Scheduling three-operation jobs in a two-machine flow shop to minimize makespan

This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented.

Two-machine flow shop scheduling problems with no-wait jobs

In this paper we provide a fairly complete complexity classification of various versions of the two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. For some version, we offer a fully polynomial-time approximation scheme and a 43-approximation algorithm.

An improved approximation algorithm for the two-machine flow shop scheduling problem with an interstage transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables

An approximation algorithm for the two-machine flow shop with a single transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables.

An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.

Approximation results for flow shop scheduling problems with machine availability constraints

This paper considers two-machine flow shop scheduling problems with machine availability constraints. When the processing of a job is interrupted by an unavailability period of a machine, we consider both the resumable scenario in which the processing can be resumed when the machine next becomes available, and the semi-resumable scenario in which some portion of the processing is repeated but the job is otherwise resumable. For the problem with several non-availability intervals on the first machine under the resumable scenario, we present a fast (3/2)-approximation algorithm. For the problem with one non-availability interval under the semi-resumable scenario, a polynomial-time approximation scheme is developed.

Transporting jobs through a two-machine open shop

We consider the two-machine open shop scheduling problem in which the jobs are brought to the system by a single transporter and moved between the processing machines by the same transporter. The purpose is to split the jobs into batches and to find the sequence of moves of the transporter so that the time by which the completed jobs are collected together on board the transporter is minimal. We present a 7/5-approximation algorithm. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009

A new Nawaz–Enscore–Ham-based heuristic for permutation flow-shop problem with bicriteria of makespan and machine idle-time

A new heuristic based on Nawaz–Enscore–Ham (NEH) algorithm is proposed for solving permutation flowshop scheduling problem in this paper. A new priority rule is proposed by accounting for the average, mean absolute deviation, skewness and kurtosis, in order to fully describe the distribution style of processing times. A new tie-breaking rule is also introduced for achieving effective job insertion for the objective of minimizing both makespan and machine idle-time. Statistical tests illustrate better solution quality of the proposed algorithm, comparing to existing benchmark heuristics.

Press shop machine analysis and trending

Historically downtime data collection and reporting systems in many automotive body panel press shops has been somewhat adhoc. The impetus for this study stems from frustration in respect of how this data is collected, assessed for trends and presented. Ideally this data should be used to identify costly repetitious faults for actioning of maintenance work and for feedback to tool design for consideration when designing new parts.

Presently this data is stored largely in the form of tacit knowledge by press shop operators; the encumbrance of transferring such information being that there is very often only limited channels to quantify it into something more tangible. Findings show that there tend to be two related obstacles to plant data recording. The first is that automation of down time data collection alone cannot determine fault causes as the majority of press shop events are initiated primarily from operator observation. The second is that excessive subjective operator input can often result in confusion and end up taking greater time in recording than remedying the actual fault.

This Paper presents the development of a system that through press mounted touchscreens encourages basic subjective operator input and relates this with basic objective data such as timekeeping. In this way all responses for a given press line become valuable and can be trended and placed in a hierarchy based on their percentage contribution to downtime or statistical importance. This then is capable of statistically alerting maintenance, line flow and/or toolbuild areas as to what issues require their most urgent attention.

Pareto archived simulated annealing for single machine job shop scheduling with multiple objectives

In this paper, the single machine job shop scheduling problem is studied with the objectives of minimizing the tardiness and the material cost of jobs. The simultaneous consideration of these objectives is the multi-criteria optimization problem under study. A metaheuristic procedure based on simulated annealing is proposed to find the approximate Pareto optimal (non-dominated) solutions. The two objectives are combined in one composite utility function based on the decision maker’s interest in having a schedule with weighted combination. In view of the unknown nature of the weights for the defined objectives, a priori approach is applied to search for the non-dominated set of solutions based on the Pareto dominance. The obtained solutions set is presented to the decision maker to choose the best solution according to his preferences. The performance of the algorithm is evaluated in terms of the number of non-dominated schedules generated and the proximity of the obtained non-dominated front to the true Pareto front. Results show that the produced solutions do not differ significantly from the optimal solutions.

Lockwood's dictionary of terms used in the practice of mechanical engineering, embracing those current in the drawing office, pattern shop, foundry, fitting, turning, smiths' and boiler shops, etc., etc., comprising upwards of seven thousand definitions,

Mode of access: Internet.

Notes [on] basic engineering sciences; hydraulics, machine design, thermodynamics, hygrometry, economics and practice.

Mode of access: Internet.

Problems and solutions; New York State professional engineering examinations, parts II and III. Hydraulics, machine design, thermodynamics, economics and practice, hygrometry.

[v.1.] 1950-1954.--v.2. 1955-1958.

The absorption refrigerating machine, elementary theory and practice, a complete practical elementary treatise on the absorption system of refrigeration, and its general fundamental principles of operation.

Mode of access: Internet.