Subanatarajan Subbiah

Scheduling of Multi-Product Batch Plants based upon Timed Automata Models

This paper reports on the successful application of a recently proposed method for solving scheduling problems by reachability analysis of timed automata. The jobs and the resources are modeled by a set of synchronized timed automata, and the scheduling problem is solved by a cost-optimal symbolic reachability analysis. The analysis searches for a path of states and state transitions from an initial state to a terminal state in which all jobs have been finished. The appeal of the approach is the intuitive and modular graphical modeling, and an efficient solution, as is illustrated here for a well-known case study from the chemical industry.

Multi-product batch scheduling with intermediate due dates using priced timed automata models

In this contribution, we discuss an extension of the earlier work on scheduling using reachability analysis of timed automata (TA) models, specifically addressing the problem of tardiness minimization. In the TA-based approach the resources, recipes and additional timing constraints are modeled independently as sets of priced timed automata. The sets of individual automata are synchronized by means of synchronization labels and are composed by parallel composition to form a global automaton. The global automaton has an initial location where no operations have been started and at least one target location where all operations that are required to produce the demanded quantities of end-products within the specified due dates have been finished. A cost-optimal symbolic reachability analysis is performed on the composed automaton to derive schedules with the objective of minimizing tardiness. The model formulation is extended to include release dates of the raw materials and due dates of the production orders. The meeting of due dates is modeled by causing additional costs (e.g. penalties for late delivery and storage costs for early production). The modeling approach and the performance of the approach are tested for two different case studies and the results are compared with that of a MILP formulation solved using the standard solver CPLEX. The numerical experiments demonstrate, that the TA-based approach is competitive compared to standard commercial solvers and good feasible solutions are obtained with considerably reduced computational effort.

Short-Term Scheduling of Multi-Product Batch Plants with Sequence-Dependent Changeovers Using Timed Automata Models

Abstract In this contribution we propose an approach to model and solve scheduling problems with sequence-dependent changeover procedures using timed automata (TA). The processing units and the recipes are modeled as sets of interacting TA in a modular fashion. The setup and changeover procedures are modeled explicitly as operations in the recipe. The problem modeled as TA is then solved to derive schedules by performing a cost-optimal reachability analysis starting from an initial location where no recipe operation is started to a target location where all required demands are met. The proposed approach is applied to two case studies and the results are presented. The comparison of the experimental results from the TA-based approach with established MILP techniques shows that the proposed approach is efficient in the sense that optimal schedules are found within a limited computation time that are comparable to or better than those obtained with the MILP formulations and the solvers considered.

Efficient Scheduling of Batch Plants Using Reachability Tree Search for Timed Automata with Lower Bound Computations

Abstract In this paper we discuss an extension of a recent approach to solve batch scheduling problems using reachability analysis for timed automata (TA) by embedding lower bound computations in the reachability algorithm. We propose an extension of the embedded LP-formulation to handle scheduling problems with NIS policy and an improved minimum remaining processing time (MRPT) procedure to compute the lower bounds. The proposed bounding procedures are tested on typical batch scheduling problems. The comparative study shows that the MRPT-based bounding procedure is efficient and increases the overall performance significantly in comparison to the LP-based bounding procedure.

Timed Automata Models for Batch Scheduling with Sequence-Dependent Changeovers

Abstract The standard approach to solve scheduling problems in the process industries is to use mathematical model formulations such as MI(N)LP. Recently, an alternative approach that has gained attention is to use reachability analysis for timed automata (TA) to solve such problems. In this contribution, we discuss an application of the TA based framework to model and solve batch scheduling problems with sequence-dependent changeovers. The resources and the jobs are modeled as sets of interacting TA in a modular fashion and are composed to form a global automaton which represents the complete model of the scheduling problem. The solutions for the scheduling problem are computed by performing a cost-optimal reachability analysis in the global automaton.

Modeling and Solving Batch Scheduling Problems with Various Storage Policies and Operational Policies using Timed Automata

Abstract In this contribution we present the conceptual ideas on modeling deterministic batch scheduling problems with various storage policies and operational policies using timed automata (TA) and on solving them using reachability analysis for TA. We propose a new reduction technique to improve the efficiency of the search algorithm for scheduling problems with non-intermediate storage policy. The performance of the proposed modeling approach and the reduction technique is evaluated by investigating it on benchmark instances from OR literature and on typical batch scheduling problems. The comparative study shows that the proposed modeling approach handles the crucial aspects of the storage policies and operational policies in straightforward way and the new reduction technique increases the overall performance of the solution algorithm.

Timed automata based scheduling for a miniature pipeless plant with mobile robots

In this contribution we present a conceptual idea on modeling a scheduling problem in a miniature pipeless plant with mobile robots by timed automata (TA) and solving it using reachability analysis. Two TA-based tools, TAOpt and UPPAAL, are evaluated on the miniature pipeless plant, and on job shop benchmark instances from the OR literature. The comparative study shows that the proposed modeling approach handles the crucial constraints of the miniature pipeless plant in an effective and straightforward way.

Effective Batch Scheduling with Sequence-dependent Changeovers Using Reachability Analysis of Timed Automata Combined with Lower Bound Computations

Abstract In this contribution we discuss an extension of a recent approach to solve batch scheduling problems using reachability analysis for timed automata (TA) with embedded lower bound computations. We propose two bounding procedures embedded in the reachability algorithm to handle scheduling problems with sequence-dependent changeovers: (i) a MILP formulation (originally proposed by Manne 1960) extended with additional constraints to model setup and changeover operations and (ii) an improved minimum remaining processing time (MRPT) procedure. The efficiency of the proposed bounding procedures is evaluated on job shop problems with sequence-dependent changeovers. The comparative study shows that the MRPT-based bounding procedure is efficient and increases the overall performance significantly in comparison to the MILP-based bounding procedure.

Batch scheduling with intermediate due dates using timed automata models

Abstract In the process industries, the problem of scheduling multi-product batch plants to satisfy the demand for various end-products within specified due dates occurs frequently. In contrast to the state-of-the art approach of using mathematical model formulations to solve such scheduling problems, an alternative approach is to use reachability analysis for timed automata (TA). In this paper, we discuss an extension of our earlier work on scheduling using TA models where the problem of makespan minimization was addressed. We extend the formulation to the meeting of due dates, modelled as causing additional costs (e.g. penalties for late delivery and storage costs for early production). The proposed solution by reachability analysis of priced timed automata is tested on a case study to demonstrate its successful application.

Optimal Management of Shuttle Robots in a High-Rise Warehouse Using Timed Automata Models

Abstract In warehousing systems, the speed of the removal and distribution of goods often represents a bottleneck as it limits the achievable throughput and, thus, the efficiency of the complete warehousing system. Consequently, an optimal management of the distribution of goods can lead to large efficiency and financial gains. In this contribution, it is shown for an accurate model of an industrial real-world high-rise warehouse (HRW), which is connected to a polymer production plant, that rigorous optimization of the distribution procedure can lead to a large efficiency increase in comparison to standard techniques. To this end, the distribution problem is modelled using timed automata (TA) in which the jobs arrive one after the other and are not known in advance. The TA-based approach, which was originally developed for standard scheduling problems, is extended to a reactive moving window approach that employs a cost-optimal reachability algorithm to compute optimal plans for the goods distribution. We show that compared to a typical first-come first-served dispatching rule, this approach can lead to throughput gains of more than 40%.