cycles. Then we describe a counterexample with a three-unit production cycle, thus, settling completely the one-cycle conjecture.

Identical part production in cyclic robotic cells: Concepts, overview and open questions

Robotic cells consist of a flow-shop with a robot for material handling. A single part is to be produced cyclically and the objective is to minimize production rate. This document introduces basic concepts and tools for dealing with cyclic production. In particular, it concentrates on k-cycles which are production cycles where exactly k parts enter and leave the cell. One defines the cycle function K which is the smallest value of k so that the set of all k-cycles up to size K contains an optimal cycle for all instances. Known results and conjectures on these functions are given for the classical case where parts can remain on the machine waiting for the robot and for the no-wait case where parts have to be removed from the machine as soon as their processing is finished.

On A Conjecture About Robotic Cells: New Simplified Proof For The Three-Machine Case

AbstractWe consider a robotic cell, consisting of a flow-shop in which the machines are served by a single central robot. We concentrate on the case where only one part type is produced and want to analyze the conjecture of Sethi, Sriskandarajah, Sorger, Blazewicz and Kubiak. This well-known conjecture claims that the repetition of the best one-unit production cycle will yield the maximum throughput rate in the set of all possible robot moves. The conjecture holds for two and three machines, but the existing proof by van de Klundert and Crama for the three-machine case is extremely tedious.We adopt the theoretical background developed by Crama and van de Klundert. Using a particular state graph, the k-unit production cycles are represented as special paths and cycles for which general properties and bounds for the m-machine robotic cell can be obtained. By means of these concepts, we shall give a concise proof for the validity of the conjecture for the three-machine case.

Complexity of one-cycle robotic flow-shops

We study the computational complexity of finding the shortest route the robot should take when moving parts between machines in a flow-shop. Though this complexity has already been addressed in the literature, the existing attempts made crucial assumptions which were not part of the original problem. Therefore, they cannot be deemed satisfactory. We drop these assumptions in this paper and prove that the problem is NP-hard in the strong sense when the travel times between the machines of the cell are symmetric and satisfy the triangle inequality. We also impose no restrictions on the times of robot arrival at and departure from machines as it is the case in the related, but different, hoist scheduling problem. Our results hold for processing times equal on all machines in the cell. However, the equidistant case for equal processing times can be solved in O(1) time.

The maximum deviation just-in-time scheduling problem

This note revisits the maximum deviation just-in-time (MDJIT) scheduling problem previously investigated by Steiner and Yeomans. Its main result is a set of algebraic necessary and sufficient conditions for the existence of a MDJIT schedule with a given objective function value. These conditions are used to provide a finer analysis of the complexity of the MDJTT problem. The note also investigates various special cases of the MDJIT problem and suggests several questions for further investigation.

Optimal moves of the material handling system in a robotic cell

Abstract We consider the so-called robotic cells, i.e. flow-shops with a central robot that carries out the transfers of the parts between the machines. The objective is to describe the robot moves which optimize the throughput rate of a given product. In 1992, a conjecture about the optimal production rate was stated, referred to as the one-cycle conjecture. We shall give the state-of-the-art on this conjecture and add new results on specialized robotic cell arrangements.

Pricing techniques for self regulation in Vehicle Sharing Systems

We study self regulation through pricing for Vehicle Sharing Systems (VSS). Without regulation VSS have poor performances. We want to improve the efficiency of VSS using pricing as incentive. We take as base model a Markovian formulation of a closed queuing network with finite buffer and time dependent service time. This model is unfortunately intractable for the size of instances we want to tackle. We discuss heuristics: a scenario approach, a fluid approximation, simplified stochastic models and asymptotic approximations. We compare these heuristics on toy cities.

Single machine scheduling with small operator-non-availability periods

For an industrial application in the chemical industry, we were confronted with the planning of experiments, where human intervention of a chemist is required to handle the starting and termination of each of the experiments. This gives rise to a new type of scheduling problem, namely problems of finding schedules with time periods when the tasks can neither start nor finish. We consider in this paper the natural case of small periods where the duration of the periods is smaller than any processing time. This assumption corresponds to our chemical experiments lasting several days, whereas the operator unavailability periods are typically single days or week-ends. These problems are analyzed on a single machine with the makespan as criterion.We first prove that, contrary to the case of machine unavailability periods, the problem with one small operator non-availability period can be solved in polynomial time. We then derive approximation and inapproximability results for the general case of k small unavailability periods, where k may be part of the input or k may be fixed. We consider in particular the practical case of periodic and equal small unavailability periods. We prove that all these problems become NP-hard if one has k≥2 small unavailability periods and the problems do not allow fully polynomial time approximation schemes (FPTAS) for k≥3. We then analyze list scheduling algorithms and establish their performance guarantee.

Logical Analysis of Computed Tomography Data to Differentiate Entities of Idiopathic Interstitial Pneumonias

The aim of this chapter is to analyze computed tomography (CT) data by using the Logical Analysis of Data (LAD) methodology in order to distinguish between three types of idiopathic interstitial pneumonias (IIPs). The chapter demonstrates that LAD can distinguish different forms of IIPs with high accuracy It shows also that the patterns developed by LAD techniques provide additional information about outliers, redundant features, the relative significance of attributes, and makes possible the identification of promoters and blockers of various forms of IIPs.

Operator non-availability periods

In the scheduling literature, the notion of machine non-availability periods is well known, for instance for maintenance. In our case of planning chemical experiments, we have special periods (the week-ends, holidays, vacations) where the chemists are not available. However, human intervention by the chemists is required to handle the starting and termination of the experiments. This gives rise to a new type of scheduling problems, namely problems of finding schedules that respect the operator non-availability periods. These problems are analyzed on a single machine with the makespan as criterion. Properties are described and performance ratios are given for list scheduling and other polynomial-time algorithms.