Algorithms for scheduling parallel batch processing machines with non-identical job ready times

This research is motivated by a practical application observed at a printed circuit board (PCB) manufacturing facility. After assembly, the PCBs (or jobs) are tested in environmental stress screening (ESS) chambers (or batch processing machines) to detect early failures. Several PCBs can be simultaneously tested as long as the total size of all the PCBs in the batch does not violate the chamber capacity. PCBs from different production lines arrive dynamically to a queue in front of a set of identical ESS chambers, where they are grouped into batches for testing. Each line delivers PCBs that vary in size and require different testing (or processing) times. Once a batch is formed, its processing time is the longest processing time among the PCBs in the batch, and its ready time is given by the PCB arriving last to the batch. ESS chambers are expensive and a bottleneck. Consequently, its makespan has to be minimized. ^ A mixed-integer formulation is proposed for the problem under study and compared to a formulation recently published. The proposed formulation is better in terms of the number of decision variables, linear constraints and run time. A procedure to compute the lower bound is proposed. For sparse problems (i.e. when job ready times are dispersed widely), the lower bounds are close to optimum. ^ The problem under study is NP-hard. Consequently, five heuristics, two metaheuristics (i.e. simulated annealing (SA) and greedy randomized adaptive search procedure (GRASP)), and a decomposition approach (i.e. column generation) are proposed—especially to solve problem instances which require prohibitively long run times when a commercial solver is used. Extensive experimental study was conducted to evaluate the different solution approaches based on the solution quality and run time. ^ The decomposition approach improved the lower bounds (or linear relaxation solution) of the mixed-integer formulation. At least one of the proposed heuristic outperforms the Modified Delay heuristic from the literature. For sparse problems, almost all the heuristics report a solution close to optimum. GRASP outperforms SA at a higher computational cost. The proposed approaches are viable to implement as the run time is very short. ^

Analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.

Makespan minimization in a job shop with a batch processing machine

A job shop with one batch processing and several discrete machines is analyzed. Given a set of jobs, their process routes, processing requirements, and size, the objective is to schedule the jobs such that the makespan is minimized. The batch processing machine can process a batch of jobs as long as the machine capacity is not violated. The batch processing time is equal to the longest processing job in the batch. The problem under study can be represented as Jm:batch:Cmax. If no batches were formed, the scheduling problem under study reduces to the classical job shop scheduling problem (i.e. Jm:: Cmax), which is known to be NP-hard. This research extends the scheduling literature by combining Jm::Cmax with batch processing. The primary contributions are the mathematical formulation, a new network representation and several solution approaches. The problem under study is observed widely in metal working and other industries, but received limited or no attention due to its complexity. A novel network representation of the problem using disjunctive and conjunctive arcs, and a mathematical formulation are proposed to minimize the makespan. Besides that, several algorithms, like batch forming heuristics, dispatching rules, Modified Shifting Bottleneck, Tabu Search (TS) and Simulated Annealing (SA), were developed and implemented. An experimental study was conducted to evaluate the proposed heuristics, and the results were compared to those from a commercial solver (i.e., CPLEX). TS and SA, with the combination of MWKR-FF as the initial solution, gave the best solutions among all the heuristics proposed. Their results were close to CPLEX; and for some larger instances, with total operations greater than 225, they were competitive in terms of solution quality and runtime. For some larger problem instances, CPLEX was unable to report a feasible solution even after running for several hours. Between SA and the experimental study indicated that SA produced a better average Cmax for all instances. The solution approaches proposed will benefit practitioners to schedule a job shop (with both discrete and batch processing machines) more efficiently. The proposed solution approaches are easier to implement and requires short run times to solve large problem instances.

Intuition and its component parts in the heuristic processing of deception detection: Hunch, *evidence, and reliance on intuitive efficacy

Rated trust in intuitive efficacy (measured as trust, belief, use, accuracy and weighting of intuition) was investigated as a predictor of self-designated use of intuitive (hunch and hunch plus evidential belief) vs. deliberative (evidential belief and evidential belief plus hunch) deception detection judgments and actual accuracy. Twenty-nine student participants were filmed as they made true and deceptive statements about their everyday activities on a given evening (last Friday night), and college students (N=238) judged 20 (10=true, 10=deceptive) of these filmed statements as truthful or deceptive. Participants provided ratings of reliance on hunches vs. evidential belief, confidence in film judgments, intuitive efficacy, accuracy in deception detection, reliance on cues to deception, and experiences with intuition. Generalized estimated equation modeling using binary logistics demonstrated accuracy in identifying true vs. deceptive statements was predicted by film number, hunch-evidence ratings, weighting of intuition, and total cues cited. Weighting of intuition was predictive of accuracy across participants, with higher weighting predictive of higher accuracy in general. Participants who cited evidential belief plus hunch and moderate to high weighting incorrectly reversed their true vs. deceptive judgments. Accuracy for true statements was higher for hunches and hunch plus evidential belief, whereas accuracy for deceptive statements was higher for evidential belief Accuracy for participants who relied on evidential belief plus hunch was at chance. Subjective experiences underlying judgments differed by participant and type of film viewed (true vs. deceptive) and were predicted by hunch-evidence ratings, trust, use, intuitive accuracy, and total cues cited. Trust predicted increases in judging films to be true, whereas use and accuracy predicted increases in judging films as deceptive; none were predictive of accuracy. Increased number of cues cited predicted judgments of deception, whereas decreased number of cues cited predicted truth. The study concluded that participants have the capacity to self-define their judgments as subjectively vs. deliberately based, provide subjective assessments of the influence of intuitive vs. objective information on their judgments, and can apply this self-knowledge, through effective weighting of intuition vs. other types of information, in making accurate judgments of true and deceptive everyday statements.

Analytical Approximations to Predict Performance Measures of Manufacturing Systems with Job Failures and Parallel Processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.