Min-Max Regret Scheduling To Minimize the Total Weight of Late Jobs With Interval Uncertainty

We study the single machine scheduling problem with the objective to minimize the total weight of late jobs. It is assumed that the processing times of jobs are not exactly known at the time when a complete schedule must be dispatched. Instead, only interval bounds for these parameters are given. In contrast to the stochastic optimization approach, we consider the problem of finding a robust schedule, which minimizes the maximum regret of a solution. Heuristic algorithm based on mixed-integer linear programming is presented and examined through computational experiments

Database query optimisation based on measures of regret

The query optimiser in a database management system (DBMS) is responsible for �nding a good order in which to execute the operators in a given query. However, in practice the query optimiser does not usually guarantee to �nd the best plan. This is often due to the non-availability of precise statistical data or inaccurate assumptions made by the optimiser. In this thesis we propose a robust approach to logical query optimisation that takes into account the unreliability in database statistics during the optimisation process. In particular, we study the ordering problem for selection operators and for join operators, where selectivities are modelled as intervals rather than exact values. As a measure of optimality, we use a concept from decision theory called minmax regret optimisation (MRO). When using interval selectivities, the decision problem for selection operator ordering turns out to be NP-hard. After investigating properties of the problem and identifying special cases which can be solved in polynomial time, we develop a novel heuristic for solving the general selection ordering problem in polynomial time. Experimental evaluation of the heuristic using synthetic data, the Star Schema Benchmark and real-world data sets shows that it outperforms other heuristics (which take an optimistic, pessimistic or midpoint approach) and also produces plans whose regret is on average very close to optimal. The general join ordering problem is known to be NP-hard, even for exact selectivities. So, for interval selectivities, we restrict our investigation to sets of join operators which form a chain and to plans that correspond to left-deep join trees. We investigate properties of the problem and use these, along with ideas from the selection ordering heuristic and other algorithms in the literature, to develop a polynomial-time heuristic tailored for the join ordering problem. Experimental evaluation of the heuristic shows that, once again, it performs better than the optimistic, pessimistic and midpoint heuristics. In addition, the results show that the heuristic produces plans whose regret is on average even closer to the optimal than for selection ordering

Regret Models and Preprocessing Techniques for Combinatorial Optimization under Uncertainty

Ph.DDOCTOR OF PHILOSOPH

Database query optimisation based on measures of regret

The query optimiser in a database management system (DBMS) is responsible for �nding a good order in which to execute the operators in a given query. However, in practice the query optimiser does not usually guarantee to �nd the best plan. This is often due to the non-availability of precise statistical data or inaccurate assumptions made by the optimiser. In this thesis we propose a robust approach to logical query optimisation that takes into account the unreliability in database statistics during the optimisation process. In particular, we study the ordering problem for selection operators and for join operators, where selectivities are modelled as intervals rather than exact values. As a measure of optimality, we use a concept from decision theory called minmax regret optimisation (MRO). When using interval selectivities, the decision problem for selection operator ordering turns out to be NP-hard. After investigating properties of the problem and identifying special cases which can be solved in polynomial time, we develop a novel heuristic for solving the general selection ordering problem in polynomial time. Experimental evaluation of the heuristic using synthetic data, the Star Schema Benchmark and real-world data sets shows that it outperforms other heuristics (which take an optimistic, pessimistic or midpoint approach) and also produces plans whose regret is on average very close to optimal. The general join ordering problem is known to be NP-hard, even for exact selectivities. So, for interval selectivities, we restrict our investigation to sets of join operators which form a chain and to plans that correspond to left-deep join trees. We investigate properties of the problem and use these, along with ideas from the selection ordering heuristic and other algorithms in the literature, to develop a polynomial-time heuristic tailored for the join ordering problem. Experimental evaluation of the heuristic shows that, once again, it performs better than the optimistic, pessimistic and midpoint heuristics. In addition, the results show that the heuristic produces plans whose regret is on average even closer to the optimal than for selection ordering

Resource-constrained project scheduling for timely project completion with stochastic activity durations.

We investigate resource-constrained project scheduling with stochastic activity durations. Various objective functions related to timely project completion are examined, as well as the correlation between these objectives. We develop a GRASP-heuristic to produce high-quality solutions, using so-called descriptive sampling. The algorithm outperforms other existing algorithms for expected-makespan minimization. The distribution of the possible makespan realizations for a given scheduling policy is studied, and problem difficulty is explored as a function of problem parameters.GRASP; Project scheduling; Uncertainty;

Models and algorithms for deterministic and robust discrete time/cost trade-off problems

Ankara : The Department of Management, Bilkent University, 2008.Thesis (Ph.D.) -- Bilkent University, 2008.Includes bibliographical references leaves 136-145Projects are subject to various sources of uncertainties that often negatively impact activity durations and costs. Therefore, it is of crucial importance to develop effective approaches to generate robust project schedules that are less vulnerable to disruptions caused by uncontrollable factors. This dissertation concentrates on robust scheduling in project environments; specifically, we address the discrete time/cost trade-off problem (DTCTP). Firstly, Benders Decomposition based exact algorithms to solve the deadline and the budget versions of the deterministic DTCTP of realistic sizes are proposed. We have included several features to accelerate the convergence and solve large instances to optimality. Secondly, we incorporate uncertainty in activity costs. We formulate robust DTCTP using three alternative models. We develop exact and heuristic algorithms to solve the robust models in which uncertainty is modeled via interval costs. The main contribution is the incorporation of uncertainty into a practically relevant project scheduling problem and developing problem specific solution approaches. To the best of our knowledge, this research is the first application of robust optimization to DTCTP. Finally, we introduce some surrogate measures that aim at providing an accurate estimate of the schedule robustness. The pertinence of proposed measures is assessed through computational experiments. Using the insight revealed by the computational study, we propose a two-stage robust scheduling algorithm. Furthermore, we provide evidence that the proposed approach can be extended to solve a scheduling problem with tardiness penalties and earliness rewards.Hazır, ÖncüPh.D