Een callcenter is een afdeling of organisatie die is gespecialiseerd in het afhandelen van telefoonverkeer. Klanten, die bellen naar een callcenter, worden geholpen als er een werknemer beschikbaar...Show moreEen callcenter is een afdeling of organisatie die is gespecialiseerd in het afhandelen van telefoonverkeer. Klanten, die bellen naar een callcenter, worden geholpen als er een werknemer beschikbaar is, anders komen ze in een wachtrij. Er is geen limiet voor de lengte van de wachtrij. De klanten komen aan volgens een Poisson proces met parameter λ. De gespreksduur met een werknemer is exponentieel verdeeld met parameter µ en er zijn s werknemers die de gesprekken voeren. Ten slotte is het ongeduld van de klanten exponentieel verdeeld met parameter γ. Met ongeduld wordt bedoeld de tijd die klanten bereid zijn te wachten voordat ze geholpen worden. Er wordt aangenomen dat klanten niet ophangen tijdens een gesprek met een werknemer. In deze scriptie wordt verder aangenomen dat een callcenter-manager alleen invloed uit kan oefenen op het aantal werknemers s. In veel callcenters wordt momenteel voor het bepalen van het aantal werknemers gezocht naar het aantal werknemers dat nodig is om meer dan tachtig procent van de klanten binnen twintig seconden te helpen. Het is niet eenvoudig te zeggen wat de negatieve gevolgen zijn voor het callcenter door het later behandelen van de overgebleven twintig procent. Ook wordt er in dit systeem geen rekening gehouden met het feit dat klanten voor het ene callcenter langer willen wachten dan voor een ander callcenter. Deze twee nadelen hebben geleid tot het zoeken naar een nieuw systeem. Het nieuwe systeem waar hier naar wordt gekeken, zoekt het aantal werknemers dat nodig is om ervoor te zorgen dat minder dan ´e´en procent van de klanten ongeduldig wegloopt. Hierdoor weet je precies wat het gevolg is van het systeem en je houdt rekening met het verschil tussen callcenters. Er zal in deze scriptie worden uitgelegd hoeveel werknemers een callcenter-manager minimaal in dienst moet nemen om ervoor te zorgen dat minder dan ´e´en procent van de klanten ongeduldig wegloopt. Hierbij wordt eerst gekeken naar het stationaire geval. Vervolgens worden de resultaten van het stationaire geval gebruikt in simulaties om te testen of ze op korte termijn ook bruikbaar zijn.Show less
Robustness is the ability of a network to continue performing well when it is subject to failures or attacks. In this thesis we survey robustness measures on simple, undirected and unweighted...Show moreRobustness is the ability of a network to continue performing well when it is subject to failures or attacks. In this thesis we survey robustness measures on simple, undirected and unweighted graphs, network failures being interpreted as vertex or edge deletions. We study graph measures based on connectivity, distance, betweenness and clustering. Besides these, reliability polynomials and measures based on the Laplacian eigenvalues are considered. In addition to surveying existing measures, we propose a new robustness measure, the normalized effective resistance, which is derived from the total effective resistance. Total effective resistance is — within the field of electric circuit analysis — defined as the sum of the pairwise effective resistances over all pairs of vertices. The strength of this measure lies in the fact that all (not necessarily disjoint) paths are considered, in other words, the more backup possibilities, the larger the normalized effective resistance and the larger the robustness. A chapter is dedicated to optimizing the normalized effective resistance, first for graphs with a fixed number of vertices and diameter, and second for the addition of an edge to a given graph. For all of the measures described above we evaluate the effectiveness as a measure of network robustness. The discussion and comparison of robustness measures is illustrated by a number of examples. Where possible we make extensions to weighted graphs and for all statements we provide either an elaboration of the original proof, or — when a rigorous proof is not available — we provide one ourselves.Show less
This thesis describes the result and the process of a research to determine an optimal trading strategy for storage systems in the low voltage grid. To give a clear insight in the problem and in...Show moreThis thesis describes the result and the process of a research to determine an optimal trading strategy for storage systems in the low voltage grid. To give a clear insight in the problem and in the algorithms to solve the problem, a phased approach is used. First a simple model of a storage system is described, that is extended in three steps to the final model that is a realistic model of a storage system. All four models are described and for each of these models an algorithm is developed to determine an optimal trading strategy. In these models the energy prices per quarter of an hour are given in advance for 24 hours, the model is discrete in time. We use n intervals of a quarter of an hour in which the storage system can charge energy, discharge energy or do nothing. We assume that there is no residual value of energy. Though the problem solved is a normal LP problem, the phased approach and the description of the problem and the algorithm give insight in the solution that is required. In the first model, Model A, the state of charge of the storage system of interval i, SOC(i), is either full or empty, this can be naturally modeled as a binary integer problem. Algorithm 1 is developed to determine an optimal trading strategy as described above. Algorithm 1 has complexity O(n). In Model B the charge capacity, the discharge capacity and the capacity of the storage system can have different values. With three different values for these physical constrains, the SOC cannot be modeled as a discrete model and thus the SOC is modeled as a continuous model. Algorithm 2 is developed to determine an optimal trading strategy for Model B as described above, Algorithm 2 has complexity O(n 2 ). As an extension to Model B, in Model C energy losses from using the storage system are taken into account. There is energy required for charging and for discharging the storage system. This is energy that cannot be used for trading. Also, in time the energy in the storage system decreases, this is energy that cannot be sold. The energy that cannot be sold constitutes a loss from using the storage system. To take the losses into account, there are two virtual energy prices developed, the virtual charge price and the virtual discharge price. Similar to the previous model, the maximum amount of energy to trade can be determined, using the new determined SOC(i). Algorithm 3 is developed to determine an optimal trading strategy for Model C, as described above. This Algorithm has complexity O(n 2 ). In the final model, Model D, there are bounds included in the model. With these bounds it is possible to use the storage system for trading as well as for solving problems in the low voltage grid. To solve problems in the low voltage grid, space to store too much energy that is in the low voltage grid is required. It is also possible that not all the energy demanded can be transported, for instance because of the capacity of the network. If there is a storage system nearby the problem it is possible that the energy available in the storage system can help to overcome the problem. For such a problem, the storage system is used to supply energy. To be able to help overcome both types of problems, there is a lower and an upper bound required. With these bounds, there is less storage space available for trading. To be able to solve problems in the low voltage grid, every interval must have a SOC within the bounds. Algorithm 4 is developed to determine an optimal trading strategy for Model D. While the complexity of Algorithm 2 and 3 is O(n 2 ), the complexity of Algorithm 4 is O(n 3 ). To reduce the complexity, a greedy algorithm is developed. For every iteration i, interval i is first used to discharge the maximum amount of energy that is possible with respect to the discharge capacity. After this, the minimum amount of energy must be charged to get the SOC(i) equal to the LB. The absolute local minimum before interval i is used to charge energy for minimum cost. This is done for all intervals, and gives an optimal trading strategy. Algorithm 5 determines an optimal trading strategy for Model D with complexity O(n 2 ). For KEMA the program ATMP1 is developed. The code of the algorithms that are used in ATMP are written in Visual Basic Application of Excel. Therefore these algorithms can be used by KEMA for the overal program PLATOS2 . ATMP is used to give clear insight in the algorithms developed and the output of the algorithms is processed graphically. The user can even try to develop a trading strategy that is better than the trading strategy developed by ATMP. This helps the user to get a good insight in the problem and trust in the solution. In the Appendices the algorithms used are described.Show less
