Single machine scheduling with job-dependent machine deterioration

We consider the single machine scheduling problem with job-dependent machine deterioration. In the problem, we are given a single machine with an initial non-negative maintenance level, and a set of jobs each with a non-preemptive processing time and a machine deterioration. Such a machine deterioration quantifies the decrement in the machine maintenance level after processing the job. To avoid machine breakdown, one should guarantee a non-negative maintenance level at any time point; and whenever necessary, a maintenance activity must be allocated for restoring the machine maintenance level. The goal of the problem is to schedule the jobs and the maintenance activities such that the total completion time of jobs is minimized. There are two variants of maintenance activities: in the partial maintenance case each activity can be allocated to increase the machine maintenance level to any level not exceeding the maximum; in the full maintenance case every activity must be allocated to increase the machine maintenance level to the maximum. In a recent work, the problem in the full maintenance case has been proven NP-hard; several special cases of the problem in the partial maintenance case were shown solvable in polynomial time, but the complexity of the general problem is left open. In this paper we first prove that the problem in the partial maintenance case is NP-hard, thus settling the open problem; we then design a $2$-approximation algorithm.Comment: 15 page

Tactical fixed job scheduling with spread-time constraints

We address the tactical fixed job scheduling problem with spread-time constraints. In such a problem, there are a fixed number of classes of machines and a fixed number of groups of jobs. Jobs of the same group can only be processed by machines of a given set of classes. All jobs have their fixed start and end times. Each machine is associated with a cost according to its machine class. Machines have spread-time constraints, with which each machine is only available for L consecutive time units from the start time of the earliest job assigned to it. The objective is to minimize the total cost of the machines used to process all the jobs. For this strongly NP-hard problem, we develop a branch-and-price algorithm, which solves instances with up to 300 jobs, as compared with CPLEX, which cannot solve instances of 100 jobs. We further investigate the influence of machine flexibility by computational experiments. Our results show that limited machine flexibility is sufficient in most situations

Modeling and solving the periodic maintenance problem.

We study the problem of scheduling maintenance services. Given is a set of m machines and integral cost-coefficients a(i) and b(i) for each machine i (1Branch-and-price; Column generation; Costs; Linear programming; Model; Models; Optimal; Scheduling; Structure; Studies; Time;

Overcommitment in Cloud Services -- Bin packing with Chance Constraints

This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the provider's risk tolerance

State-of-the-art on research and applications of machine learning in the building life cycle

Fueled by big data, powerful and affordable computing resources, and advanced algorithms, machine learning has been explored and applied to buildings research for the past decades and has demonstrated its potential to enhance building performance. This study systematically surveyed how machine learning has been applied at different stages of building life cycle. By conducting a literature search on the Web of Knowledge platform, we found 9579 papers in this field and selected 153 papers for an in-depth review. The number of published papers is increasing year by year, with a focus on building design, operation, and control. However, no study was found using machine learning in building commissioning. There are successful pilot studies on fault detection and diagnosis of HVAC equipment and systems, load prediction, energy baseline estimate, load shape clustering, occupancy prediction, and learning occupant behaviors and energy use patterns. None of the existing studies were adopted broadly by the building industry, due to common challenges including (1) lack of large scale labeled data to train and validate the model, (2) lack of model transferability, which limits a model trained with one data-rich building to be used in another building with limited data, (3) lack of strong justification of costs and benefits of deploying machine learning, and (4) the performance might not be reliable and robust for the stated goals, as the method might work for some buildings but could not be generalized to others. Findings from the study can inform future machine learning research to improve occupant comfort, energy efficiency, demand flexibility, and resilience of buildings, as well as to inspire young researchers in the field to explore multidisciplinary approaches that integrate building science, computing science, data science, and social science