Hans F. Ravn

A heuristic algorithm for a dial-a-ride problem with time windows, multiple capacities, and multiple objectives

The paper describes a system for the solution of a static dial-a-ride routing and scheduling problem with time windows (DARPTW). The problem statement and initialization of the development project was made by the Copenhagen Fire-Fighting Service (CFFS). The CFFS needed a new system for scheduling elderly and disabled persons, involving about 50.000 requests per year. The problem is characterized by, among other things, multiple capacities and multiple objectives. The capacities refer to the fact that a vehicle may be equipped with e.g. normal seats, children seats or wheel chair places. The objectives relate to a number of concerns such as e.g. short driving time, high vehicle utilization or low costs. A solution algorithm REBUS based on an insertion heuristics was developed. The algorithm permits in a flexible way weighting of the various goals such that the solution reflects the users preferences. The algorithm is implemented in a dynamic environment intended for on-line scheduling. Thus, a new request for service is treated in less than 1 second, permitting an interactive user interface.

Aggregated dynamic simulation model of district heating networks

Abstract The dynamic properties of district heating (DH) networks include water flow and propagation of heat from production plants to consumers. Mathematical models of such networks can be applied, either for general understanding of DH systems, or in combination with production planning and optimization. One type of mathematical model involves a full physical modeling of the network, taking into account individual pipes, dimensions, material properties etc. Such full models tend to be computationally intensive when applied in network simulations, which can be a problem when considering large DH systems. In the current paper, a method is presented in which a fully described model of a DH network is replaced by a simplified one, with the purpose of reducing simulation time. This simplified model is generated by gradually reducing the topological complexity of the original network. The method is validated by applying it on a real case study, in which a network with over 1000 pipes is reduced to less than 10 pipes. The results show that such relatively simple networks can maintain most of the dynamic characteristics of the original networks.

Hydrogen as an energy carrier: scenarios for future use of hydrogen in the Danish energy system☆

Scenarios for a transition to a hydrogen society are constructed for Denmark. The physical basis for the scenarios is the exploitation of renewable energy resources already in progress in Denmark. Hydrogen is proposed as a convenient energy carrier due to its versatility in use, transmission and as an energy storage medium. Two main scenarios are constructed, differing in the degree of decentralisation of energy production and management: one resembles the current system with centralised facilities and commercial management, the other being based upon a projected scale-independent cost structure of energy producing and handling equipment, that will allow extreme decentralisation of the physical energy conversion system, possibly accompanied by a similar decentralisation of ownership and control. The simulation studies show that both scenarios are technically feasible, and that the storage problems arising from the mismatch between demand and intermittent sources can be solved in both a centralised and a decentralised fashion.

OPTIMAL SCHEDULING OF COPRODUCTION WITH A STORAGE

Abstract The problem considered concerns the optimal scheduling of a system with combined heat and power (CHP) units and a heat storage. The purpose of the heat storage is to permit a partial decoupling of the variations in the demand for heat and electrical power. The problem of optimal scheduling is formulated as that of minimizing the total costs over the planning period. The heat demand from the district heating system and the shadow prices for the electrical power system are taken as externally given parameters. The resulting model is solved by dynamic programming. Implementation details and examples of result of the optimization are given.

Economic and environmental optimization of waste treatment.

This article presents the new systems engineering optimization model, OptiWaste, which incorporates a life cycle assessment (LCA) methodology and captures important characteristics of waste management systems. As part of the optimization, the model identifies the most attractive waste management options. The model renders it possible to apply different optimization objectives such as minimizing costs or greenhouse gas emissions or to prioritize several objectives given different weights. A simple illustrative case is analysed, covering alternative treatments of one tonne of residual household waste: incineration of the full amount or sorting out organic waste for biogas production for either combined heat and power generation or as fuel in vehicles. The case study illustrates that the optimal solution depends on the objective and assumptions regarding the background system--illustrated with different assumptions regarding displaced electricity production. The article shows that it is feasible to combine LCA methodology with optimization. Furthermore, it highlights the need for including the integrated waste and energy system into the model.

Challenges when performing economic optimization of waste treatment: a review

Strategic and operational decisions in waste management, in particular with respect to investments in new treatment facilities, are needed due to a number of factors, including continuously increasing amounts of waste, political demands for efficient utilization of waste resources, and the decommissioning of existing waste treatment facilities. Optimization models can assist in ensuring that these investment strategies are economically feasible. Various economic optimization models for waste treatment have been developed which focus on different parameters. Models focusing on transport are one example, but models focusing on energy production have also been developed, as well as models which take into account a plants economies of scale, environmental impact, material recovery and social costs. Finally, models combining different criteria for the selection of waste treatment methods in multi-criteria analysis have been developed. A thorough updated review of the existing models is presented, and the main challenges and crucial parameters that need to be taken into account when assessing the economic performance of waste treatment alternatives are identified. The review article will assist both policy-makers and model-developers involved in assessing the economic performance of waste treatment alternatives.

The discrete-time maximum principle : a survey and some new results

In this paper we present a review of the development of the discrete maximum principle. In the presentation, the emphasis is on a geometrical interpretation. The crucial assumptions in the theory developed are pointed out, and the attempts to overcome the limitation in the resulting theorems ore exposed. Following the review, we present a new approach to optimization of the multi-stage optimization problems called the ’ upper boundary approach ’. The classical methods of solving this problem are shown to fit smoothly into the new approach. Moreover, using this approach a number of new results have been developed, among these a new generalized version of the discrete maximum principle. The new version does not require the assumption of directional convexity.

Timetabling by Simulated Annealing

We describe in this paper the timetabling problem for Danish primary schools and how we have solved it. The timetabling problem is characterized as a combinatorial problem with many constraints and a variety of “soft” and “hard” criteria.

Stochastic heat storage problem—solved by the progressive hedging algorithm

Abstract In the present study, a problem concerning operation of a heat storage tank in connection with a combined heat and power (CHP) plant is considered. The heat storage is used to supply the district heating system when the CHP plant is producing electric power alone and also to redistribute optimally over time the required heat production. Stochasticity is assumed attached to the future power production, and it is assumed that accurate predictions of the future heat consumption are available. A receding horizon idea is used. The problem is solved by the Progressive Hedging Algorithm (PHA), a recently developed method to deal with multi-period optimization problems under uncertainty. The application of the method is explained in detail.

Probabilistic production simulation including combined heat and power plants

Expansion planning of combined heat and power systems requires simulation tools for estimating key indicators for decision making. For power systems, so-called probability production simulation techniques have been used extensively. These techniques have been extended to include combined heat and power (CHP) systems with a single heat area and back-pressure type CHP units. In this paper, existing simulation methods for CHP are extended to include extraction power plants. Furthermore, the case of multiple heat areas is addressed and three different simulation strategies are presented for such systems. The results show that an assumption of perfectly correlated heat demands in all heat areas gives results that are very similar to a general case, whereas working with a system with all heat areas aggregated into one gives rather poor results. It is demonstrated that it is possible to use the traditional concepts and methods for power-only analysis on a CHP system. Additional concepts are presented, depending on the heat criterion applied. It is concluded that probabilistic production simulation including CHP units can be performed with reasonable effort and accuracy.