Application of submodular optimization to single machine scheduling with controllable processing times subject to release dates and deadlines

In this paper, we study a scheduling problem on a single machine, provided that the jobs have individual release dates and deadlines, and the processing times are controllable. The objective is to find a feasible schedule that minimizes the total cost of reducing the processing times. We reformulate the problem in terms of maximizing a linear function over a submodular polyhedron intersected with a box. For the latter problem of submodular optimization, we develop a recursive decomposition algorithm and apply it to solving the single machine scheduling problem to achieve the best possible running time

Handling Scheduling Problems with Controllable Parameters by Methods of Submodular Optimization

In this paper, we demonstrate how scheduling problems with controllable processing times can be reformulated as maximization linear programming problems over a submodular polyhedron intersected with a box. We explain a decomposition algorithm for solving the latter problem and discuss its implications for the relevant problems of preemptive scheduling on a single machine and parallel machines

Data-driven Algorithm for Scheduling with Total Tardiness

In this paper, we investigate the use of deep learning for solving a classical NP-Hard single machine scheduling problem where the criterion is to minimize the total tardiness. Instead of designing an end-to-end machine learning model, we utilize well known decomposition of the problem and we enhance it with a data-driven approach. We have designed a regressor containing a deep neural network that learns and predicts the criterion of a given set of jobs. The network acts as a polynomial-time estimator of the criterion that is used in a single-pass scheduling algorithm based on Lawler's decomposition theorem. Essentially, the regressor guides the algorithm to select the best position for each job. The experimental results show that our data-driven approach can efficiently generalize information from the training phase to significantly larger instances (up to 350 jobs) where it achieves an optimality gap of about 0.5%, which is four times less than the gap of the state-of-the-art NBR heuristic

Data-driven algorithm for single machine scheduling problem

V této práci představuje metodu pro řešení problému Single machine total tardiness problem. Analyzovali jsme užití Deep learning metod, pro Single machine total tardiness problem. Využili jsme rozděl a panuj algoritmu a odvodili z něj data-driven přístup. Vytvořili jsme hlubokou neuronovou síť se schopností predikovat hodnotu kritéria problému. Tato neuronová síť jedná jako optimální orákulum s polynomiální dobou běhu. Orákulum řídí rozděl a panuj metodu v každém kroku. Náš data-driven přístup překonává state-of-the-art heuristiku ve kvalitě řešení.In this thesis, we present a method for solving a single machine total tardiness problem a classical NP-hard scheduling problem. We investigate the use of deep learning method for this problem. We utilize known decomposition method from operation research, and we derive data-driven method. We introduce a deep neural network that predicts the objective value and acts as a polynomial-time oracle. Oracle drive decomposition method in each step. Our data-driven method outperforms the state-of-the-art heuristic in terms of optimality gap

A decomposition based algorithm for flexible flow shop scheduling with machine breakdown

Research on flow shop scheduling generally ignores uncertainties in real-world production because of the inherent difficulties of the problem. Scheduling problems with stochastic machine breakdown are difficult to solve optimally by a single approach. This paper considers makespan optimization of a flexible flow shop (FFS) scheduling problem with machine breakdown. It proposes a novel decomposition based approach (DBA) to decompose a problem into several sub-problems which can be solved more easily, while the neighbouring K-means clustering algorithm is employed to group the machines of an FFS into a few clusters. A back propagation network (BPN) is then adopted to assign either the shortest processing time (SPT) or the genetic algorithm (GA) to each cluster to solve the sub-problems. If two neighbouring clusters are allocated with the same approach, they are subsequently merged. After machine grouping and approach assignment, an overall schedule is generated by integrating the solutions to the sub-problems. Computation results reveal that the proposed approach is superior to SPT and GA alone for FFS scheduling with machine breakdown. © 2009 IEEE.published_or_final_versionThe IEEE International Conference on Computational Intelligence for Measurement Systems and Applications (CIMSA 2009), Hong Kong, 11-13 May 2009. In Proceedings of CIMSA, 2009, p. 134-13

A decomposition-based approach to flexible flow shop scheduling under stochastic setup times

Research on production scheduling under uncertainty has recently received much attention. This paper presents a novel decomposition-based approach (DBA) to flexible flow shop (FFS) scheduling under stochastic setup times. In comparison with traditional methods using a single approach, the proposed DBA combines and takes advantage of two different approaches, namely the Genetic Algorithm (GA) and the Shortest Processing Time Algorithm (SPT), to deal with uncertainty. A neighbouring K-means clustering algorithm is developed to firstly decompose an FFS into an appropriate number of machine clusters. A back propagation network (BPN) is then adopted to assign either GA or SPT to generate a sub-schedule for each machine cluster. Finally, an overall schedule is generated by integrating the sub-schedules of the machine clusters. Computation results reveal that the DBA is superior to SPT and GA alone for FFS scheduling under stochastic setup times. © 2010 IEEE.published_or_final_versionThe 5th IEEE International Conference on Intelligent Systems (IS 2010), London, UK., 7-9 July 2010. In Proceedings of the 5th IS, 2010, p. 55-6

Decomposition algorithm for the single machine scheduling polytope

Given an $n$-vector $p$ of processing times of jobs, the single machine scheduling polytope $C$ arises as the convex hull of completion times of jobs when these are scheduled without idle time on a single machine. Given a point (x\ud in C), Carathéodory's theorem implies that $x$ can be written as convex combination of at most $n$ vertices of $C$. We show that this convex combination can be computed from $x$ and $p$ in time O(n2), which is linear in the naive encoding of the output. We obtain this result using essentially two ingredients. First, we build on the fact that the scheduling polytope is a zonotope. Therefore, all of its faces are centrally symmetric. Second, instead of $C$, we consider the polytope $Q$ of half times and its barycentric subdivision. We show that the subpolytopes of this barycentric subdivison of $Q$ have a simple, linear description. The final decomposition algorithm is in fact an implementation of an algorithm proposed by Grötschel, Lovász, and Schrijver applied to one of these subpolytopes

The Integration of Process Planning and Shop Floor Scheduling in Small Batch Part Manufacturing

In this paper we explore possibilities to cut manufacturing leadtimes and to improve delivery performance in a small batch part manufacturing shop by integrating process planning and shop floor scheduling. Using a set of initial process plans (one for each order in the shop), we exploit a resource decomposition procedure to determine schedules to determine schedules which minimize the maximum lateness, given these process plans. If the resulting schedule is still unsatisfactory, a critical path analysis is performed to select jobs as candidates for alternative process plans. In this way, an excellent due date performance can be achieved, with a minimum of process planning and scheduling effort

Flexible flow shop scheduling with stochastic processing times: A decomposition-based approach

Flexible flow shop scheduling problems are NP-hard and tend to become more complex when stochastic uncertainties are taken into consideration. Although some methods have been developed to address such problems, they remain inherently difficult to solve by any single approach. This paper presents a novel decomposition-based approach (DBA), which combines both the shortest processing time (SPT) and the genetic algorithm (GA), to minimizing the makespan of a flexible flow shop (FFS) with stochastic processing times. In the proposed DBA, a neighbouring K-means clustering algorithm is developed to firstly group the machines of an FFS into an appropriate number of machine clusters, based on their stochastic nature. Two optimal back propagation networks (BPN), corresponding to the scenarios of simultaneous and non-simultaneous job arrivals, are then selectively adopted to assign either SPT or GA to each machine cluster for sub-schedule generation. Finally, an overall schedule is generated by integrating the sub-schedules of machine clusters. Computation results show that the DBA outperforms SPT and GA alone for FFS scheduling with stochastic processing times. © 2012 Elsevier Ltd. All rights reserved.postprin