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

Scheduling for Service Stability and Supply Chain Coordination

This dissertation studies scheduling for service stability and for supply chain coordination as well. The scheduling problems for service stability are studied from the single perspective of a firm itself, while the scheduling problems for supply chain coordination are investigated from the perspective of a supply chain. Both the studies have broad applications in real life. In the first study, several job scheduling problems are addressed, with the measure of performance being job completion time variance (CTV). CTV minimization is used to represent service stability, since it means that jobs are completed in a relative concentrated period of time. CTV minimization also conforms to the Just-in-time philosophy. Two scheduling problems are studied on multiple identical parallel machines. The one problem does not restrict the idle times of machines before their job processing, while the other does. For these two scheduling problems, desirable properties are explored and heuristic algorithms are proposed. Computational results show the excellent performances of the proposed algorithms. The third scheduling problem in the first study is considered on a single machine and from the users’ perspective rather than the system’s perspective. The performance measure is thus class-based completion time variance (CB-CTV). This problem is shown to be able to be transformed into multiple CTV problems. Therefore, the well-developed desirable properties of the CTV problem can be applied to solve the CB-CTV problem. The tradeoff between the CB-CTV problem and the CTV problem is also investigated. The second study deals with scheduling coordination in a supply chain, since supply chain coordination is increasingly critical in recent years. Usually, different standpoints prevent decision makers in a supply chain from having agreement on a certain scheduling decision. Therefore conflicts arise. In pursuit of excellent performance of the whole supply chain, coordination among decision makers is needed. In this study, the scheduling conflicts are measured and analyzed from different perspectives of decision makers, and cooperation mechanisms are proposed based on different scenarios of the relative bargaining power among decision makers. The cooperation savings are examined as well

Energy-efficient algorithms for non-preemptive speed-scaling

We improve complexity bounds for energy-efficient speed scheduling problems for both the single processor and multi-processor cases. Energy conservation has become a major concern, so revisiting traditional scheduling problems to take into account the energy consumption has been part of the agenda of the scheduling community for the past few years. We consider the energy minimizing speed scaling problem introduced by Yao et al. where we wish to schedule a set of jobs, each with a release date, deadline and work volume, on a set of identical processors. The processors may change speed as a function of time and the energy they consume is the $\alpha$th power of its speed. The objective is then to find a feasible schedule which minimizes the total energy used. We show that in the setting with an arbitrary number of processors where all work volumes are equal, there is a $2(1+\varepsilon)(5(1+\varepsilon))^{\alpha -1}\tilde{B}_{\alpha}=O_{\alpha}(1)$ approximation algorithm, where $\tilde{B}_{\alpha}$ is the generalized Bell number. This is the first constant factor algorithm for this problem. This algorithm extends to general unequal processor-dependent work volumes, up to losing a factor of $(\frac{(1+r)r}{2})^{\alpha}$ in the approximation, where $r$ is the maximum ratio between two work volumes. We then show this latter problem is APX-hard, even in the special case when all release dates and deadlines are equal and $r$ is 4. In the single processor case, we introduce a new linear programming formulation of speed scaling and prove that its integrality gap is at most $12^{\alpha -1}$. As a corollary, we obtain a $(12(1+\varepsilon))^{\alpha -1}$ approximation algorithm where there is a single processor, improving on the previous best bound of $2^{\alpha-1}(1+\varepsilon)^{\alpha}\tilde{B}_{\alpha}$ when $\alpha \ge 25$

A Decision Support System for Ship Maintenance Capacity Planning

In this paper, the basic framework and algorithms of a decision support system are discussed, which enhance process and capacity planning at a large repair shop. The research is strongly motivated by experiences in a project carried out at a dockyard, which performs repair, overhaul and modification programs for various classes of navy ships. We outline the basic requirements placed upon order acceptance, process planning and capacity scheduling for large maintenance projects. In subsequent sections a number of procedures and algorithms to deal with these requirements, in particular a procedure for workload-based capacity planning, a database system to support process planning are developed, as well as a resource-constrained project scheduling system to support work planning at a more detailed level. The system has been designed to support decision making at the Navy Dockyard in particular, however, we believe that, due to its generic structure, it is applicable to a wide range of project-based manufacturing and maintenance environments