Hybrid Methods for Resource Allocation and Scheduling Problems in Deterministic and Stochastic Environments

This work presents exact, hybrid algorithms for mixed resource Allocation and Scheduling problems; in general terms, those consist into assigning over time finite capacity resources to a set of precedence connected activities. The proposed methods have broad applicability, but are mainly motivated by applications in the field of Embedded System Design. In particular, high-performance embedded computing recently witnessed the shift from single CPU platforms with application-specific accelerators to programmable Multi Processor Systems-on-Chip (MPSoCs). Those allow higher flexibility, real time performance and low energy consumption, but the programmer must be able to effectively exploit the platform parallelism. This raises interest in the development of algorithmic techniques to be embedded in CAD tools; in particular, given a specific application and platform, the objective if to perform optimal allocation of hardware resources and to compute an execution schedule. On this regard, since embedded systems tend to run the same set of applications for their entire lifetime, off-line, exact optimization approaches are particularly appealing. Quite surprisingly, the use of exact algorithms has not been well investigated so far; this is in part motivated by the complexity of integrated allocation and scheduling, setting tough challenges for ``pure'' combinatorial methods. The use of hybrid CP/OR approaches presents the opportunity to exploit mutual advantages of different methods, while compensating for their weaknesses. In this work, we consider in first instance an Allocation and Scheduling problem over the Cell BE processor by Sony, IBM and Toshiba; we propose three different solution methods, leveraging decomposition, cut generation and heuristic guided search. Next, we face Allocation and Scheduling of so-called Conditional Task Graphs, explicitly accounting for branches with outcome not known at design time; we extend the CP scheduling framework to effectively deal with the introduced stochastic elements. Finally, we address Allocation and Scheduling with uncertain, bounded execution times, via conflict based tree search; we introduce a simple and flexible time model to take into account duration variability and provide an efficient conflict detection method. The proposed approaches achieve good results on practical size problem, thus demonstrating the use of exact approaches for system design is feasible. Furthermore, the developed techniques bring significant contributions to combinatorial optimization methods.

Determining departure times in dynamic and stochastic maritime routing and scheduling problem

In maritime transportation, decisions are made in a dynamic setting where many aspects of the future are uncertain. However, most academic literature on maritime transportation considers static and deterministic routing and scheduling problems. This work addresses a gap in the literature on dynamic and stochastic maritime routing and scheduling problems, by focusing on the scheduling of departure times. Five simple strategies for setting departure times are considered, as well as a more advanced strategy which involves solving a mixed integer mathematical programming problem. The latter strategy is significantly better than the other methods, while adding only a small computational effort.

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^

A framework for the response time analysis of fixed-priority tasks with stochastic inter-arrival times

Real-time scheduling usually considers worst-case values for the parameters of task (or message stream) sets, in order to provide safe schedulability tests for hard real-time systems. However, worst-case conditions introduce a level of pessimism that is often inadequate for a certain class of (soft) real-time systems. In this paper we provide an approach for computing the stochastic response time of tasks where tasks have inter-arrival times described by discrete probabilistic distribution functions, instead of minimum inter-arrival (MIT) values.

Reinforcement Learning Approaches to Power System Scheduling

One major component of power system operation is generation scheduling. The objective of the work is to develop efficient control strategies to the power scheduling problems through Reinforcement Learning approaches. The three important active power scheduling problems are Unit Commitment, Economic Dispatch and Automatic Generation Control. Numerical solution methods proposed for solution of power scheduling are insufficient in handling large and complex systems. Soft Computing methods like Simulated Annealing, Evolutionary Programming etc., are efficient in handling complex cost functions, but find limitation in handling stochastic data existing in a practical system. Also the learning steps are to be repeated for each load demand which increases the computation time.Reinforcement Learning (RL) is a method of learning through interactions with environment. The main advantage of this approach is it does not require a precise mathematical formulation. It can learn either by interacting with the environment or interacting with a simulation model. Several optimization and control problems have been solved through Reinforcement Learning approach. The application of Reinforcement Learning in the field of Power system has been a few. The objective is to introduce and extend Reinforcement Learning approaches for the active power scheduling problems in an implementable manner. The main objectives can be enumerated as:(i) Evolve Reinforcement Learning based solutions to the Unit Commitment Problem.(ii) Find suitable solution strategies through Reinforcement Learning approach for Economic Dispatch. (iii) Extend the Reinforcement Learning solution to Automatic Generation Control with a different perspective. (iv) Check the suitability of the scheduling solutions to one of the existing power systems.First part of the thesis is concerned with the Reinforcement Learning approach to Unit Commitment problem. Unit Commitment Problem is formulated as a multi stage decision process. Q learning solution is developed to obtain the optimwn commitment schedule. Method of state aggregation is used to formulate an efficient solution considering the minimwn up time I down time constraints. The performance of the algorithms are evaluated for different systems and compared with other stochastic methods like Genetic Algorithm.Second stage of the work is concerned with solving Economic Dispatch problem. A simple and straight forward decision making strategy is first proposed in the Learning Automata algorithm. Then to solve the scheduling task of systems with large number of generating units, the problem is formulated as a multi stage decision making task. The solution obtained is extended in order to incorporate the transmission losses in the system. To make the Reinforcement Learning solution more efficient and to handle continuous state space, a fimction approximation strategy is proposed. The performance of the developed algorithms are tested for several standard test cases. Proposed method is compared with other recent methods like Partition Approach Algorithm, Simulated Annealing etc.As the final step of implementing the active power control loops in power system, Automatic Generation Control is also taken into consideration.Reinforcement Learning has already been applied to solve Automatic Generation Control loop. The RL solution is extended to take up the approach of common frequency for all the interconnected areas, more similar to practical systems. Performance of the RL controller is also compared with that of the conventional integral controller.In order to prove the suitability of the proposed methods to practical systems, second plant ofNeyveli Thennal Power Station (NTPS IT) is taken for case study. The perfonnance of the Reinforcement Learning solution is found to be better than the other existing methods, which provide the promising step towards RL based control schemes for practical power industry.Reinforcement Learning is applied to solve the scheduling problems in the power industry and found to give satisfactory perfonnance. Proposed solution provides a scope for getting more profit as the economic schedule is obtained instantaneously. Since Reinforcement Learning method can take the stochastic cost data obtained time to time from a plant, it gives an implementable method. As a further step, with suitable methods to interface with on line data, economic scheduling can be achieved instantaneously in a generation control center. Also power scheduling of systems with different sources such as hydro, thermal etc. can be looked into and Reinforcement Learning solutions can be achieved.

Weekly Self-Scheduling, Forward Contracting, and Offering Strategy for a Producer

Within a weekly market horizon, this paper considers a power producer that sells its energy both in the pool and through weekly forward contracts. The paper provides a methodology that allows the producer to derive the self-scheduling of its production units, to select weekly forward contracts, and to obtain the offering strategy for Monday's pool. The proposed technique is based on stochastic programming and allows the producer to maximize its expected profit while controlling the risk of profit variability. A comprehensive case study is used to illustrate the characteristics of the proposed methodology. Appropriate conclusions are finally drawn.

Integrated pulp and paper mill planning and scheduling

This article describes a real-world production planning and scheduling problem occurring at an integrated pulp and paper mill (P&P) which manufactures paper for cardboard out of produced pulp. During the cooking of wood chips in the digester, two by-products are produced: the pulp itself (virgin fibers) and the waste stream known as black liquor. The former is then mixed with recycled fibers and processed in a paper machine. Here, due to significant sequence-dependent setups in paper type changeovers, sizing and sequencing of lots have to be made simultaneously in order to efficiently use capacity. The latter is converted into electrical energy using a set of evaporators, recovery boilers and counter-pressure turbines. The planning challenge is then to synchronize the material flow as it moves through the pulp and paper mills, and energy plant, maximizing customer demand (as backlogging is allowed), and minimizing operation costs. Due to the intensive capital feature of P&P, the output of the digester must be maximized. As the production bottleneck is not fixed, to tackle this problem we propose a new model that integrates the critical production units associated to the pulp and paper mills, and energy plant for the first time. Simple stochastic mixed integer programming based local search heuristics are developed to obtain good feasible solutions for the problem. The benefits of integrating the three stages are discussed. The proposed approaches are tested on real-world data. Our work may help P&P companies to increase their competitiveness and reactiveness in dealing with demand pattern oscillations. (C) 2012 Elsevier Ltd. All rights reserved.

Performance of Scheduling Policies in Adversarial Networks with Non-synchronized Clocks

In this paper we generalize the Continuous Adversarial Queuing Theory (CAQT) model (Blesa et al. in MFCS, Lecture Notes in Computer Science, vol. 3618, pp. 144–155, 2005) by considering the possibility that the router clocks in the network are not synchronized. We name the new model Non Synchronized CAQT (NSCAQT). Clearly, this new extension to the model only affects those scheduling policies that use some form of timing. In a first approach we consider the case in which although not synchronized, all clocks run at the same speed, maintaining constant differences. In this case we show that all universally stable policies in CAQT that use the injection time and the remaining path to schedule packets remain universally stable. These policies include, for instance, Shortest in System (SIS) and Longest in System (LIS). Then, we study the case in which clock differences can vary over time, but the maximum difference is bounded. In this model we show the universal stability of two families of policies related to SIS and LIS respectively (the priority of a packet in these policies depends on the arrival time and a function of the path traversed). The bounds we obtain in this case depend on the maximum difference between clocks. This is a necessary requirement, since we also show that LIS is not universally stable in systems without bounded clock difference. We then present a new policy that we call Longest in Queues (LIQ), which gives priority to the packet that has been waiting the longest in edge queues. This policy is universally stable and, if clocks maintain constant differences, the bounds we prove do not depend on them. To finish, we provide with simulation results that compare the behavior of some of these policies in a network with stochastic injection of packets.

Performance of Scheduling Policies in Adversarial Networks with Non-synchronized Clocks

In this paper we generalize the Continuous Adversarial Queuing Theory (CAQT) model (Blesa et al. in MFCS, Lecture Notes in Computer Science, vol. 3618, pp. 144–155, 2005) by considering the possibility that the router clocks in the network are not synchronized. We name the new model Non Synchronized CAQT (NSCAQT). Clearly, this new extension to the model only affects those scheduling policies that use some form of timing. In a first approach we consider the case in which although not synchronized, all clocks run at the same speed, maintaining constant differences. In this case we show that all universally stable policies in CAQT that use the injection time and the remaining path to schedule packets remain universally stable. These policies include, for instance, Shortest in System (SIS) and Longest in System (LIS). Then, we study the case in which clock differences can vary over time, but the maximum difference is bounded. In this model we show the universal stability of two families of policies related to SIS and LIS respectively (the priority of a packet in these policies depends on the arrival time and a function of the path traversed). The bounds we obtain in this case depend on the maximum difference between clocks. This is a necessary requirement, since we also show that LIS is not universally stable in systems without bounded clock difference. We then present a new policy that we call Longest in Queues (LIQ), which gives priority to the packet that has been waiting the longest in edge queues. This policy is universally stable and, if clocks maintain constant differences, the bounds we prove do not depend on them. To finish, we provide with simulation results that compare the behavior of some of these policies in a network with stochastic injection of packets.

Optimization methods for the operating room management under uncertainty: stochastic programming vs. decomposition approach

The operating theatres are the engine of the hospitals; proper management of the operating rooms and its staff represents a great challenge for managers and its results impact directly in the budget of the hospital. This work presents a MILP model for the efficient schedule of multiple surgeries in Operating Rooms (ORs) during a working day. This model considers multiple surgeons and ORs and different types of surgeries. Stochastic strategies are also implemented for taking into account the uncertain in surgery durations (pre-incision, incision, post-incision times). In addition, a heuristic-based methods and a MILP decomposition approach is proposed for solving large-scale ORs scheduling problems in computational efficient way. All these computer-aided strategies has been implemented in AIMMS, as an advanced modeling and optimization software, developing a user friendly solution tool for the operating room management under uncertainty.

On Managing Stochastic Decentralized Projects

Thesis (Ph.D.)--University of Washington, 2016-06

Design of a genetic algorithm for bi-objective flow shop scheduling problems with re-entrant jobs

This paper presents a simulated genetic algorithm (GA) model of scheduling the flow shop problem with re-entrant jobs. The objective of this research is to minimize the weighted tardiness and makespan. The proposed model considers that the jobs with non-identical due dates are processed on the machines in the same order. Furthermore, the re-entrant jobs are stochastic as only some jobs are required to reenter to the flow shop. The tardiness weight is adjusted once the jobs reenter to the shop. The performance of the proposed GA model is verified by a number of numerical experiments where the data come from the case company. The results show the proposed method has a higher order satisfaction rate than the current industrial practices.

Coordinated Scheduling of Wind-Thermal Gencos in Day-Ahead Markets

This paper presents a stochastic mixed-integer linear programming approach for solving the self-scheduling problem of a price-taker thermal and wind power producer taking part in a pool-based electricity market. Uncertainty on electricity price and wind power is considered through a set of scenarios. Thermal units are modeled by variable costs, start-up costs and technical operating constraints, such as: ramp up/down limits and minimum up/down time limits. An efficient mixed-integer linear program is presented to develop the offering strategies of the coordinated production of thermal and wind energy generation, aiming to maximize the expected profit. A case study with data from the Iberian Electricity Market is presented and results are discussed to show the effectiveness of the proposed approach.