Lower bounds for Smith's rule in stochastic machine scheduling

We consider the problem to minimize the weighted sum of completion times in nonpreemptive parallel machine scheduling. In a landmark paper from 1986, Kawaguchi and Kyan [5] showed that scheduling the jobs according to the WSPT rule -also known as Smith's rule- has a performance guarantee of ${1\over 2}(1+\sqrt{2}) \approx 1.207$. They also gave an instance to show that this bound is tight. We consider the stochastic variant of this problem in which the processing times are exponentially distributed random variables. We show,somehow counterintuitively, that the performance guarantee of the WSEPT rule, the stochastic analogue of WSPT, is not better than 1.229. This constitutes the first lower bound for WSEPT in this setting, and in particular, it shows that even with exponentially distributed processing times, stochastic scheduling has somewhat nastier worst-case examples than deterministic scheduling. In that respect, our analysis sheds new light on the fundamental differences between deterministic and stochastic scheduling

10071 Abstracts Collection -- Scheduling

From 14.02. to 19.02.2010, the Dagstuhl Seminar 10071 ``Scheduling \u27\u27 was held in Schloss Dagstuhl-Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

08071 Abstracts Collection -- Scheduling

From 10.02. to 15.02., the Dagstuhl Seminar 08071 ``Scheduling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Games and Mechanism Design in Machine Scheduling – An Introduction

In this paper, we survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents need to interact in order to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically in order to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical Optimization, Game Theory, and Economic Theory. The paper therefore briefly introduces the most important of the underlying concepts, and gives a selection of typical research questions and recent results, focussing on applications to machine scheduling problems. This includes the study of the so-called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.computer science applications;

Minimizing total inventory cost on a single machine in just-in-time manufacturing

The just-in-time concept decrees not to accept ordered goods before their due dates in order to avoid inventory cost. This bounces the inventory cost back to the manufacturer: products that are completed before their due dates have to be stored. Reducing this type of storage cost by preclusion of early completion conflicts with the traditional policy of keeping work-in-process inventories down. This paper addresses a single-machine scheduling problem with the objective of minimizing total inventory cost, comprising cost associated with work-in-process inventories and storage cost as a result of early completion. The cost components are measured by the sum of the job completion times and the sum of the job earlinesses. This problem differs from more traditional scheduling problems, since the insertion of machine idle time may reduce total cost. The search for an optimal schedule, however, can be limited to the set of job sequences, since for any sequence there is a clear-cut way to insert machine idle time in order to minimize total inventory cost. We apply branch-and-bound to identify an optimal schedule. We present five approaches for lower bound calculation, based upon relaxation of the objective function, of the state space, and upon Lagrangian relaxation. Key Words and Phrases: just-in-time manufacturing, inventory cost, work-in-process inventory, earliness, tardiness, machine idle time, branch-and-bound algorithm, Lagrangian relaxation

Order scheduling in dedicated and flexible machine environments

Order scheduling models are relatively new in the field of scheduling. Consider a facility with m parallel machines that can process k different products (job types). Each machine can process a given subset of different product types. There are n orders from n different clients. Each order requests specific quantities of the various different products that can be produced concurrently on their given subsets of machines; it may have a release date, a weight and a due date. Preemptions may be allowed. An order can not be shipped until the processing of all the products for the order has been completed. Thus, the finish time of an order is the time when the last job of the order has been completed. Even though the idea is somewhat new that order scheduling measures the overall completion time of a set of jobs (i.e., an order requesting different product types) instead of the individual completion time of each product type for any given order, many applications require that decision-makers consider orders rather than the individual product types in orders. Research into order scheduling models is motivated by their various real-life applications in manufacturing systems, equipment maintenance, computing systems, and other industrial contexts, where the components of each order can be processed concurrently on the parallel machines. In this research, two cases of order scheduling models are studied, namely, the fully dedicated environment in which each machine can produce one and only one product type, and the fully flexible machine environment in which each machine can produce all product types. With different side constraints and objective functions, the two cases include a lot of problems that are of interest. Special interest is focused on the minimization of the total weighted completion time, the number of late orders, the maximum lateness, and so on. On the one hand, polynomial time algorithms are proposed for some problems. One the other hand, for problems that are NP-hard, complexity proofs are shown and heuristics with their worst-case performance and empirical analyses are also presented