Machine Scheduling with Resource Dependent Processing Times

We consider several parallel machine scheduling settings with the objective to minimize the schedule makespan. The most general of these settings is unrelated parallel machine scheduling. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the usage of a scarce renewable resource. A given amount of that resource, e.g. workers, can be distributed over the jobs in process at any time, and the more of that resource is allocated to a job, the smaller is its processing time. This model generalizes classical machine scheduling problems, adding a time-resource tradeoff. It is also a natural variant of a generalized assignment problem studied previously by Shmoys and Tardos. On the basis of integer programming formulations for relaxations of the respective problems, we use LP rounding techniques to allocate resources to jobs, and to assign jobs to machines. Combined with Graham''s list scheduling, we thus prove the existence of constant factor approximation algorithms. Our performance guarantee is 6.83 for the most general case of unrelated parallel machine scheduling. We improve this bound for two special cases, namely to 5.83 whenever the jobs are assigned to machines beforehand, and to (5+e), e>0, whenever the processing times do not depend on the machine. Moreover, we discuss tightness of the relaxations, and derive inapproximability results.operations research and management science;

Scheduling Parallel Jobs with Linear Speedup

We consider a scheduling problem where a set of jobs is distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g., personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3+e)-approximation algorithm for that problem, for any e>0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve in general. We also briefly discuss variants of the problem and derive lower bounds.operations research and management science;

A Minimum-Cost Flow Model for Workload Optimization on Cloud Infrastructure

Recent technology advancements in the areas of compute, storage and networking, along with the increased demand for organizations to cut costs while remaining responsive to increasing service demands have led to the growth in the adoption of cloud computing services. Cloud services provide the promise of improved agility, resiliency, scalability and a lowered Total Cost of Ownership (TCO). This research introduces a framework for minimizing cost and maximizing resource utilization by using an Integer Linear Programming (ILP) approach to optimize the assignment of workloads to servers on Amazon Web Services (AWS) cloud infrastructure. The model is based on the classical minimum-cost flow model, known as the assignment model.Comment: 2017 IEEE 10th International Conference on Cloud Computin

The energy scheduling problem: Industrial case-study and constraint propagation techniques

This paper deals with production scheduling involving energy constraints, typically electrical energy. We start by an industrial case-study for which we propose a two-step integer/constraint programming method. From the industrial problem we derive a generic problem,the Energy Scheduling Problem (EnSP). We propose an extension of specific resource constraint propagation techniques to efficiently prune the search space for EnSP solving. We also present a branching scheme to solve the problem via tree search.Finally,computational results are provided

Scheduling in the manufacture of evaporative air conditioners

The MISG examined the problem of scheduling production of air conditioners at Seeley International. Seeley's objective was to meet their demand in a more cost-effective way. Two models are proposed to achieve this objective. A long term master production schedule with a yearly planning horizon was formulated to give Seeley a broad based schedule for planning production to meet forecast demands and production constraints. Output from this model is designed to provide the appropriate number of units of each product type or sub-assembly item to be produced in the following week. This output is then designed to be the input to a more detailed short term model for scheduling production at the machine level. The short term model is formulated to handle a mixture of both finished products and sub-assemblies. The objective of the short term model is to minimise total production time to free up the use of resources in order to allow for external orders. Directions for further work are discussed