Brigitte Werners

An interactive fuzzy programming system

Abstract An interactive system is introduced which supports a decision maker in solving programming models with crisp or fuzzy constraints and crisp or fuzzy goals. One part of the system is the determination of membership functions representing goals. To this purpose fuzzy extreme solutions are computed and are presented to the decision maker. These and each of the proposed compromise solutions are fuzzy-efficient.

Aggregation Models in Mathematical Programming

A conventional mathematical programming problem can be described as a maximization of a well-defined objective function subject to well-defined constraints on a set of possible alternatives. Standard software tools (for example MPSX, APEX, etc.) can be used to calculate the optimal solution of the model, if the objective function and the constraints are linear functions and the possible alternatives are vectors of real or integer values. This is a very important advantage, but the possibility of application of mathematical programming is limited by the strict structure of the model. The underlying restricting assumptions are as follows: The considerations focus on a single objective function. The set of constraints differentiates exactly between feasible solutions and infeasible ones even if these violate a constraint only to a very small degree. Constraints are aggregated by intersection. This corresponds to the logical “and”. The set of feasible solutions is independent of the objective function. The objective function depends hierarchically on the constraints.

Interactive multiple objective programming subject to flexible constraints

Abstract An interactive decision support system is introduced which aids in solving multiple objective programming problems subject to strict and flexible constraints. Integral part is an extension of a well-known fuzzy sets approach evaluating possible solutions by their degrees of membership to objectives and constraints. This approach is linked to classical multiple objective programming models. If the decision maker cannot determine membership functions a priori the system suggests functions dependent on the given information and interactive modifications are allowed.

Planning models for research and development

Abstract The importance of research and development has been increasing steadily during the last decades and it will grow further in the future. As a consequence, models which can support the planning process for R&D become also more numerous and sophisticated. This contribution first reviews the existing literature in these areas. Starting from a rather basic model, the structure of planning models for R&D is developed. The main focus is on models which use the mathematical programming framework. Special attention is given to the modelling of uncertainty which is particularly important in R&D planning. Future developments which seem to be desirable and necessary are considered as extensions of models described before.

Interaktive Entscheidungsunterstützung Durch ein Flexibles Mathematisches Programmierungssystem

Wesentlicher Bestandteil des hier vorgestellten interaktiven Entscheidungsunterstutzungssysterms ist ein flexibles Programmierungsmodell auf der Basis der Theorie unscharfer Mengen. Es dient der modellmasigen Erfassung auch solcher Probleme, deren Abbildung durch klassische mathematische programmierungsmodelle nur unzureichend erfolgen kann. Durch die Moglichkeit der Berucksichtigung vager Auserungen ist das Modell dem haufig unprazisen Formulierungsverhalten des Entscheidungsfallers starker anpasbar und vage, subjektive Informationen oder Anforderungen konnen berucksichtigt werden. Die Modellierung der Vagheit erfolgt uber Erweiterungen klassischer mathematischer Begriffe auf unscharfe Begriffe, die als Spezialfall die entsprechenden klassischen Definitionen enthalten.

A decision support system for business process planning

Abstract In application and theory, great importance is attached to the optimisation of business processes, mostly without explaining into detail the criteria and the alternatives considered for an optimisation. Especially, quantitative criteria can be valuable to evaluate improvements of business processes, then quantitative methods of operations research are of special importance. Many problems of business processes have similarities to problems in the context of project management or production process planning which have already been solved successfully. Particularly simulation-based approaches have been proven to be appropriate in supporting decision making with respect to complex dynamic systems with uncertain data as is the optimisation of business processes. In the following, a generally applicable, object-oriented, simulation-based decision support system GEPSIS is introduced which is specifically developed for the improvement of business processes. The objects are designed in such a way that they are sufficient to model a great variety of different business processes. The pictorial representation assists in analysing the static structure of the process, the simulation system allows the quantitative evaluation of the dynamic behaviour. A case study shows its advantages.

Robust optimization of internal transports at a parcel sorting center operated by Deutsche Post World Net

Competitiveness in global markets requires the ongoing identification and full utilization of improvement potential. To cut costs by means of process optimization, logistics service providers need to focus on efficient planning -- not only for external but also for internal transports. This contribution will demonstrate that significant reductions in internal transports at one of the Deutsche Post World Nets main parcel sorting centers can be achieved by applying the robust solution of a modified three-dimensional linear assignment model. The proposed MILP model minimizes necessary manual transportation effort by layout modifications. Additionally, it takes into account the specific characteristics and requirements of the parcel sorting center. The large-scale model is hierarchically decomposed and all resulting models are solved using MILP software. Uncertain data concerning the structure and quantities of transportation demand over time are considered adequately by applying robustness criteria. The transportation effort of the robust solution is close to every scenario-optimal objective value. The achieved reduction of manual transportation effort leads to a significant increase in runtime quality, to a decrease in costs and to a balanced utilization of the sorting and distribution unit. The approach proposed is not only valuable for parcel sorting centers operated by Deutsche Post World Net; it can also be generally applied to develop robust solutions in an uncertain dynamic decision situation.

A simulation-based decision support system for business process planning

Over the last few years, there has been wide discussion in the field of economics research with regard to the process-oriented approach. Extensive restructuring took place in practice. To improve business processes, a generally applicable, object-oriented, simulation-based decision support system abbreviated as GEPSIS has been developed. It is used to model business processes and to evaluate different process alternatives quantitatively. The aim is to determine the optimal process. Within a business process context, tasks, work flows and decisions are influenced by persons whose behavior is not deterministic. Such a behavior cannot be described adequately taking crisp approaches. For this reason, consideration of uncertainty and vagueness is of special importance. Both stochastic and linguistic types of uncertainty are considered. The vagueness of verbal formulations is modeled using linguistic variables. Several specific procedures are developed for process control. They result from specific priority rules for the object classes. Furthermore, a knowledge-based procedure comprising approximate inference is developed. In this way, rules for the sequencing of workflow objects can be modeled approximating reality. The suitability of GEPSIS and the effects of the application of different procedures to process control are demonstrated. This is achieved by considering a mail order book and record store and analyzing its actual business - e.g. the order process. The example covers some typical flow structures which can be found in many order processing situations.

A robust approach for scheduling in hospitals using multiple objectives

Scheduling in hospitals is a challenging task and stochastic influences have a major impact on the final schedule. Therefore, uncertainties of treatment durations and of emergency arrivals have to be taken into account explicitly. In order to avoid re-scheduling we integrate information on stochastic parameters into a scenario-based mixed-integer optimization model. Besides, we focus on different stakeholders’ objectives that are simultaneously considered within a multi-criteria optimization model. Individually optimal solutions are likely to differ and the overall aim is to identify a good and acceptable compromise solution. The presented approach is based on fuzzy sets and merges the interests of several stakeholders. Different schedules are calculated and later on evaluated with randomly generated scenarios for surgery times and emergencies. The resulting objective function values are close to the individually optimal solutions. Finally, the schedules lead to a high rate of utilization and a low amount of overtime.

Time-Dependent Ambulance Allocation Considering Data Driven Empirically Required Coverage

Empirical studies considering the location and relocation of emergency medical service (EMS) vehicles in an urban region provide important insight into dynamic changes during the day. Within a 24-hour cycle, the demand, travel time, speed of ambulances and areas of coverage change. Nevertheless, most existing approaches in literature ignore these variations and require a (temporally and spatially) fixed (double) coverage of the planning area. Neglecting these variations and fixation of the coverage could lead to an inaccurate estimation of the time-dependent fleet size and individual positioning of ambulances. Through extensive data collection, now it is possible to precisely determine the required coverage of demand areas. Based on data-driven optimization, a new approach is presented, maximizing the flexible, empirically determined required coverage, which has been adjusted for variations due to day-time and site. This coverage prevents the EMS system from unavailability of ambulances due to parallel operations to ensure an improved coverage of the planning area closer to realistic demand. An integer linear programming model is formulated in order to locate and relocate ambulances. The use of such a programming model is supported by a comprehensive case study, which strongly suggests that through such a model, these objectives can be achieved and lead to greater cost-effectiveness and quality of emergency care.