The harsh competition in the airline industry continuously forces airline carriers to streamline their production and cut back on costs. Manpower constitutes the largest expense in Scandinavian Airline System, closely followed by fuel costs. Thus effective crew planning is vital to face the competition from international actors and low cost carriers. Creating efficient schedules for airline crew is a very complex combinatorial task and the process is heavily dependent on optimization. A large set of constraints comprised of union- and governmental rules as well as company policies and quality factors must be taken into consideration when the schedules are created. This master thesis examines how the distribution of rank in the SAS international pilot corps affects the total cost associated with flight deck crew. Long haul flights at SAS intercontinental are manned with a captain, a first officer and a relief pilot. Pilots may man lower ranking positions on any given flight in order to make efficient use of the pilot corps and to minimize the need of full time equivalents. This work discusses the development and evaluation of a simulation environment developed in order to create and analyze fictitious crew populations with different distributions of rank. Furthermore the solution methods to the scheduling problem implemented at SAS and the optimization theory associated with them are discussed. The project has resulted in an evaluation of the developed simulation environment and a discussion about the difficulties of analyzing crew populations with the systems currently in use at SAS.

Syftet med detta examensarbete var att på uppdrag av Skellefteå Kraft AB studera produktionsplanering för regleringsbar vattenkraft och avgöra hur vatten i ett magasin kan värderas. Vidare skulle även en applikation skapas för att kunna beräkna dessa vattenvärden.   Produktionsplanering för vattenkraft visade sig oftast delas upp i tre nivåer, i en lång-, säsong- och korttidsplaneringsdel, där detaljrikedomen i modellbeskrivningarna ökar med minskande tidshorisont. Anledningen till uppdelningen är en följd av att både noggrannhet och långsiktighet önskas, tanken är därmed att låta den högre nivån ge den lägre en långsiktighet den annars saknat. Möjliga kopplingar mellan nivåerna diskuterades, där en priskoppling genom vattenvärden argumenterades för att vara den bästa.   Därefter studerades metoder för vattenvärdeberäkningar och matematiska villkor för optimal produktion, varvid ett eget program i Matlab kunde skrivas. Programmet beräknar vattenvärden vid en enmagasinmodell utifrån tillrinnings- och prisprognoser, där prognoserna tillåts att delas upp i ett valfritt antal scenarion.   Testkörningar av programmet visar att vattenvärdena går ned inför en prognostiserad vårflod, för att på så vis skapa plats åt det inkommande vattnet. Det visas även att vattenvärdenas ISO-kurvor, som markerar var i tid och magasinsnivå ett visst vattenvärde gäller, blir flackare vid större magasin och djupare vid mindre inför den kommande vårfloden. Men även att ISO-kurvorna påverkas av produktionskapaciteten.   Vidare visar testkörningarna att vattenvärdena är starkt kopplade till både tillrinningarnas- och prisprognosernas form och nivå, eftersom att spill vill undvikas samtidigt som produktionen önskas styras till perioder av höga priser.   Innan vattenvärdena från programmet används i praktiken bör ytterligare testkörningar göras för att jämföra ekonomiskt utfall i förhållande till nuvarande arbetssätt. Därför är detta också ett förslag på vidare arbete, tillsammans med en eventuell utvidgning av programmet till en flermagasinsmodell. / The purpose of this master's thesis was to study hydropower production scheduling on behalf of Skellefteå Kraft AB and to determine how water in a reservoir could be priced. Furthermore an application for calculating these water values was to be made.   Hydropower production scheduling was found most often divided into three levels, into a long-, medium- and short-term scheduling part, where the degree of detail increases with decreasing time horizon. The reason for this breakdown into levels are that a high detail in the model descriptions is desired, while still maintaining a good long-term planning. The idea is thus to let the higher level give the lower one an insight for future events it would otherwise lack. Possible couplings between the levels was discussed, where a coupling through price and water values was argued to be the best.   Subsequently methods for water value calculations and mathematical conditions for optimal production was studied, in which an own program in Matlab could be written. The program calculates water values at a single reservoir model by the help of forecasts of future inflow and price, where the forecasts are allowed to be divided into any number of scenarios.   Test runs of the program shows that water levels are reduced before the spring flood, thus to make room for the incoming water. It is also shown that the ISO-curves for the water values, which indicates where in time and reservoir level a certain water value is located, becomes flatter at larger reservoirs and steeper at smaller reservoirs before the incoming spring flood. But also that the ISO-curves are affected by the production capacity.   The test runs further shows that the water values are strongly linked to both the shape and level of the inflow and price forecasts, since it is desired to avoid spill while directing the production to periods of high prices.   Additional runs to compare the economic outcomes relative to current practice should be made before using the water values of the program in practice. Therefore this is also a proposal for further work, along with a possible extension of the program into a multi-reservoir model.

<p>Sweden experiences heavy snowfall during the winter season and cost effective road maintenance is significantly affected by the routing of snowplows. The routing problem becomes more complex as the SwedishNational Road Administration (Vägverket) sets operational requirements such as satisfying a time window for each road segment. </p><p>This thesis focuses on route optimization for snowplows after snowfall; to develop and implement an algorithm for finding combinations of generated routes which minimize the total cost. The results are compared to those stated in the licentiate thesis by Doctoral student Nima Golbaharan (2001). </p><p>The algorithm calculates a lower bound to the problem using a Lagrangian master problem. A common subgradient approach is used to find near-optimal dual variables to be sent to a column-generation program which returns routes for the snowplows. A greedy heuristic chooses a feasible solution, which gives an upper bound to the problem. This entire process is repeated as needed. </p><p>This method for routing snowplows produces favorable results with a relatively small number of routes and are comparable to Golbaharan's results. An interesting observation involves the allocation of vehicles in which certain depots were regularly over- or under-utilized. This suggests that the quantity and/or distribution of available vehicles may not be optimal.</p>

<p>Nynas produces bitumen at two refineries in Sweden. The bitumen is shipped to seven depots along the swedish coast line, and from the depots special trucks handle the transportation to customers. Recently Nynas has transformed its supply chain and closed down a few depots. At the moment the company is considering a further reduction of the number of depots. In connection to these discussions an analyse of the companys distributionsystem and of possible changes is required. In this thesis an optimization model is developed that simulates Nynas distribution of bitumen from the depots to the customers. The model is used to investigate the required vehicle fleet size for a number of different scenarios, that is with different depots closed down. The question to be answered is, thus, what depots could be closed without any dramatic increase in the required vehicle fleet size? Scenarios where customers are allocated an increased storage capacity are also studied. </p><p>The distribution model that is developed is an inventory route planning problem. It is solved by column generation. Each column represents a route and is generated by a subproblem with restrictions on permitted working hours for the truck drivers. Integer solutions are generated heuristically. </p><p>Simulations that have been performed with the model reveals interesting differences concerning how the distribution is handled in different parts of Sweden. In western Sweden the transportation planning works well, but the distribution in the central parts of the country could be planned in a better way. Results from simulations also show that the depots in Norrköping and Västerås could be closed down without increasing the vehicle fleet. Probably, the existing vehicle fleet size will be sufficient even with the Kalmar-depot closed down. Nevertheless, Nynas transportation suppliers will have to purchase new vehicles if the Sandarne-depot is to be closed. </p><p>Another interesting conclusion that can be drawn from this thesis is that there is a potential for reducing the vehicle fleet size if the storage capacity is increased at a few chosen customers. A considerably small increase in the storage capacity at a few big customers that are located far from the depots will have a great effect.</p>

<p>We analyse several facets of bilevel decision problems under uncertainty. These problems can be interpreted as an extension of stochastic programming problems where part of the uncertainty is attributed to the behaviour of another actor.</p><p>The field of decision making under uncertainty with bilevel features is quite new and most approaches focus on the interactions and relations between the decision makers. In contrast to these studies, the approach of bilevel stochastic programming pursued here stresses the stochastic programming aspect of the problem formulation. The framework enables a direct application of stochastic programming concepts and solution methods to the bilevel relationship between the actors. Thus more complex problem structures can be studied and the aspect of uncertainty can be treated adequately.</p><p>Our analysis covers both theoretical and more practically oriented issues. We study different formulations of one and two stage bilevel stochastic programming problems and state necessary optimality conditions for each of the problem instances. Additionally we present a solution algorithm utilising a stochastic quasi-gradient method. A further study is concerned with the uniqueness of the minima of a convex stochastic programming problem with uncertainty about the decision variables. We state conditions on the distribution of the parameters representing the uncertainty such that the minima of the optimisation problem are unique. We formulate a model of competition and collaboration of two different types of telecom service providers, the owner of a bottleneck facility and a virtual network operator. This represents an application of a bilevel stochastic programming formulation to a liberalised telecommunications environment. Furthermore, the utilisation of the bilevel stochastic programming framework and the developed solution concepts for the analysis of principal agent models is demonstrated. Also here the background of a regulated telecom environment, more specific the relations between a regulator and a regulated telecommunications company, was chosen.</p>

We analyse several facets of bilevel decision problems under uncertainty. These problems can be interpreted as an extension of stochastic programming problems where part of the uncertainty is attributed to the behaviour of another actor. The field of decision making under uncertainty with bilevel features is quite new and most approaches focus on the interactions and relations between the decision makers. In contrast to these studies, the approach of bilevel stochastic programming pursued here stresses the stochastic programming aspect of the problem formulation. The framework enables a direct application of stochastic programming concepts and solution methods to the bilevel relationship between the actors. Thus more complex problem structures can be studied and the aspect of uncertainty can be treated adequately. Our analysis covers both theoretical and more practically oriented issues. We study different formulations of one and two stage bilevel stochastic programming problems and state necessary optimality conditions for each of the problem instances. Additionally we present a solution algorithm utilising a stochastic quasi-gradient method. A further study is concerned with the uniqueness of the minima of a convex stochastic programming problem with uncertainty about the decision variables. We state conditions on the distribution of the parameters representing the uncertainty such that the minima of the optimisation problem are unique. We formulate a model of competition and collaboration of two different types of telecom service providers, the owner of a bottleneck facility and a virtual network operator. This represents an application of a bilevel stochastic programming formulation to a liberalised telecommunications environment. Furthermore, the utilisation of the bilevel stochastic programming framework and the developed solution concepts for the analysis of principal agent models is demonstrated. Also here the background of a regulated telecom environment, more specific the relations between a regulator and a regulated telecommunications company, was chosen.

Sweden experiences heavy snowfall during the winter season and cost effective road maintenance is significantly affected by the routing of snowplows. The routing problem becomes more complex as the SwedishNational Road Administration (Vägverket) sets operational requirements such as satisfying a time window for each road segment. This thesis focuses on route optimization for snowplows after snowfall; to develop and implement an algorithm for finding combinations of generated routes which minimize the total cost. The results are compared to those stated in the licentiate thesis by Doctoral student Nima Golbaharan (2001). The algorithm calculates a lower bound to the problem using a Lagrangian master problem. A common subgradient approach is used to find near-optimal dual variables to be sent to a column-generation program which returns routes for the snowplows. A greedy heuristic chooses a feasible solution, which gives an upper bound to the problem. This entire process is repeated as needed. This method for routing snowplows produces favorable results with a relatively small number of routes and are comparable to Golbaharan's results. An interesting observation involves the allocation of vehicles in which certain depots were regularly over- or under-utilized. This suggests that the quantity and/or distribution of available vehicles may not be optimal.

Nynas produces bitumen at two refineries in Sweden. The bitumen is shipped to seven depots along the swedish coast line, and from the depots special trucks handle the transportation to customers. Recently Nynas has transformed its supply chain and closed down a few depots. At the moment the company is considering a further reduction of the number of depots. In connection to these discussions an analyse of the companys distributionsystem and of possible changes is required. In this thesis an optimization model is developed that simulates Nynas distribution of bitumen from the depots to the customers. The model is used to investigate the required vehicle fleet size for a number of different scenarios, that is with different depots closed down. The question to be answered is, thus, what depots could be closed without any dramatic increase in the required vehicle fleet size? Scenarios where customers are allocated an increased storage capacity are also studied. The distribution model that is developed is an inventory route planning problem. It is solved by column generation. Each column represents a route and is generated by a subproblem with restrictions on permitted working hours for the truck drivers. Integer solutions are generated heuristically. Simulations that have been performed with the model reveals interesting differences concerning how the distribution is handled in different parts of Sweden. In western Sweden the transportation planning works well, but the distribution in the central parts of the country could be planned in a better way. Results from simulations also show that the depots in Norrköping and Västerås could be closed down without increasing the vehicle fleet. Probably, the existing vehicle fleet size will be sufficient even with the Kalmar-depot closed down. Nevertheless, Nynas transportation suppliers will have to purchase new vehicles if the Sandarne-depot is to be closed. Another interesting conclusion that can be drawn from this thesis is that there is a potential for reducing the vehicle fleet size if the storage capacity is increased at a few chosen customers. A considerably small increase in the storage capacity at a few big customers that are located far from the depots will have a great effect.

No description available.

<p>The transportation cost of logs from forest to customers is a large part of the overall cost for the Swedish forestry industry. Finding good routes from harvesting points to saw and pulp mills is a complex task, where the total number of feasible routes is extremely high. In this thesis we present two methods for log truck scheduling. </p><p>The first is to, from a given set of routes, find the most valuable subset that fulfils the customers demand. We use a model that is similar to the set partitioning problem and a method that is referred to as a composite pricing coupled with Branch and Bound. The composite pricing based method prices the routes (columns) and chooses the most valuable ones that are then added to the LP relaxation. Once an LP optimum is found, the Branch and Bound method is used to find an integer optimum solution. We have tested this on a case of realistic size. </p><p>The second method is a tabu search heuristic. Here, the purpose is to create efficient and qualitative routes from a given number of trips (referred to as predefined trips). From a start solution tabu search systematically generates new solutions. This method was tested on a small problem and on a five times larger problem to study how the size of the problem affected the result. It was also tested and compared on two cases in which the backhauling possibilities (i.e. instead of traveling empty the truck picks up another load on the return trip) had and had not been studied. The composite pricing based method and the tabu search method proved to be very useful for this kind of scheduling.</p>