The lockmaster's problem.

Inland waterways form a natural network that is an existing, congestion free infrastructure with capacity for more traffic.Transportation of goods by ship is widely promoted as it is a reliable, efficient and environmental friendly way of transport. A bottleneck for transportation over water are the locks that manage the water level. The lockmaster's problem concerns the optimal strategy for operating such a lock. In the lockmaster's problem we are given a lock, a set of ships coming from downstream that want to go upstream, and another set of ships coming from upstream that want to go downstream. We are given the arrival times of the ships and a constant lockage time; the goal is to minimize total waiting time of the ships. In this paper a dynamic programming algorithm (DP) is proposed that solves the lockmaster's problem in polynomial time. We extend this DP to different generalizations that consider weights, water usage, capacity, and (a fixed number of) multiple chambers. Finally, we prove that the problem becomes strongly NP-hard when the number of chambers is part of the input.Lock scheduling; Batch scheduling; Dynamic programming; Complexity;

Compatibility graphs in scheduling on batch processing machines

We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are modeled by an undirected graph $G$, in which compatible jobs are represented by adjacent vertices. We show that several subproblems are polynomial. We propose some exact polynomial algorithms to solve these subproblems. To solve the general case, we propose a mixed-integer linear programming (MILP) formulation alongside with heuristic approaches. Furthermore, computational experiments are carried out to measure the performance of the proposed methods.Comment: 25 pages, 11 figure

Scheduling of Batch Processors in Semiconductor Manufacturing – A Review

In this paper a review on scheduling of batch processors (SBP) in semiconductor manufacturing (SM) is presented. It classifies SBP in SM into 12 groups. The suggested classification scheme organizes the SBP in SM literature, summarizes the current research results for different problem types. The classification results are presented based on various distributions and various methodologies applied for SBP in SM are briefly highlighted. A comprehensive list of references is presented. It is hoped that, this review will provide a source for other researchers/readers interested in SBP in SM research and help simulate further interest.Singapore-MIT Alliance (SMA

Scheduling hybrid flowshop with parallel batching machines and compatibilities.

International audienceThis paper considers a two-stage hybrid flowshop problem in which the first stage contains several identical discrete machines, and the second stage contains several identical batching machines. Each discrete machine can process no more than one task at time, and each batching machine can process several tasks simultaneously in a batch with the additional feature that the tasks of the same batch have to be compatible. A compatibility relation is defined between each pair of tasks, so that an undirected compatibility graph is obtained which turns out to be an interval graph. The batch processing time is equal to the maximal processing time of the tasks in this batch, and all tasks of the same batch start and finish together. The goal is to make batching and sequencing decisions in order to minimize the makespan. Since the problem is NP-hard, we develop several heuristics along with their worst cases analysis. We also consider the case in which tasks have the same processing time on the first stage, for which a polynomial time approximation scheme (PTAS) algorithm is presented

Scheduling Bidirectional Traffic on a Path

We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively

Heuristics for scheduling a two-stage hybrid flow shop with parallel batching machines: application at a hospital sterilisation plant

The model of a two-stage hybrid (or flexible) flow shop, with sequence-independent uniform setup times, parallel batching machines and parallel batches has been analysed with the purpose of reducing the number of tardy jobs and the makespan in a sterilisation plant. Jobs are processed in parallel batches by multiple identical parallel machines. Manual operations preceding each of the two stages have been dealt with as machine setup with standardised times and are sequence-independent. A mixed-integer model is proposed. Two heuristics have been tested on real benchmark data from an existing sterilisation plant: constrained size of parallel batches and fixed time slots. Computation experiments performed on combinations of machines and operator numbers suggest balancing the two stages by assigning operators proportionally to the setup time requirements

Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

Scheduling Hybrid Flow Lines of Aerospace Composite Manufacturing Systems

Composite manufacturing is a vital part of aerospace manufacturing systems. Applying effective scheduling within these systems can cut the costs in aerospace companies significantly. These systems can be characterized as two-stage Hybrid Flow Shops (HFS) with identical, non-identical and unrelated parallel discrete-processing machines in the first stage and non-identical parallel batch-processing machines in the second stage. The first stage is normally the lay-up process in which the carbon fiber sheets are stacked on the molds (tools). Then, the parts are batched based on the compatibility of their cure recipe before going to the second stage into the autoclave for curing. Autoclaves require enormous capital investment and maximizing their utilization is of utmost importance. In this thesis, a Mixed Integer Linear Programming (MILP) model is developed to maximize the utilization of the resources in the second stage of this HFS. CPLEX, with an underlying branch and bound algorithm, is used to solve the model. The results show the high level of flexibility and computational efficiency of the proposed model when applied to small and medium-size problems. However, due to the NP-hardness of the problem, the MILP model fails to solve large problems (i.e. problems with more than 120 jobs as input) in reasonable CPU times. To solve the larger instances of the problem, a novel heuristic method along with a Genetic Algorithm (GA) are developed. The heuristic algorithm is designed based on a careful observation of the behavior of the MILP model for different problem sets. Moreover, it is enhanced by adding a number of proper dispatching rules. As its output, this heuristic algorithm generates eight initial feasible solutions which are then used as the initial population of the proposed GA. The GA improves the initial solutions obtained from the aforementioned heuristic through its stochastic iterations until it reaches the satisfactory near-optimal solutions. A novel crossover operator is introduced in this GA which is unique to the HFS of aerospace composite manufacturing systems. The proposed GA is proven to be very efficient when applied to large-size problems with up to 300 jobs. The results show the high quality of the solutions achieved by the GA when compared to the optimal solutions which are obtained from the MILP model. A real case study undertaken at one of the leading companies in the Canadian aerospace industry is used for the purpose of data experiments and analysis

Planning and Scheduling Optimization

Although planning and scheduling optimization have been explored in the literature for many years now, it still remains a hot topic in the current scientific research. The changing market trends, globalization, technical and technological progress, and sustainability considerations make it necessary to deal with new optimization challenges in modern manufacturing, engineering, and healthcare systems. This book provides an overview of the recent advances in different areas connected with operations research models and other applications of intelligent computing techniques used for planning and scheduling optimization. The wide range of theoretical and practical research findings reported in this book confirms that the planning and scheduling problem is a complex issue that is present in different industrial sectors and organizations and opens promising and dynamic perspectives of research and development