Tamás Kis

Computing lower and upper bounds for a large-scale industrial job shop scheduling problem

In this paper we present a case study from the lighting industry concerned with the scheduling of a set of job families each representing the production of a particular end-item in a given quantity. It is a job shop type problem, where each job family has a number of routing alternatives, and the solution has to respect batching and machine availability constraints. All jobs of the same job family have a common release date and a common due date, and they differ only in size. The objective is to minimize the total tardiness of the job families, rather than that of individual jobs. We propose a two-phase method based on solving a mixed-integer linear program and then improving the initial solution by tabu search. We evaluate our method on real-world as well as generated instances.

Resource leveling in a machine environment

We address resource leveling problems in a machine environment. Given a set of m machines, one or more renewable resources, and a set of n tasks, each assigned to exactly one of the machines. Each task has a processing time, an earliest start time, a deadline, and resource requirements. There are no precedence relations between the tasks. The tasks have to be sequenced on the machines while minimizing a function of the level of resource utilization from each resource over time. We provide various complexity results including a polynomial time algorithm for a one machine special case. We also propose an exact method using various techniques to find optimal or close-to-optimal solutions. The computational experiments show that our exact method significantly outperforms heuristics and a commercial MIP solver.

Scheduling of inventory releasing jobs to minimize a regular objective function of delivery times

In this note we provide new complexity and algorithmic results for scheduling inventory releasing jobs, a new class of single machine scheduling problems proposed recently by Boysen et al. We focus on tardiness related criteria, while known results are concerned with inventory levels between fixed delivery points. Our interest is motivated by the fact that deciding whether a feasible schedule exists is NP-hard in the strong sense, provided that all delivery deadlines are fixed, and there are no restrictions on the amount of products released by the jobs, nor on the job processing times. We will establish NP-hardness results, or provide polynomial or pseudo-polynomial time algorithms for various special cases, and describe a fully polynomial approximation scheme for one of the variants with the maximum tardiness criterion.

Hard Planning and Scheduling Problems in the Digital Factory

Production planning and scheduling with the aid of software tools in today’s manufacturing industries have become a common practice which is indispensable for providing high level customer service, and at the same time to utilize the production resources, like workforce, machine tools, raw materials, energy, etc., efficiently. To meet the new requirements, problem modeling tools, optimization techniques, and visualization of data and results have become part of the software packages. In this chapter some recent developments in problem modeling and optimization techniques applied to important and challenging industrial planning and scheduling problems are presented. We will focus on new problem areas which are still at the edge of current theoretical research, but they are motivated by practical needs. On the one hand, we will discuss project based production planning, and on the other hand, we will tackle a resource leveling problems in a machine environment. We will present the problems, some modeling and solution approaches, and various extensions and applications.

Car Sequencing with respect to Regular Expressions and Linear Bounds

Abstract In this paper we introduce a new model and a computational approach for sequencing assembly lines with two types of constraints: (i) patterns described by regular expressions and (ii) linear bounds on the number of certain products that may occur in pre-specified intervals. If we restrict the problem to the second type of constraints only we obtain a generalization of the familiar car sequencing problem , whereas constraints of type (i) may be useful to add extra structure. Constraints of both types may have priorities and can be violated, and a Pareto optimal solution is sought minimizing the violation of constraints in the given priority order. We describe a computational method based on mathematical programming and genetic algorithms for finding suboptimal solutions.