Geometric Approach and Taboo Search for Scheduling Flexible Manufacturing Systems

This paper addresses the scheduling and deadlock avoidance of a class of automated manufacturing systems. In such systems, a set of jobs is to be performed on a set of resources and each job requires several operations- . An operation may require several types of resources with several units of each type. Further, upon the completion of an operation, its related resources cannot be released until resources needed for the next operation become available. One important characteristic of such systems is the possibility of deadlock. The scheduling problem deals with the allocation of resources such that jobs are completed within a minimal makespan and deadlocks are avoided. We extend the classical geometric approach to solve the two­job case of our model. A greedy algorithm based on this result and the taboo search heuristic is then developed for the general case. Numerical results show that the proposed algorithm is fast and provides good schedules

Scheduling of Flexible Manufacturing Systems using Intelligent heuristic search algorithm (IHSA*)

The complete scheduling of FMS includes two independent processes: sequencing of jobs and scheduling those prioritized jobs. In a flow shop or a Progressive type FMS, scheduling problem involves sequencing of ‘n’ jobs on ‘m’ machines with minimum makespan. Intelligent heuristic search algorithm (IHSA*) is used in this paper, which ensure to find an optimal solution for flow-shop problem involving arbitrary number of machines and jobs provided the job sequence is same on each machine. The initial version of IHSA* is based on the A* algorithm. The final version of IHSA* is the modification of the initial IHSA*. There are three modifications: first modification concerned with the selection of an admissible heuristic function, second modification concerned with the procedure which determine heuristic estimate as the search progresses and the third modification concerned with the searching of multiple optimal solution, if they exist. Both version of the IHSA* are presented in this paper with an example which illustrates the use of both

Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Manufacturing plays a significant role in promoting economic development, production, exports, and job creation, which ultimately contribute to improving the quality of life. The presence of manufacturing defects is, however, inevitable leading to products being discarded, i.e. scrapped. In some cases, defective products can be repaired through rework. Scrap and rework cause a longer completion time, which can contribute to the order being shipped late. In addition, complex manufacturing scheduling becomes much more challenging when the above uncertainties are present. Motivated by the presence of uncertainties as well as combinatorial complexity, this paper addresses the challenge illustrated through a case study of stochastic job-shop scheduling problems arising within low-volume high-variety manufacturing. To ensure on-time delivery, high-quality solutions are required, and near-optimal solutions must be obtained within strict time constraints to ensure smooth operations on the job-shop floor. To efficiently solve the stochastic job-shop scheduling (JSS) problem, a recently-developed Surrogate "Level-Based" Lagrangian Relaxation is used to reduce computational effort while efficiently exploiting the geometric convergence potential inherent to Polyak's step-sizing formula thereby leading to fast convergence. Numerical testing demonstrates that the new method is more than two orders of magnitude faster as compared to commercial solvers

A new neighborhood and tabu search for the blocking job shop

The Blocking Job Shop is a version of the job shop scheduling problem with no intermediate buffers, where a job has to wait on a machine until being processed on the next machine. We study a generalization of this problem which takes into account transfer operations between machines and sequence-dependent setup times. After formulating the problem in a generalized disjunctive graph, we develop a neighborhood for local search. In contrast to the classical job shop, there is no easy mechanism for generating feasible neighbor solutions. We establish two structural properties of the underlying disjunctive graph, the concept of closures and a key result on short cycles, which enable us to construct feasible neighbors by exchanging critical arcs together with some other arcs. Based on this neighborhood, we devise a tabu search algorithm and report on extensive computational experience, showing that our solutions improve most of the benchmark results found in the literature

Delivery pattern planning in retailing with transport and warehouse workload balancing

Goods from warehouses must be scheduled in advance, prepared, routed, and delivered to shops. At least three systems directly interact within such a process: warehouse workforce scheduling, delivery scheduling, and routing system. Ideally, the whole problem with the preceding inventory management (restocking) would be solved in one optimization pass. In order to make the problem simpler, we first decompose the total problem by isolating the delivery scheduling. Then we connect the optimization model to the rest of the system by workload balancing goal that is a surrogate of coordination and criterion for the system robustness. This paper presents the practical application of top-down discrete optimization that streamlines operations and enables better reactivity to changes in circumstances. We search for repetitive weekly delivery patterns that balance the daily warehouse and transportation utilization in the absence of capacity constraints. Delivery patterns are optimized for the quality criteria regarding specific store-warehouse pair types, with a special focus on fresh food delivery that aims at reducing inventory write-offs due to aging. The previous setup included semimanual scheduling based on templates, historical prototypes, and domain knowledge. We have found that the system augmented with the new automated delivery scheduling system brings an improvement of 3% in the performance measure as well as speed in adjusting to the changes, such was the case with changes in policies during COVID-19 lockdowns

Algoritam planiranja operacija "flow shop" u cilju smanjivanja vremena izvršenja kod problema n-poslova i m-strojeva

In multi stage job problems, simple priority dispatching rules such as shortest processing time (SPT) and earliest due date (EDD) can be used to obtain solutions of minimum total processing time, but may not sometimes give sequences as expected that are close to optimal. The Johnson\u27s algorithm is especially popular among analytical approaches that are used for solving n-jobs, 2-machines sequence problem. In this paper the presented algorithm is based on converting an m-machine problem to a 2-machine problem. Based on testing and comparison with other relevant methods, the proposed algorithm is offered as a competitive alternative for practical application when solving n-jobs and m-machines problems.U problemima posla s više faza, mogu se koristiti jednostavna prioritetna dispečerska pravila kao što su najkraće vrijeme obrade (PT) i najraniji datum dospijeća (EDD) za dobivanje rješenja najmanjega ukupnog vremena obrade. Međutim, ona ponekad ne daju slijed za koji se očekuje da je blizu optimalnom. Johnsonov algoritam je posebno popularan među analitičkim pristupima koji se koriste za rješavanje problema slijeda n-poslova i 2-stroja. Algoritam prikazan u ovom radu se temelji na pretvaranju problema m-strojeva u problem 2-stroja. Na temelju ispitivanja i usporedbe s drugim relevantnim metodama, predloženi algoritam se nudi kao konkurentna alternativa za praktičnu primjenu pri rješavanju problema n-poslova i m-strojeva

MPM Job-shop under Availability Constraints

International audienc

MPM Job-shop under Availability Constraints

A large part of scheduling literature assumes that machines are available all the time. In this paper, the MPM Job-shop scheduling problem, where the machine maintenance has to be performed within certain time intervals inducing machine unavailability, is studied. Two approaches to solve the problem are proposed. The first is a two-phase approach where the assignment and the sequencing are solved separately. The second is an integrated approach based on the exact resolution of the 2-job problem using the geometric approach

A new innovative cooling law for simulated annealing algorithms

The present paper proposes an original and innovative cooling law in the field of Simulated Annealing (SA) algorithms. Particularly, such a law is based on the evolution of different initial seeds on which the algorithm works in parallel. The efficiency control of the new proposal, executed on problems of different kind, shows that the convergence quickness by using such a new cooling law is considerably greater than that obtained by traditional laws. Furthermore, it is shown that the effectiveness of the SA algorithm arising from the proposed cooling law is independent of the problem type. This last feature reduces the number of parameters to be initially fixed, so simplifying the preliminary calibration process necessary to optimize the algorithm efficiency

An Empirical Performance Comparison of Meta-heuristic Algorithms for School Bus Routing Problem

School Bus Routing Problem is an NP-hard Combinatorial Optimization problem. Thus, mega-heuristic algorithms are widely used to solve instances of the School Bus Routing Problem with large data. In this work we present a model of the School Bus Routing Problem and empirical performances comparison between three meta-heuristic algorithms named Simulated Annealing (SA), Tabu Search (TS) and Ant-Colony Optimization (ACO) on the problem. We have analyzed their performances in terms of solution quality. The results show that all three algorithms have the ability to solve the School Bus Routing Problem. In addition, computational results show that TS performed best when execution time is not restricted while ACO had relative good performance when time is restricted but poor when the time is unrestricted.Keywords:  School Bus Routing Problem; Combinatorial Optimization; Meta-heuristic Algorithm