Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 10

Dynamic Programming Related Abstracts

10 Assignment of Airlines Technical Members under Disruption

Authors: Walid MOUDANI

Abstract:

The Crew Reserve Assignment Problem (CRAP) considers the assignment of the crew members to a set of reserve activities covering all the scheduled flights in order to ensure a continuous plan so that operations costs are minimized while its solution must meet hard constraints resulting from the safety regulations of Civil Aviation as well as from the airlines internal agreements. The problem considered in this study is of highest interest for airlines and may have important consequences on the service quality and on the economic return of the operations. In this communication, a new mathematical formulation for the CRAP is proposed which takes into account the regulations and the internal agreements. While current solutions make use of Artificial Intelligence techniques run on main frame computers, a low cost approach is proposed to provide on-line efficient solutions to face perturbed operating conditions. The proposed solution method uses a dynamic programming approach for the duties scheduling problem and when applied to the case of a medium airline while providing efficient solutions, shows good potential acceptability by the operations staff. This optimization scheme can then be considered as the core of an on-line Decision Support System for crew reserve assignment operations management.

Keywords: combinatorial optimization, Dynamic Programming, airlines operations management, crew scheduling

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9 A Dynamic Solution Approach for Heart Disease Prediction

Authors: Walid MOUDANI

Abstract:

The healthcare environment is generally perceived as being information rich yet knowledge poor. However, there is a lack of effective analysis tools to discover hidden relationships and trends in data. In fact, valuable knowledge can be discovered from application of data mining techniques in healthcare system. In this study, a proficient methodology for the extraction of significant patterns from the coronary heart disease warehouses for heart attack prediction, which unfortunately continues to be a leading cause of mortality in the whole world, has been presented. For this purpose, we propose to enumerate dynamically the optimal subsets of the reduced features of high interest by using rough sets technique associated to dynamic programming. Therefore, we propose to validate the classification using Random Forest (RF) decision tree to identify the risky heart disease cases. This work is based on a large amount of data collected from several clinical institutions based on the medical profile of patient. Moreover, the experts’ knowledge in this field has been taken into consideration in order to define the disease, its risk factors, and to establish significant knowledge relationships among the medical factors. A computer-aided system is developed for this purpose based on a population of 525 adults. The performance of the proposed model is analyzed and evaluated based on set of benchmark techniques applied in this classification problem.

Keywords: Rough Sets, Dynamic Programming, multi-classifier decisions tree, features reduction

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8 Regret-Regression for Multi-Armed Bandit Problem

Authors: Deyadeen Ali Alshibani

Abstract:

In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail.

Keywords: Optimization, Optimal, Dynamic Programming, bandit problem

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7 Optimal Maintenance and Improvement Policies in Water Distribution System: Markov Decision Process Approach

Authors: Go Bong Choi, Jong Min Lee, Jong Woo Kim, Sang Hwan Son, Dae Shik Kim, Jung Chul Suh

Abstract:

The Markov Decision Process (MDP) based methodology is implemented in order to establish the optimal schedule which minimizes the cost. Formulation of MDP problem is presented using the information about the current state of pipe, improvement cost, failure cost and pipe deterioration model. The objective function and detailed algorithm of dynamic programming (DP) are modified due to the difficulty of implementing the conventional DP approaches. The optimal schedule derived from suggested model is compared to several policies via Monte Carlo simulation. Validity of the solution and improvement in computational time are proved.

Keywords: Monte Carlo Simulation, Dynamic Programming, Weibull distribution, Markov decision processes, periodic replacement

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6 Optimal Scheduling for Energy Storage System Considering Reliability Constraints

Authors: Jin-O Kim, Wook-Won Kim, Je-Seok Shin

Abstract:

This paper propose the method for optimal scheduling for battery energy storage system with reliability constraint of energy storage system in reliability aspect. The optimal scheduling problem is solved by dynamic programming with proposed transition matrix. Proposed optimal scheduling method guarantees the minimum fuel cost within specific reliability constraint. For evaluating proposed method, the timely capacity outage probability table (COPT) is used that is calculated by convolution of probability mass function of each generator. This study shows the result of optimal schedule of energy storage system.

Keywords: Dynamic Programming, energy storage system (ESS), optimal scheduling, reliability constraints

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5 Dynamic Programming Based Algorithm for the Unit Commitment of the Transmission-Constrained Multi-Site Combined Heat and Power System

Authors: A. Rong, P. B. Luh, R. Lahdelma

Abstract:

High penetration of intermittent renewable energy sources (RES) such as solar power and wind power into the energy system has caused temporal and spatial imbalance between electric power supply and demand for some countries and regions. This brings about the critical need for coordinating power production and power exchange for different regions. As compared with the power-only systems, the combined heat and power (CHP) systems can provide additional flexibility of utilizing RES by exploiting the interdependence of power and heat production in the CHP plant. In the CHP system, power production can be influenced by adjusting heat production level and electric power can be used to satisfy heat demand by electric boiler or heat pump in conjunction with heat storage, which is much cheaper than electric storage. This paper addresses multi-site CHP systems without considering RES, which lay foundation for handling penetration of RES. The problem under study is the unit commitment (UC) of the transmission-constrained multi-site CHP systems. We solve the problem by combining linear relaxation of ON/OFF states and sequential dynamic programming (DP) techniques, where relaxed states are used to reduce the dimension of the UC problem and DP for improving the solution quality. Numerical results for daily scheduling with realistic models and data show that DP-based algorithm is from a few to a few hundred times faster than CPLEX (standard commercial optimization software) with good solution accuracy (less than 1% relative gap from the optimal solution on the average).

Keywords: Dynamic Programming, multi-site combined heat and power system, relaxed states, transmission-constrained generation unit commitment

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4 Revenue Management of Perishable Products Considering Freshness and Price Sensitive Customers

Authors: Onur Kaya, Halit Bayer

Abstract:

Global grocery and supermarket sales are among the largest markets in the world and perishable products such as fresh produce, dairy and meat constitute the biggest section of these markets. Due to their deterioration over time, the demand for these products depends highly on their freshness. They become totally obsolete after a certain amount of time causing a high amount of wastage and decreases in grocery profits. In addition, customers are asking for higher product variety in perishable product categories, leading to less predictable demand per product and to more out-dating. Effective management of these perishable products is an important issue since it is observed that billions of dollars’ worth of food is expired and wasted every month. We consider coordinated inventory and pricing decisions for perishable products with a time and price dependent random demand function. We use stochastic dynamic programming to model this system for both periodically-reviewed and continuously-reviewed inventory systems and prove certain structural characteristics of the optimal solution. We prove that the optimal ordering decision scenario has a monotone structure and the optimal price value decreases by time. However, the optimal price changes in a non-monotonic structure with respect to inventory size. We also analyze the effect of 1 different parameters on the optimal solution through numerical experiments. In addition, we analyze simple-to-implement heuristics, investigate their effectiveness and extract managerial insights. This study gives valuable insights about the management of perishable products in order to decrease wastage and increase profits.

Keywords: Pricing, Dynamic Programming, age-dependent demand, perishable inventory

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3 A Stochastic Vehicle Routing Problem with Ordered Customers and Collection of Two Similar Products

Authors: Epaminondas G. Kyriakidis, Theodosis D. Dimitrakos, Constantinos C. Karamatsoukis

Abstract:

The vehicle routing problem (VRP) is a well-known problem in Operations Research and has been widely studied during the last fifty-five years. The context of the VRP is that of delivering or collecting products to or from customers who are scattered in a geographical area and have placed orders for these products. A vehicle or a fleet of vehicles start their routes from a depot and visit the customers in order to satisfy their demands. Special attention has been given to the capacitated VRP in which the vehicles have limited carrying capacity for the goods that are delivered or collected. In the present work, we present a specific capacitated stochastic vehicle routing problem which has many realistic applications. We develop and analyze a mathematical model for a specific vehicle routing problem in which a vehicle starts its route from a depot and visits N customers according to a particular sequence in order to collect from them two similar but not identical products. We name these products, product 1 and product 2. Each customer possesses items either of product 1 or product 2 with known probabilities. The number of the items of product 1 or product 2 that each customer possesses is a discrete random variable with known distribution. The actual quantity and the actual type of product that each customer possesses are revealed only when the vehicle arrives at the customer’s site. It is assumed that the vehicle has two compartments. We name these compartments, compartment 1 and compartment 2. It is assumed that compartment 1 is suitable for loading product 1 and compartment 2 is suitable for loading product 2. However, it is permitted to load items of product 1 into compartment 2 and items of product 2 into compartment 1. These actions cause costs that are due to extra labor. The vehicle is allowed during its route to return to the depot to unload the items of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. The objective is to find the optimal routing strategy, i.e. the routing strategy that minimizes the total expected cost among all possible strategies for servicing all customers. It is possible to develop a suitable dynamic programming algorithm for the determination of the optimal routing strategy. It is also possible to prove that the optimal routing strategy has a specific threshold-type strategy. Specifically, it is shown that for each customer the optimal actions are characterized by some critical integers. This structural result enables us to design a special-purpose dynamic programming algorithm that operates only over these strategies having this structural property. Extensive numerical results provide strong evidence that the special-purpose dynamic programming algorithm is considerably more efficient than the initial dynamic programming algorithm. Furthermore, if we consider the same problem without the assumption that the customers are ordered, numerical experiments indicate that the optimal routing strategy can be computed if N is smaller or equal to eight.

Keywords: Dynamic Programming, Vehicle Routing Problem, similar products, stochastic demands, stochastic preferences

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2 Optimal Delivery of Two Similar Products to N Ordered Customers

Authors: Epaminondas G. Kyriakidis, Theodosis D. Dimitrakos, Constantinos C. Karamatsoukis

Abstract:

The vehicle routing problem (VRP) is a well-known problem in Operations Research and has been widely studied during the last fifty-five years. The context of the VRP is that of delivering products located at a central depot to customers who are scattered in a geographical area and have placed orders for these products. A vehicle or a fleet of vehicles start their routes from the depot and visit the customers in order to satisfy their demands. Special attention has been given to the capacitated VRP in which the vehicles have limited carrying capacity of the goods that must be delivered. In the present work, we present a specific capacitated stochastic vehicle routing problem which has realistic applications to distributions of materials to shops or to healthcare facilities or to military units. A vehicle starts its route from a depot loaded with items of two similar but not identical products. We name these products, product 1 and product 2. The vehicle must deliver the products to N customers according to a predefined sequence. This means that first customer 1 must be serviced, then customer 2 must be serviced, then customer 3 must be serviced and so on. The vehicle has a finite capacity and after servicing all customers it returns to the depot. It is assumed that each customer prefers either product 1 or product 2 with known probabilities. The actual preference of each customer becomes known when the vehicle visits the customer. It is also assumed that the quantity that each customer demands is a random variable with known distribution. The actual demand is revealed upon the vehicle’s arrival at customer’s site. The demand of each customer cannot exceed the vehicle capacity and the vehicle is allowed during its route to return to the depot to restock with quantities of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. If there is shortage for the desired product, it is permitted to deliver the other product at a reduced price. The objective is to find the optimal routing strategy, i.e. the routing strategy that minimizes the expected total cost among all possible strategies. It is possible to find the optimal routing strategy using a suitable stochastic dynamic programming algorithm. It is also possible to prove that the optimal routing strategy has a specific threshold-type structure, i.e. it is characterized by critical numbers. This structural result enables us to construct an efficient special-purpose dynamic programming algorithm that operates only over those routing strategies having this structure. The findings of the present study lead us to the conclusion that the dynamic programming method may be a very useful tool for the solution of specific vehicle routing problems. A problem for future research could be the study of a similar stochastic vehicle routing problem in which the vehicle instead of delivering, it collects products from ordered customers.

Keywords: Dynamic Programming, Vehicle Routing Problem, stochastic demands, stochastic preferences, collection of similar products

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1 Adaption Model for Building Agile Pronunciation Dictionaries Using Phonemic Distance Measurements

Authors: Akella Amarendra Babu, Rama Devi Yellasiri, Natukula Sainath

Abstract:

Where human beings can easily learn and adopt pronunciation variations, machines need training before put into use. Also humans keep minimum vocabulary and their pronunciation variations are stored in front-end of their memory for ready reference, while machines keep the entire pronunciation dictionary for ready reference. Supervised methods are used for preparation of pronunciation dictionaries which take large amounts of manual effort, cost, time and are not suitable for real time use. This paper presents an unsupervised adaptation model for building agile and dynamic pronunciation dictionaries online. These methods mimic human approach in learning the new pronunciations in real time. A new algorithm for measuring sound distances called Dynamic Phone Warping is presented and tested. Performance of the system is measured using an adaptation model and the precision metrics is found to be better than 86 percent.

Keywords: Machine Learning, natural language processing, Dynamic Programming, pronunciation variations

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