Multi-homing is a technology used by Internet Service Provider (ISP) to connect to the Internet via multiple networks. This connectivity enhances the network reliability and service quality of the ISP. However, using multi-networks may imply multiple costs on the ISP. To make full use of the underlying networks with minimum cost, a routing strategy is requested by ISPs. Of course, this optimal routing strategy depends on the pricing regime used by network providers. In this study we investigate a relatively new pricing regime – top-percentile pricing. Under top-percentile pricing, network providers divide the charging period into several fixed length time intervals and calculate their cost according to the traffic volume that has been shipped during the θ-th highest time interval. Unlike traditional pricing regimes, the network design under top-percentile pricing has not been fully studied. This paper investigates the optimal routing strategy in case where network providers charge ISPs according to top-percentile pricing. We call this problem the Top-percentile Traffic Routing Problem (TpTRP). As the ISP cannot predict next time interval’s traffic volume in real world application, in our setting up the TpTRP is a multi-stage stochastic optimisation problem. Routing decisions should be made at the beginning of every time period before knowing the amount of traffic that is to be sent. The stochastic nature of the TpTRP forms the critical difficulty of this study. In this paper several approaches are investigated in either the modelling or solving steps of the problem. We begin by exploring several simplifications of the original TpTRP to get an insight of the features of the problem. Some of these allow analytical solutions which lead to bounds on the achievable optimal solution. We also establish bounds by investigating several “naive” routing policies. In the second part of this work, we build the multi-stage stochastic programming model of the TpTRP, which is hard to solve due to the integer variables introduced in the calculation of the top-percentile traffic. A lift-and-project based cutting plane method is investigated in solving the SMIP for very small examples of TpTRP. Nevertheless it is too inefficient to be applicable on large sized instances. As an alternative, we explore the solution of the TpTRP as a Stochastic Dynamic Programming (SDP) problem by a discretization of the state space. This SDP model gives us achievable routing policies on small size instances of the TpTRP, which of course improve the naive routing policies. However, the solution approach based on SDP suffers from the curse of dimensionality which restricts its applicability. To overcome this we suggest using Approximate Dynamic Programming (ADP) which largely avoids the curse of dimensionality by exploiting the structure of the problem to construct parameterized approximations of the value function in SDP and train the model iteratively to get a converged set of parameters. The resulting ADP model with discrete parameter for every time interval works well for medium size instances of TpTRP, though it still requires too long to be trained for large size instances. To make the realistically sized TpTRP problem solvable, we improve on the ADP model by using Bezier Curves/Surfaces to do the aggregation over time. This modification accelerates the efficiency of parameter training in the solution of the ADP model, which makes the realistically sized TpTRP tractable.

We propose a new approach to optimize operations of hydro storage systems with multiple connected reservoirs whose operators participate in wholesale electricity markets. Our formulation integrates short-term intraday with long-term interday decisions. The intraday problem considers bidding decisions as well as storage operation during the day and is formulated as a stochastic program. The interday problem is modeled as a Markov decision process of managing storage operation over time, for which we propose integrating stochastic dual dynamic programming with approximate dynamic programming. We show that the approximate solution converges towards an upper bound of the optimal solution. To demonstrate the efficiency of the solution approach, we fit an econometric model to actual price and in inflow data and apply the approach to a case study of an existing hydro storage system. Our results indicate that the approach is tractable for a real-world application and that the gap between theoretical upper and a simulated lower bound decreases sufficiently fast. (authors' abstract)

The thesis focuses on a model that seeks to address patient scheduling step of the surgical scheduling process to determine the number of surgeries to perform in a given day. Specifically, provided a master schedule that provides a cyclic breakdown of total OR availability into specific daily allocations to each surgical specialty, we look to provide a scheduling policy for all surgeries that minimizes a combination of the lead time between patient request and surgery date, overtime in the ORs and congestion in the wards. We cast the problem of generating optimal control strategies into the framework of Markov Decision Process (MDP). The Approximate Dynamic Programming (ADP) approach has been employed to solving the model which would otherwise be intractable due to the size of the state space. We assess performance of resulting policy and quality of the driven policy through simulation and we provide our policy insights and conclusions.

The thesis focuses on a model that seeks to address patient scheduling step of the surgical scheduling process to determine the number of surgeries to perform in a given day. Specifically, provided a master schedule that provides a cyclic breakdown of total OR availability into specific daily allocations to each surgical specialty, we look to provide a scheduling policy for all surgeries that minimizes a combination of the lead time between patient request and surgery date, overtime in the ORs and congestion in the wards. We cast the problem of generating optimal control strategies into the framework of Markov Decision Process (MDP). The Approximate Dynamic Programming (ADP) approach has been employed to solving the model which would otherwise be intractable due to the size of the state space. We assess performance of resulting policy and quality of the driven policy through simulation and we provide our policy insights and conclusions.

The thesis focuses on a model that seeks to address patient scheduling step of the surgical scheduling process to determine the number of surgeries to perform in a given day. Specifically, provided a master schedule that provides a cyclic breakdown of total OR availability into specific daily allocations to each surgical specialty, we look to provide a scheduling policy for all surgeries that minimizes a combination of the lead time between patient request and surgery date, overtime in the ORs and congestion in the wards. We cast the problem of generating optimal control strategies into the framework of Markov Decision Process (MDP). The Approximate Dynamic Programming (ADP) approach has been employed to solving the model which would otherwise be intractable due to the size of the state space. We assess performance of resulting policy and quality of the driven policy through simulation and we provide our policy insights and conclusions.

No description available.

Data-driven decision making has become more popular in today’s businesses including logistics and vehicle routing. Leveraging historical data, companies can achieve goals such as customer satisfaction management, scalable and efficient operation, and higher overall revenue. In the management of customer satisfaction, logistics companies use consistent assignment of their drivers to customers over time. Creating this consistency takes time and depends on the history experienced between the company and the customer. While pursuing this goal, companies trade off the cost of capacity with consistency because demand is unknown on a daily basis. We propose concepts and methods that enable a parcel delivery company to balance the trade-off between cost and customer satisfaction. We use clustering methods that use cumulative historical service data to generate better consistency using the information entropy measure. Parcel delivery companies route many vehicles to serve customer requests on a daily basis. While clustering was important to the development of early routing algorithms, modern solution methods rely on metaheuristics, which are not easily deployable and often do not have open source code bases. We propose a two-stage, shape-based clustering approach that efficiently obtains a clustering of delivery request locations. Our solution technique is based on creating clusters that form certain shapes with respect to the depot. We obtain a routing solution by ordering all locations in every cluster separately. Our results are competitive with a state-of-the-art vehicle routing solver in terms of quality. Moreover, the results show that the algorithm is more scalable and is robust to problem parameters in terms of runtime. Fish trawling can be considered as a vehicle routing problem where the main objective is to maximize the amount of fish (revenue) facing uncertainty on catch. This uncertainty creates an embedded prediction problem before deciding where to harvest. Using previous catch data to train prediction models, we solve the routing problem a fish trawler faces using dynamically updated routing decisions allowing for spatiotemporal correlation in the random catch. We investigate the relationship between the quality of predictions and the quality of revenue generated as a result.

We study simulation optimization methods for the stochastic economic lot scheduling problem. In contrast to prior research, we focus on methods that treat this problem as a black box. Based on a large-scale numerical study, we compare approximate dynamic programming with a global search for parameters of simple control policies. We propose two value function approximation schemes based on linear combinations of piecewise- constant functions as well as control policies that can be described by a small set of parameters. While approximate value iteration worked well for small problems with three products, it was clearly outperformed by the global policy search as soon as problem size increased. The most reliable choice in our study was a globally optimized fixed-cycle policy. An additional analysis of the response surface of model parameters on optimal average cost revealed that the cost effect of product diversity was negligible. (authors' abstract)

No description available.

<p>We propose an approximation scheme for single-product periodic-review inventory systems with L-natural-convex structure. We lay out three well-studied inventory models, namely the lost-sales system, the perishable inventory system, and the joint inventory-pricing problem. We approximate the value functions for these models by the class of L-natural-convex quadratic functions, through the technique of linear programming approach to approximate dynamic programming. A series of heuristics are derived based on the quadratic approximation, and their performances are evaluated by comparison with existing heuristics. We present the numerical results and show that our heuristics outperform the benchmarks for majority of cases and scale well with long lead times. In this dissertation we also discuss the alternative strategies we have tried but with unsatisfactory result.</p> / Dissertation