Quality- and profit-oriented scheduling of flexible resource-constrained projects

We study the problem of determining both the structure and the schedule of projects subject to capacity constraints. We assume that those projects are flexible in the sense that the activities to be implemented are not entirely known in advance. In such a setting, decisions must be made with respect to the implementation of the optional activities. Such decisions affect the duration, cost, quality and eventual revenue of the project. Examples of this type of problem can often be found when complex capital goods such as aircraft engines are overhauled, when buildings are renovated to meet higher environmental and efficiency standards, or in productdevelopment processes. We describe the problem, develop a mixed-integer optimisation model, explain specific features of a genetic algorithm to solve the problem and report the results of a numerical study

Simultaneous production and maintenance planning for a single capacitated resource facing both a dynamic demand and intensive wear and tear

This paper presents a generic modeling framework to simultaneously decide about production quantities and maintenance operations for a capacitated resource facing a dynamic demand for di erent types of products. As the resource needs to be setup for each speci c type of product, a lot-sizing problem occurs. In addition it is assumed that production causes intensive wear and tear. For this reason frequent maintenance activities need to be coordinated with the production operations in order to e ciently use the capacitated resource. A single generic model is presented to capture alternative forms of maintenance and di erent modes of interaction between maintenance and setups. As the model is numerically intractable for standard branch & bound algorithms, we solve it heuristically via a decomposition using a Fix-and-Optimize approach. Numerical results show that the proposed solution method produces high-quality results quickly. We further study the impact of simultaneous vs. sequential decisions about production and maintenance in the case of intensive wear and tear

A fix-and-optimize approach for the multi-level capacitated lot sizing problem

This paper presents an optimization-based solution approach for the dynamic multi-level capacitated lot sizing problem (MLCLSP) with positive lead times. The key idea is to solve a series of mixed-integer programs in an iterative fix-and-optimize algorithm. Each of these programs is optimized over all real-valued variables, but only a small subset of binary setup variables. The remaining binary setup variables are tentatively fixed to values determined in previous iterations. The resulting algorithm is transparent, flexible, accurate and relatively fast. Its solution quality outperforms those of the approaches by Tempelmeier/Derstroff and by Stadtler

Profit-oriented shift scheduling of inbound contact centers with skills-based routing, impatient customers, and retrials

This paper presents a profit-oriented shift scheduling approach for inbound contact centers. The focus is on systems in which multiple agent classes with different qualifications serve multiple customer classes with different needs. We assume that customers are impatient, abandon if they have to wait, and that they may retry. A discrete-time modeling approach is used to capture the dynamics of the system due to time-dependent arrival rates. Staffing levels and shift schedules are simultaneously optimized over a set of different approximate realizations of the underlying stochastic processes to consider the randomness of the system. The numerical results indicate that the presented approach works best for medium-sized and large contact centers with skills-based routing of customers for which stochastic queueing models are rarely applicable

Scheduling resource-constrained projects with a flexible project structure

In projects with a flexible project structure, the activities that have to be scheduled are not completely known beforehand. Instead, scheduling such a project includes the decision whether to carry out particular activities at all. This also effects precedence constraints between the finally implemented activities. However, established model formulations and solution approaches for the resource-constrained project scheduling problem (RCPSP) assume that the project structure is given in advance. In this paper, the traditional RCPSP is hence extended by a highly general model-endogenous decision on this flexible project structure. This is illustrated by the example of the aircraft turnaround process at airports. We present a genetic algorithm to solve this type of scheduling problem and evaluate it in an extensive numerical study

Dynamic capacitated lot sizing with random demand and dynamic safety stocks

We present a stochastic version of the single-level, multi-product dynamic lotsizing problem subject to a capacity constraint. A production schedule has to be determined for random demand so that expected costs are minimized and a constraint based on a new backlog-oriented -service-level measure is met. This leads to a non-linear model that is approximated by two different linear models. In the first approximation, a scenario approach based on random samples is used. In the second approximation model, the expected values of physical inventory and backlog as functions of the cumulated production are approximated by piecewise linear functions. Both models can be solved to determine efficient, robust and stable production schedules in the presence of uncertain and dynamic demand. They lead to dynamic safety stocks that are endogenously coordinated with the production quantities. A numerical analysis based on a set of (artificial) problem instances is used to evaluate the relative performance of the two different approximation approaches. We furthermore show under which conditions precise demand forecasts are particularly useful from a production-scheduling perspective

Decision support for rehabilitation hospital scheduling

We present a detailed analysis of the patient and resource scheduling problem in rehabilitation hospitals. In practice, the predominantly therapeutical treatments and activities which are prescribed for the patients are typically scheduled manually. This leads to rigid and inefficient schedules which can have negative effects on the quality of care and the patients' satisfaction. We outline the conceptual framework of a decision support system for the scheduling process that is based on formal optimization models. To this end, we first develop a large-scale monolithic optimization model. Then we derive a numerically tractable hierarchical model system in order to deal with problem instances of realistic sizes. We report numerical results with respect to solution times, model sizes and solution quality

Evaluation of stochastic flow lines with provisioning of auxiliary material

Flow lines are often used to perform assembly operations in multi-stage processes. During these assembly operations, components that are relatively small, compared to the work pieces travelling down the flow line, are mounted to the work pieces at a given stage. Those components, or more generally, any kind of auxiliary material, are provisioned to the corresponding production stage in a repetitive but not necessarily deterministic manner using a certain delivery frequency, each time filling the local storage up to a predetermined order-up-to level. Just like random processing times, machine failures, and repairs, the randomness of the provisioning process can impact the long-term throughput of such a flow line. In this paper, we develop a fast and accurate analytical performance evaluation method to estimate the long-term throughput of a Markovian flow line of this type for the practically important case of limited buffer capacities between the production stages. We first give an exact characterization of a two-machine line of that type and show how to determine system state probabilities and aggregate performance measures. Furthermore, we show how to use this two-machine model as the building block of an approximate decomposition approach for longer flow lines. As opposed to previous decomposition approaches, even the state space of the two-machine lines can become so large that an exact solution of the Markov chains can become impractical. We hence show how to set up, train, and use an artificial neural network to replace the Markov chain solver embedded in the decomposition approach, which then leads to an accurate and extremely fast flow line evaluation tool. The proposed methodology is evaluated by a comparison with simulation results and used to characterize the structural patterns describing the behaviour of flow lines of this type. The method can be used to systematically consider the combined impact of the delivery frequency and the local order-up-to levels for the auxiliary material when designing a flow line of this type

Simultaneous structuring and scheduling of multiple projects with flexible project structures

We study the problem to simultaneously decide on the structures and the schedules for an entire portfolio of flexible projects. The projects are flexible as alternative technologies and procedures can be used to achieve the respective project task. The choice between different technologies and procedures affects the activities to be implemented and thus the precedence relations, i.e., the structure of the project. The different projects have given due dates with specific delay payments and compete for scarce resources. In this situation, project structure decisions and scheduling decisions are highly intertwined and have to be made simultaneously in order to achieve the assumed objective of minimizing the delay payments for the entire project portfolio. The problem is formally stated and solved via novel and problem-specific genetic algorithms. The performance of the new algorithms is evaluated with respect to speed and accuracy in a systematic and comprehensive numerical study. © 2020, The Author(s)

Designing Dynamic Inductive Charging Infrastructures for Airport Aprons with Multiple Vehicle Types

In the effort to combat climate change, the CO2 emissions of the aviation sector must be reduced. The traffic caused by numerous types of ground vehicles on airport aprons currently contributes to those emissions as the vehicles typically operate with combustion engines, which is why an electrification of those vehicles has already begun. While stationary conductive charging of the vehicles is the current standard technology, dynamic wireless charging might be an attractive technological alternative, in particular for airport aprons; however, designing a charging network for an airport apron is a challenging task with important technical and economic aspects. In this paper, we propose a model to characterize the problem, especially for cases of multiple types of vehicles sharing the same charging network, such as passenger buses and baggage vehicles. In a numerical study inspired by real-world airports, we design such charging networks subject to service level constraints and evaluate the resulting structures via a discrete-event simulation, and thus, show the way to assess the margin of safety with respect to the vehicle batteries’ state of charge that is induced by the spatial structure of the charging network