Scheduling reentrant jobs on parallel machines with a remote server

This paper explores a specific combinatorial problem relating to re-entrant jobs on parallel primary machines, with a remote server machine. A middle operation is required by each job on the server before it returns to its primary processing machine. The problem is inspired by the logistics of a semi-automated micro-biology laboratory. The testing programme in the laboratory corresponds roughly to a hybrid flowshop, whose bottleneck stage is the subject of study. We demonstrate the NP-hard nature of the problem, and provide various structural features. A heuristic is developed and tested on randomly generated benchmark data. Results indicate solutions reliably within 1.5% of optimum. We also provide a greedy 2-approximation algorithm. Test on real-life data from the microbiology laboratory indicate a 20% saving relative to current practice, which is more than can be achieved currently with 3 instead of 2 people staffing the primary machines

Pilot, Rollout and Monte Carlo Tree Search Methods for Job Shop Scheduling

Greedy heuristics may be attuned by looking ahead for each possible choice, in an approach called the rollout or Pilot method. These methods may be seen as meta-heuristics that can enhance (any) heuristic solution, by repetitively modifying a master solution: similarly to what is done in game tree search, better choices are identified using lookahead, based on solutions obtained by repeatedly using a greedy heuristic. This paper first illustrates how the Pilot method improves upon some simple well known dispatch heuristics for the job-shop scheduling problem. The Pilot method is then shown to be a special case of the more recent Monte Carlo Tree Search (MCTS) methods: Unlike the Pilot method, MCTS methods use random completion of partial solutions to identify promising branches of the tree. The Pilot method and a simple version of MCTS, using the $\varepsilon$-greedy exploration paradigms, are then compared within the same framework, consisting of 300 scheduling problems of varying sizes with fixed-budget of rollouts. Results demonstrate that MCTS reaches better or same results as the Pilot methods in this context.Comment: Learning and Intelligent OptimizatioN (LION'6) 7219 (2012

Simulation and optimization techniques applied in semiconductor assembly and test operations

The importance of back-end operations in semiconductor manufacturing has been growing steadily in the face of higher customer expectations and stronger competition in the industry. In order to achieve low cycle times, high throughput, and high utilization while improving due-date performance, more effective tools are needed to support machine setup and lot dispatching decisions. In previous work, the problem of maximizing the weighted throughput of lots undergoing assembly and test (AT), while ensuring that critical lots are given priority, was investigated and a greedy randomized adaptive search procedure (GRASP) developed to find solutions. Optimization techniques have long been used for scheduling manufacturing operations on a daily basis. Solutions provide a prescription for machine setups and job processing over a finite the planning horizon. In contrast, simulation provides more detail but in a normative sense. It tells you how the system will evolve in real time for a given demand, a given set of resources and rules for using them. A simulation model can also accommodate changeovers, initial setups and multi-pass requirements easily. The first part of the research is to show how the results of an optimization model can be integrated with the decisions made within a simulation model. The problem addressed is defined in terms of four hierarchical objectives: minimize the weighted sum of key device shortages, maximize weighted throughput, minimize the number of machines used, and minimize makespan for a given set of lots in queue, and a set of resources that includes machines and tooling. The facility can be viewed as a reentrant flow shop. The basic simulation was written in AutoSched AP (ASAP) and then enhanced with the help of customization features available in the software. Several new dispatch rules were developed. Rule_First_setup is able to initialize the simulation with the setups obtained with the GRASP. Rule_All_setups enables a machine to select the setup provided by the optimization solution whenever a decision is about to be made on which setup to choose subsequent to the initial setup. Rule_Hotlot was also proposed to prioritize the processing of the hot lots that contain key devices. The objective of the second part of the research is to design and implement heuristics within the simulation model to schedule back-end operations in a semiconductor AT facility. Rule_Setupnum lets the machines determine which key device to process according to a machine setup frequency table constructed from the GRASP solution. GRASP_asap embeds a more robust selection features of GRASP in the ASAP model through customization. This allows ASAP to explore a larger portion of the feasible region at each decision point by randomizing machine setups using adaptive probability distributions that are a function of solution quality. Rule_Greedy, which is a simplification of GRASP_asap, always picks the setup for a particular machine that gives the greatest marginal improvement in the objective function among all candidates. The purpose of the third part of the research is to statistically validate the relative effectiveness of our top six dispatch rules by comparing their performance on 30 real and randomly generated data sets. Using both GRASP and our ASAP discrete event simulation model, we have (1) identified the general order of dispatch rule performance, (2) investigated the impact of having setups installed on machines at time zero on rule performance, (3) determined the conditions under which restricting the maximum number of changeover affects the rule performance, and (4) studied the factors that might simultaneously affect rule performance with the help of a common random numbers experimental design. In the analysis, the first two objectives, weighted key device shortages and weighted throughput, are used to measure outcomes.Operations Research and Industrial Engineerin

Scheduling of job shop, make-to-order industries with recirculation and assembly: discrete versus continuous time models

This work studies the performance of two Mixed Integer Linear Programming (MILP) models to solve scheduling problems in a flexible job shop environment with recirculation and assembly using a due-date-based objective function. The models convey different approaches both in the modelling of time (discrete and continuous approaches) as well as in the assignment of jobs to machines. The comparison is carried out for a job shop system considered closer to the industrial reality than the classical job shop problem of a single machine per operation that has been extensively studied in the literature, with the mould making industry providing the motivatin

On the exact solution of the no-wait flow shop problem with due date constraints

Peer ReviewedThis paper deals with the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, the jobs should be completed before their respective due dates; due date constraints are dealt with as hard constraints. The considered performance criterion is makespan. The problem is strongly NP-hard. This paper develops a number of distinct mathematical models for the problem based on different decision variables. Namely, a mixed integer programming model, two quadratic mixed integer programming models, and two constraint programming models are developed. Moreover, a novel graph representation is developed for the problem. This new modeling technique facilitates the investigation of some of the important characteristics of the problem; this results in a number of propositions to rule out a large number of infeasible solutions from the set of all possible permutations. Afterward, the new graph representation and the resulting propositions are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the mathematical models and to compare them with the developed exact algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models

Scheduling aircraft landings - the static case

This is the publisher version of the article, obtained from the link below.In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a plane and the landing of all successive planes are respected. We present a mixed-integer zero–one formulation of the problem for the single runway case and extend it to the multiple runway case. We strengthen the linear programming relaxations of these formulations by introducing additional constraints. Throughout, we discuss how our formulations can be used to model a number of issues (choice of objective function, precedence restrictions, restricting the number of landings in a given time period, runway workload balancing) commonly encountered in practice. The problem is solved optimally using linear programming-based tree search. We also present an effective heuristic algorithm for the problem. Computational results for both the heuristic and the optimal algorithm are presented for a number of test problems involving up to 50 planes and four runways.J.E.Beasley. would like to acknowledge the financial support of the Commonwealth Scientific and Industrial Research Organization, Australia

Robust Fluid Processing Networks

Fluid models provide a tractable and useful approach in approximating multiclass processing networks. However, they ignore the inherent stochasticity in arrival and service processes. To address this shortcoming, we develop a robust fluid approach to the control of processing networks. We provide insights into the mathematical structure, modeling power, tractability, and performance of the resulting model. Specifically, we show that the robust fluid model preserves the computational tractability of the classical fluid problem and retains its original structure. From the robust fluid model, we derive a (scheduling) policy that regulates how fluid from various classes is processed at the servers of the network. We present simulation results to compare the performance of our policies to several commonly used traditional methods. The results demonstrate that our robust fluid policies are near-optimal (when the optimal can be computed) and outperform policies obtained directly from the fluid model and heuristic alternatives (when it is computationally intractable to compute the optimal).National Science Foundation (U.S.) (Grant CNS-1239021)National Science Foundation (U.S.) (Grant IIS-1237022)United States. Army Research Office (Grant W911NF-11-1-0227)United States. Army Research Office (Grant W911NF-12-1-0390)United States. Office of Naval Research (Grant N00014-10-1-0952

Study on quantum-inspired optimization approaches for flow shop scheduling problems

制度:新 ; 報告番号:甲3741号 ; 学位の種類:博士(工学) ; 授与年月日:2012/9/10 ; 早大学位記番号:新6112Waseda Universit