Workforce management is a complex problem involving the optimisation of the makespan and travel distance required for a team of operators to complete a set of jobs, using a set of instruments. A crucial challenge in workforce management is accommodating changes at execution time so that explanations are provided to all stakeholders involved. Here, we show that, by understanding workforce management as abstract argumentation in an industrial application, we can accommodate change and obtain faithful explanations. We show, with a user study, that our tool and explanations lead to faster and more accurate problem solving than conventional manual approaches.

We consider the single-machine time-dependent scheduling problem with linearly deteriorating jobs arriving over time. Each job i is associated with a release time ri and a processing time pi(si)=αi+βisi, where αi,βi>0 are parameters and si is the job's start time. In this setting, the approximability of both single-machine minimum makespan and total completion time problems remains open. We develop new bounds and approximation results for the special case of the problems with uniform deterioration, i.e. βi=β, for each i. The main contribution is a O(1+1/β)-approximation algorithm for the makespan problem and a O(1+1/β2) approximation algorithm for the total completion time problem. Further, we propose greedy constant-factor approximation algorithms for instances with β=O(1/n) and β=Ω(n), where n is the number of jobs. Our analysis is based on an approach for comparing computed and optimal schedules via bounding pseudomatchings.

Decision trees usefully represent sparse, high-dimensional, and noisy data. Having learned a function from these data, we may want to thereafter integrate the function into a larger decision-making problem, for example, for picking the best chemical process catalyst. We study a large-scale, industrially relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pretrained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models or they may wish to optimize a discrete model that accurately represents a data set. We develop several heuristic methods to find feasible solutions and an exact branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on a concrete mixture design instance and a chemical catalysis industrial instance.

Mathematical optimization offers highly-effective tools for finding solutions for problems with well-defined goals, notably scheduling. However, optimization solvers are often unexplainable black boxes whose solutions are inaccessible to users and which users cannot interact with. We define a novel paradigm using argumentation to empower the interaction between optimization solvers and users, supported by tractable explanations which certify or refute solutions. A solution can be from a solver or of interest to a user (in the context of ‘what-if’ scenarios). Specifically, we define argumentative and natural language explanations for why a schedule is (not) feasible, (not) efficient or (not) satisfying fixed user decisions, based on models of the fundamental makespan scheduling problem in terms of abstract argumentation frameworks (AFs). We define three types of AFs, whose stable extensions are in one-to-one correspondence with schedules that are feasible, efficient and satisfying fixed decisions, respectively. We extract the argumentative explanations from these AFs and the natural language explanations from the argumentative ones.

We consider the problem of scheduling a set of jobs, each one specified by its release date, its deadline and its processing volume, on a set of heterogeneous speed-scalable processors, where the energy-consumption rate is processor-dependent. Our objective is to minimize the total energy consumption when both the preemption and the migration of jobs are allowed. We propose a new algorithm based on a compact linear programming formulation. Our method approaches the value of the optimal solution within any desired accuracy for a large set of continuous power functions. Furthermore, we develop a faster combinatorial algorithm based on flows for standard power functions and jobs whose density is lower bounded by a small constant. Finally, we extend and analyze the AVerage Rate (AVR) online algorithm in the heterogeneous setting.

We consider the problem of scheduling a set of jobs, under precedence constraints, on a set of speed scalable parallel processors. The goal is to minimize the makespan of the schedule, i.e. the time at which the last job finishes its execution, without violating a given energy budget. This situation finds applications in computer devices whose lifetime depends on a limited battery efficiency. In order to handle the energy consumption we use the energy model introduced in [Yao et al., FOCS'95], which captures the intuitive idea that the higher is the processor's speed the higher is the energy consumption. We propose a (2-1/m)-approximation algorithm improving the best known poly-log(m)-approximation algorithm for the problem [Pruhs et al., TOCS 2008], where m is the number of the processors. We also extend the simple idea used for the above problem, in order to propose a generalized framework that finds applications to other scheduling problems in the speed scaling setting.

We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed-scalable processors in a fully heterogeneous setting. For both the preemptive-non-migratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-non-migratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.