How Unsplittable-Flow-Covering helps Scheduling with Job-Dependent Cost Functions

Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time $(1+\epsilon)$-approximation algorithm that yields an $(e+\epsilon)$-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with \emph{optimal }cost at $1+\epsilon$ speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most $\log n$ many classes. This algorithm allows the jobs even to have up to $\log n$ many distinct release dates.Comment: 2 pages, 1 figur

Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine

We consider a scheduling problem in which the jobs are generated by two agents and have time-dependent proportional-linear deteriorating processing times. The two agents compete for a common single batching machine to process their jobs, and each agent has its own criterion to optimize. The jobs may have identical or different release dates. The batching machine can process several jobs simultaneously as a batch and the processing time of a batch is equal to the longest of the job processing times in the batch. The problem is to determine a schedule for processing the jobs such that the objective of one agent is minimized, while the objective of the other agent is maintained under a fixed value. For the unbounded model, we consider various combinations of regular objectives on the basis of the compatibility of the two agents. For the bounded model, we consider two different objectives for incompatible and compatible agents: minimizing the makespan of one agent subject to an upper bound on the makespan of the other agent and minimizing the number of tardy jobs of one agent subject to an upper bound on the number of tardy jobs of the other agent. We analyze the computational complexity of various problems by either demonstrating that the problem is intractable or providing an efficient exact algorithm for the problem. Moreover, for certain problems that are shown to be intractable, we provide efficient algorithms for certain special cases

The complexity of generating robust resource-constrained baseline schedules.

Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that will change little when variations in the input parameters arise. Robustness can also be achieved by making the schedule makespan insensitive to variability. In this paper, we describe models for the generation of stable and insensitive baseline schedules for resource-constrained scheduling problems and present results on their complexity status. We start from a project scheduling viewpoint and derive results on machine scheduling sub-problems.Complexity; Information; Product scheduling; Robustness; sensitivity; stability;

Project scheduling under undertainty – survey and research potentials.

The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.Management; Project management; Robustness; Scheduling; Stability;

A common framework and taxonomy for multicriteria scheduling problems with Interfering and competing Jobs: Multi-agent scheduling problems

Most classical scheduling research assumes that the objectives sought are common to all jobs to be scheduled. However, many real-life applications can be modeled by considering different sets of jobs, each one with its own objective(s), and an increasing number of papers addressing these problems has appeared over the last few years. Since so far the area lacks a uni ed view, the studied problems have received different names (such as interfering jobs, multi-agent scheduling, mixed-criteria, etc), some authors do not seem to be aware of important contributions in related problems, and solution procedures are often developed without taking into account existing ones. Therefore, the topic is in need of a common framework that allows for a systematic recollection of existing contributions, as well as a clear de nition of the main research avenues. In this paper we review multicriteria scheduling problems involving two or more sets of jobs and propose an uni ed framework providing a common de nition, name and notation for these problems. Moreover, we systematically review and classify the existing contributions in terms of the complexity of the problems and the proposed solution procedures, discuss the main advances, and point out future research lines in the topic

Order acceptance and scheduling in a single-machine environment: exact and heuristic algorithms.

In this paper, we develop exact and heuristic algorithms for the order acceptance and scheduling problem in a single-machine environment. We consider the case where a pool consisting of firm planned orders as well as potential orders is available from which an over-demanded company can select. The capacity available for processing the accepted orders is limited and orders are characterized by known processing times, delivery dates, revenues and the weight representing a penalty per unit-time delay beyond the delivery date promised to the customer. We prove the non-approximability of the problem and give two linear formulations that we solve with CPLEX. We devise two exact branch-and-bound procedures able to solve problem instances of practical dimensions. For the solution of large instances, we propose six heuristics. We provide a comparison and comments on the efficiency and quality of the results obtained using both the exact and heuristic algorithms, including the solution of the linear formulations using CPLEX.Order acceptance; Scheduling; Single machine; Branch-and-bound; Heuristics; Firm planned orders;

Cyclic scheduling of perishable products in parallel machine with release dates, due dates and deadlines

This paper deals with a realistic cyclic scheduling problem in the food industry environment in which parallel machines are considered to process perishable jobs with given release dates, due dates and deadlines. Jobs are subject to post-production shelf life limitation and must be delivered to retailers during the corresponding time window bounded by due dates and deadlines. Both early and tardy jobs are penalized by partial weighted earliness/tardiness functions and the overall problem is to provide a cyclic schedule of minimum cost. A mixed integer programming model is proposed and a heuristic solution beside an iterated greedy algorithm is developed to generate good and feasible solutions for the problem. The proposed MIP, heuristic and iterated greedy produce a series of solutions covering a wide range of cases from slow optimal solutions to quick and approximated schedules.Ruben Ruiz is partially supported by the Spanish Ministry of Economy and Competitiveness, under the project "RESULT - Realistic Extended Scheduling Using Light Techniques" with reference DPI2012-36243-C02-01 co-financed by the European Union and FEDER funds and by the Universitat Politecnica de Valencia, for the project MRPIV with reference PAID/2012/202.Shirvani, N.; Ruiz García, R.; Shadrokh, S. (2014). Cyclic scheduling of perishable products in parallel machine with release dates, due dates and deadlines. International Journal of Production Economics. 156:1-12. https://doi.org/10.1016/j.ijpe.2014.04.013S11215

Order Acceptance and Scheduling: A Taxonomy and Review

Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area

Minimizing the sum of flow times with batching and delivery in a supply chain

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The aim of this thesis is to study one of the classical scheduling objectives that is of minimizing the sum of flow times, in the context of a supply chain network. We consider the situation that a supplier schedules a set of jobs for delivery in batches to several manufacturers, who in tum have to schedule and deliver jobs in batches to several customers. The individual problem from the viewpoint of supplier and manufacturers will be considered separately. The decision problem faced by the supplier is that of minimizing the sum of flow time and delivery cost of a set of jobs to be processed on a single machine for delivery in batches to manufacturers. The problem from the viewpoint of manufacturer is similar to the supplier's problem and the only difference is that the scheduling, batching and delivery decisions made by the supplier define a release date for each job, before which the manufacturer cannot start the processing of that job. Also a combined problem in the light of cooperation between the supplier and manufacturer will be considered. The objective of the combined problem is to find the best scheduling, batching, and delivery decisions that benefit the entire system including the supplier and manufacturer. Structural properties of each problem are investigated and used to devise a branch and bound solution scheme. Computational experience shows significant improvements over existing algorithms and also shows that cooperation between a supplier and a manufacturer reduces the total system cost of up to 12.35%, while theoretically the reduction of up to 20% can be achieved for special cases

Quantitative Methods For Select Problems In Facility Location And Facility Logistics

This dissertation presented three logistics problems. The first problem is a parallel machine scheduling problems that considers multiple unique characteristics including release dates, due dates, limited machine availability and job splitting. The objective of is to minimize the total amount of time required to complete work. A mixed integer programming model is presented and a heuristic is developed for solving the problem. The second problem extends the first parallel scheduling problem to include two additional practical considerations. The first is a setup time that occurs when warehouse staff change from one type of task to another. The second is a fixed time window for employee breaks. A simulated annealing (SA) heuristic is developed for its solution. The last problem studied in this dissertation is a new facility location problem variant with application in disaster relief with both verified data and unverified user-generated data are available for consideration during decision making. A total of three decision strategies that can be used by an emergency manager faced with a POD location decision for which both verified and unverified data are available are proposed: Consider Only Verified, Consider All and Consider Minimax Regret. The strategies differ according to how the uncertain user-generated data is incorporated in the planning process. A computational study to compare the performance of the three decision strategies across a range of plausible disaster scenarios is presented