On Index Policies for Stochastic Minsum Scheduling

Minimizing the sum of completion times when scheduling jobs on identical parallel machines is a fundamental scheduling problem. Unlike the well-understood deterministic variant, it is a major open problem how to handle stochastic processing times. We show for the prominent class of index policies that no such policy can achieve a distribution-independent approximation factor. This strong lower bound holds even for simple instances with deterministic and two-point distributed jobs. For such instances, we give an -approximative list scheduling policy

Stochastic scheduling on unrelated machines

Two important characteristics encountered in many real-world scheduling problems are heterogeneous machines/processors and a certain degree of uncertainty about the actual sizes of jobs. The first characteristic entails machine dependent processing times of jobs and is captured by the classical unrelated machine scheduling model.The second characteristic is adequately addressed by stochastic processing times of jobs as they are studied in classical stochastic scheduling models. While there is an extensive but separate literature for the two scheduling models, we study for the first time a combined model that takes both characteristics into account simultaneously. Here, the processing time of job $j$ on machine $i$ is governed by random variable $P_{ij}$, and its actual realization becomes known only upon job completion. With $w_j$ being the given weight of job $j$, we study the classical objective to minimize the expected total weighted completion time $E[\sum_j w_jC_j]$, where $C_j$ is the completion time of job $j$. By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee $(3+\Delta)/2+\epsilon$. Here, $\epsilon>0$ is arbitrarily small, and $\Delta$ is an upper bound on the squared coefficient of variation of the processing times. We show that the dependence of the performance guarantee on $\Delta$ is tight, as we obtain a $\Delta/2$ lower bound for the type of policies that we use. When jobs also have individual release dates $r_{ij}$, our bound is $(2+\Delta)+\epsilon$. Via $\Delta=0$, currently best known bounds for deterministic scheduling are contained as a special case

Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work, and depend linearly on an upper bound on the squared coefficient of variation of the jobs' processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 7.216, respectively. As to the technical contribution, the paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.Comment: Preliminary version appeared in IPCO 201

Regional forestry sector modelling of options for industrial forest plantations in Indonesia

Regional resource planning and decision-making for industrial forest plantation development increasingly involves participation by members of the public. Motivation to maximise or minimise the degree to which groups with various interests can satisfy their individual objectives should recognise outcomes arrived at in a consensus decision-making environment. In this study, a planning framework is devised and adopted, which describes a regional planning system prepared in order to assist in the design and evaluation of strategic industrial forest plantation development in Indonesia. The central component of this planning system is interactive Multi-Objective Decision Making (MODM) modelling with linkages between optimisation and simulation models. The framework of the whole planning system demonstrates the capability and feasibility of resolving important and conflicting objectives through discussion and communicative decision processes that can be reinforced with modelling sensitivity outputs. In other words, a methodology is developed that allows strategic options for plantation planning to be analysed interactively. The MODM models here are MINMAX and MINSUM goal programming formulations. This model has various features that characterise industrial forest plantation development planning, including physical production, social, economic, environmental, and location aspects. This formulation, moreover, has several advantages such as capturing the essence of the multi-objective decision making problem, encompassing the entire range of feasible tradeoffs among all objectives through parametric programming in order to derive forestland allocations optimally, as well as serving important implementable and practical interests. A minimum economic size (MES) spreadsheet-based model is run to determine profitable plantation sizes by using financial criteria such as IRR and NPV. The MES model outputs are then incorporated within MODM models. A major part of the research reported here was to develop a way of transferring data between simulation and LP models directly through file transfers, and transferring LP derived solutions directly back to the simulation model. This linkage has several advantages: for example, theoretically optimal LP solutions are usually unrealistic in practical or implementational terms because of administrative, social, environmental and other similar problems facing forest management; whereas simulation allows one to explore the effects of deviations from "optimal" LP solutions, and to simulate both in more detail and in broader aggregations of things such as age classes, log types and locations. If measures, e.g. wood and financial flows, are unsatisfactory, some constraints are modified and formed for the relevant LP model utilising, for example, the future log assortment flow consequences and the tradeoffs among them. The automated linkage between optimisation and simulation models provides easy data and solution transfers so that decision makers and stakeholders may gain detailed insights before any consensus decisions need to be made. A geographic information system (GIS) is utilised to enhance pictorially the preferred solutions, information, and appearance. The whole planning system is demonstrated and tested in an indicative case study. The results display the major advantages of consistency, clarity and simplicity of the approach to regional forestland allocation. The framework and results at this stage are only preliminary, because some data are still incomplete and unrefined. This study is, therefore, an initial description and explanation of methodology and an indication of the nature of desirable results rather than a firm policy recommendation pertaining to the case study area. In principle, the framework could also become multi-temporal by creating each variable in a time-dependent fashion. The planning system developed has the ability to incorporate social, financial, environmental, and technical variables in a comprehensive participatory development process. The ultimate value of the quantitative information represented in this framework (or methodology) through a background case study analysis is its ability to facilitate policy formulation to satisfy decision-makers and stakeholders when making informed choices in fundamental management decisions

A Deep Reinforcement Learning - based Hyperheuristic for the Flexible Traveling Repairman Problem with Drones

Masteroppgave i informatikkINF399MAMN-PROGMAMN-IN

Time Minimization and Online Synchronization for Multi-agent Systems under Collaborative Temporal Tasks

Multi-agent systems can be extremely efficient when solving a team-wide task in a concurrent manner. However, without proper synchronization, the correctness of the combined behavior is hard to guarantee, such as to follow a specific ordering of sub-tasks or to perform a simultaneous collaboration. This work addresses the minimum-time task planning problem for multi-agent systems under complex global tasks stated as Linear Temporal Logic (LTL) formulas. These tasks include the temporal and spatial requirements on both independent local actions and direct sub-team collaborations. The proposed solution is an anytime algorithm that combines the partial-ordering analysis of the underlying task automaton for task decomposition, and the branch and bound (BnB) search method for task assignment. Analyses of its soundness, completeness and optimality as the minimal completion time are provided. It is also shown that a feasible and near-optimal solution is quickly reached while the search continues within the time budget. Furthermore, to handle fluctuations in task duration and agent failures during online execution, an adaptation algorithm is proposed to synchronize execution status and re-assign unfinished subtasks dynamically to maintain correctness and optimality. Both algorithms are validated rigorously over large-scale systems via numerical simulations and hardware experiments, against several strong baselines.Comment: 17 pages, 14 figure