Stefan Waldherr

Complexity results for flow shop problems with synchronous movement

In this paper we present complexity results for flow shop problems with synchronous movement which are a variant of a non-preemptive permutation flow shop. Jobs have to be moved from one machine to the next by an unpaced synchronous transportation system, which implies that the processing is organized in synchronized cycles. This means that in each cycle the current jobs start at the same time on the corresponding machines and after processing have to wait until the last job is finished. Afterwards, all jobs are moved to the next machine simultaneously. Besides the general situation we also investigate special cases involving machine dominance which means that the processing times of all jobs on a dominating machine are at least as large as the processing times of all jobs on the other machines. Especially, we study flow shops with synchronous movement for a small number of dominating machines (one or two) and different objective functions.

Two-stage scheduling in shelf-board production: a case study

In this paper, we consider a production planning problem arising at a company assembling shelf boards for kitchen elements. Different products have to be produced on circular production units with a synchronous transportation system, which leads to sequence-dependent production times. Additionally, changeover times occur due to changes of resources. The objective is to find a production schedule of given orders such that the number of late orders is minimised. We propose a hierarchical approach which is split into a coarse and a fine planning stage. While the coarse planning problem is solved as a network flow problem, the fine planning is done by an asynchronous team (A-team) approach. Finally, some computational results for real-world data are presented.

Plan assessment for autonomous manufacturing as Bayesian inference

Next-generation autonomous manufacturing plants create individualized products by automatically deriving manufacturing schedules from design specifications. However, because planning and scheduling are computationally hard, they must typically be done offline using a simplified system model, meaning that online observations and potential component faults cannot be considered. This leads to the problem of plan assessment: Given behavior models and current observations of the plants (possibly faulty) behavior, what is the probability of a partially executed manufacturing plan succeeding? In this work, we propose 1) a statistical relational behavior model for a class of manufacturing scenarios and 2) a method to derive statistical bounds on plan success probabilities for each product from confidence intervals based on sampled system behaviors. Experimental results are presented for three hypothetical yet realistic manufacturing scenarios.

Decomposition algorithms for synchronous flow shop problems with additional resources and setup times

In this paper, we present decomposition algorithms for synchronous flow shop problems with additional resources and setup times. In such an environment, jobs are moved from one machine to the next by an unpaced synchronous transportation system, which implies that the processing is organized in synchronized cycles. In each cycle the current jobs start at the same time on the corresponding machines and after processing have to wait until the last job is finished. Afterwards, all jobs are moved to the next machine simultaneously. During processing, each job needs one additional resource and setup times have to be taken into account when changing from one resource to another. The goal is to find a production sequence of the jobs as well as a feasible assignment of resources to the jobs such that the total production time (makespan) is minimized. We propose two decomposition strategies dealing with the two subproblems of job sequencing and resource assignment hierarchically. Both approaches are computationally evaluated and compared. As a by-product, we also present efficient heuristics for the makespan minimization problem in synchronous flow shops without setup times.

Solution algorithms for synchronous flow shop problems with two dominating machines

In this paper, we present solution algorithms for synchronous flow shop problems with two dominating machines. In such an environment, jobs have to be moved from one machine to the next by an unpaced synchronous transportation system, which implies that the processing is organized in synchronized cycles. This means that in each cycle the current jobs start at the same time on the corresponding machines and after processing have to wait until the last job is finished. Afterwards, all jobs are moved to the next machine simultaneously. Motivated by a practical application, we investigate the special case of two dominating machines where the processing times of all jobs on these two machines are at least as large as the processing times of all jobs on the other machines and hence always determine the cycle times. After formulating the considered problem as a special vehicle routing problem, we propose mixed integer linear programming formulations and a tabu search algorithm. Finally, we present computational results for randomly generated data and show the efficiency of the approaches. HighlightsInvestigation of synchronous flow shops with machine dominance.New models based on vehicle routing problems improve existing model.Formulation and comparison of different MIP models.Efficient, well-performing tabu search algorithm.Tight lower bounds by linear programs and a constructive method.

The bottleneck transportation problem with auxiliary resources

In this paper, we introduce a new extension of the bottleneck transportation problem where additionally auxiliary resources are needed to support the transports. A single commodity has to be sent from supply to demand nodes such that the total demand is satisfied and the time at which all units of the commodity have arrived at the demand nodes is minimized. We show that already the problem with a single demand node and a single auxiliary resource is NP-hard and consider some polynomially solvable special cases.

Flow shop scheduling with flexible processing times

In numerous flow shop variants, the processing times of the operations are not fixed in advance, but may be distributed with some flexibility among the machines. In this paper, we introduce a general model which is expressive enough to cover several models from the literature. While in most cases it is

The assignment problem with nearly Monge arrays and incompatible partner indices

\mathcal {NP}