Mathematical Optimization of the Tactical Allocation of Machining Resources in Aerospace Industry

In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers (which includes, measures of quality and production lead-times) and to maintain control of the tied-up working capital. We introduce a new multi-item, multi-level capacitated planning model with a medium-to-long term planning horizon. The model can be used by most companies having functional workshops where costly and/or time- and resource demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimizes the maximum excess resource loading above a given loading threshold, while incurring as low qualification costs as possible. In Paper I (Bi-objective optimization of the tactical allocation of jobtypes to machines), we propose a new bi-objective mathematical optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. Another contribution is a modified version of the bi-directional $\epsilon$ -constraint method especially tailored for our problem. We perform numerical tests on industrial test cases generated for our class of problem which indicates computational superiority of our method over conventional solution approaches. In Paper II (Robust optimization of a bi-objective tactical resource allocation problem with uncertain qualification costs), we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. We also suggest a solution approach for identifying all the relevant robust efficient (RE) solutions. Our proposed approach is significantly faster than an existing approach for robust bi-objective optimization problems

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

Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops

In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers and to maintain control of the tied-up working capital. We introduce new multi-item, multi-level capacitated resource allocation models with a medium--to--long--term planning horizon. The model refers to functional workshops where costly and/or time- and resource-demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimize the maximum excess resource loading above a given loading threshold while incurring as low qualification costs as possible and minimizing the inventory.In Paper I, we propose a new bi-objective mixed-integer (linear) optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. In Paper II, we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. In Paper III, we extend the TRAP with an inventory of semi-finished as well as finished parts, resulting in a tri-objective mixed-integer (linear) programming model. We create a criterion space partitioning approach that enables solving sub-problems simultaneously. In Paper IV, using our knowledge from our previous work we embarked upon a task to generalize our findings to develop an approach for any discrete tri-objective optimization problem. The focus is on identifying a representative set of non-dominated points with a pre-defined desired coverage gap

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

Algorithms for Scheduling Problems

This edited book presents new results in the area of algorithm development for different types of scheduling problems. In eleven chapters, algorithms for single machine problems, flow-shop and job-shop scheduling problems (including their hybrid (flexible) variants), the resource-constrained project scheduling problem, scheduling problems in complex manufacturing systems and supply chains, and workflow scheduling problems are given. The chapters address such subjects as insertion heuristics for energy-efficient scheduling, the re-scheduling of train traffic in real time, control algorithms for short-term scheduling in manufacturing systems, bi-objective optimization of tortilla production, scheduling problems with uncertain (interval) processing times, workflow scheduling for digital signal processor (DSP) clusters, and many more

Scheduling Models with Additional Features: Synchronization, Pliability and Resiliency

In this thesis we study three new extensions of scheduling models with both practical and theoretical relevance, namely synchronization, pliability and resiliency. Synchronization has previously been studied for flow shop scheduling and we now apply the concept to open shop models for the first time. Here, as opposed to the traditional models, operations that are processed together all have to be started at the same time. Operations that are completed are not removed from the machines until the longest operation in their group is finished. Pliability is a new approach to model flexibility in flow shops and open shops. In scheduling with pliability, parts of the processing load of the jobs can be re-distributed between the machines in order to achieve better schedules. This is applicable, for example, if the machines represent cross-trained workers. Resiliency is a new measure for the quality of a given solution if the input data are uncertain. A resilient solution remains better than some given bound, even if the original input data are changed. The more we can perturb the input data without the solution losing too much quality, the more resilient the solution is. We also consider the assignment problem, as it is the traditional combinatorial optimization problem underlying many scheduling problems. Particularly, we study a version of the assignment problem with a special cost structure derived from the synchronous open shop model and obtain new structural and complexity results. Furthermore we study resiliency for the assignment problem. The main focus of this thesis is the study of structural properties, algorithm development and complexity. For synchronous open shop we show that for a fixed number of machines the makespan can be minimized in polynomial time. All other traditional scheduling objectives are at least as hard to optimize as in the traditional open shop model. Starting out research in pliability we focus on the most general case of the model as well as two relevant special cases. We deliver a fairly complete complexity study for all three versions of the model. Finally, for resiliency, we investigate two different questions: `how to compute the resiliency of a given solution?' and `how to find a most resilient solution?'. We focus on the assignment problem and single machine scheduling to minimize the total sum of completion times and present a number of positive results for both questions. The main goal is to make a case that the concept deserves further study

Energy aware hybrid flow shop scheduling

Only if humanity acts quickly and resolutely can we limit global warming' conclude more than 25,000 academics with the statement of SCIENTISTS FOR FUTURE. The concern about global warming and the extinction of species has steadily increased in recent years