**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1639

# Search results for: nonlinear integer programming.

##### 1639 Dynamic Slope Scaling Procedure for Stochastic Integer Programming Problem

**Authors:**
Takayuki Shiina

**Abstract:**

**Keywords:**
stochastic programming problem with recourse,
simple
integer recourse,
dynamic slope scaling procedure

##### 1638 Stochastic Programming Model for Power Generation

**Authors:**
Takayuki Shiina

**Abstract:**

**Keywords:**
electric power capacity expansion problem,
integerprogramming,
L-shaped method,
stochastic programming

##### 1637 Modern Method for Solving Pure Integer Programming Models

**Authors:**
G. Shojatalab

**Abstract:**

**Keywords:**
Integer,
Programming,
Operation Research,
Variables of decision.

##### 1636 Generic Model for Timetabling Problems by Integer Linear Programming Approach

**Authors:**
N. A. H. Aizam,
V. Uvaraja

**Abstract:**

The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It is widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming models to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describes about creating a general model which solves different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.

**Keywords:**
AIMMS mathematical software,
integer linear
programming,
scheduling problems,
timetabling.

##### 1635 A New Integer Programming Formulation for the Chinese Postman Problem with Time Dependent Travel Times

**Authors:**
Jinghao Sun,
Guozhen Tan,
Guangjian Hou

**Abstract:**

**Keywords:**
Chinese Postman Problem,
Time Dependent,
Integer Programming,
Upper Bound Analysis.

##### 1634 Robot Path Planning in 3D Space Using Binary Integer Programming

**Authors:**
Ellips Masehian,
Golnaz Habibi

**Abstract:**

**Keywords:**
3D C-space,
Binary Integer Programming (BIP),
Delaunay Tessellation,
Robot Motion Planning.

##### 1633 Multi-Objective Optimization of Combined System Reliability and Redundancy Allocation Problem

**Authors:**
Vijaya K. Srivastava,
Davide Spinello

**Abstract:**

This paper presents established 3** ^{n}** enumeration procedure for mixed integer optimization problems for solving multi-objective reliability and redundancy allocation problem subject to design constraints. The formulated problem is to find the optimum level of unit reliability and the number of units for each subsystem. A number of illustrative examples are provided and compared to indicate the application of the superiority of the proposed method.

**Keywords:**
Integer programming,
mixed integer programming,
multi-objective optimization,
reliability redundancy allocation.

##### 1632 Airport Check-In Optimization by IP and Simulation in Combination

**Authors:**
Ahmad Thanyan Al-Sultan

**Abstract:**

The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

**Keywords:**
Airport terminal,
Integer programming,
Scheduling,
Simulation.

##### 1631 Integer Programming Model for the Network Design Problem with Facility Dependent Shortest Path Routing

**Authors:**
Taehan Lee

**Abstract:**

**Keywords:**
Integer programming,
multicommodity network
design,
routing,
shortest path.

##### 1630 A new Heuristic Algorithm for the Dynamic Facility Layout Problem with Budget Constraint

**Authors:**
Parham Azimi,
Hamid Reza Charmchi

**Abstract:**

**Keywords:**
Budget constraint,
Dynamic facility layout problem,
Integer programming,
Simulation

##### 1629 A Mixed Integer Linear Programming Model for Flexible Job Shop Scheduling Problem

**Authors:**
Mohsen Ziaee

**Abstract:**

**Keywords:**
Scheduling,
flexible job shop,
makespan,
mixed integer linear programming.

##### 1628 Timetabling Communities’ Demands for an Effective Examination Timetabling Using Integer Linear Programming

**Authors:**
N. F. Jamaluddin,
N. A. H. Aizam

**Abstract:**

This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed.

**Keywords:**
Demands,
educational timetabling,
integer linear programming,
scheduling,
university examination timetabling problem.

##### 1627 Minimizing Energy Consumption in Wireless Sensor Networks using Binary Integer Linear Programming

**Authors:**
Chompunut Jantarasorn,
Chutima Prommak

**Abstract:**

The important issue considered in the widespread deployment of Wireless Sensor Networks (WSNs) is an efficiency of the energy consumption. In this paper, we present a study of the optimal relay station planning problems using Binary Integer Linear Programming (BILP) model to minimize the energy consumption in WSNs. Our key contribution is that the proposed model not only ensures the required network lifetime but also guarantees the radio connectivity at high level of communication quality. Specially, we take into account effects of noise, signal quality limitation and bit error rate characteristics. Numerical experiments were conducted in various network scenarios. We analyzed the effects of different sensor node densities and distribution on the energy consumption.

**Keywords:**
Binary Integer Linear Programming,
BILP,
Energy
consumption,
Optimal node placement and Wireless sensor networks.

##### 1626 Development of a Comprehensive Electricity Generation Simulation Model Using a Mixed Integer Programming Approach

**Authors:**
Erik Delarue,
David Bekaert,
Ronnie Belmans,
William D'haeseleer

**Abstract:**

This paper presents the development of an electricity simulation model taking into account electrical network constraints, applied on the Belgian power system. The base of the model is optimizing an extensive Unit Commitment (UC) problem through the use of Mixed Integer Linear Programming (MILP). Electrical constraints are incorporated through the implementation of a DC load flow. The model encloses the Belgian power system in a 220 – 380 kV high voltage network (i.e., 93 power plants and 106 nodes). The model features the use of pumping storage facilities as well as the inclusion of spinning reserves in a single optimization process. Solution times of the model stay below reasonable values.

**Keywords:**
Electricity generation modeling,
Unit Commitment(UC),
Mixed Integer Linear Programming (MILP),
DC load flow.

##### 1625 Optimal Production Planning in Aromatic Coconuts Supply Chain Based On Mixed-Integer Linear Programming

**Authors:**
Chaimongkol Limpianchob

**Abstract:**

This work addresses the problem of production planning that arises in the production of aromatic coconuts from Samudsakhorn province in Thailand. The planning involves the forwarding of aromatic coconuts from the harvest areas to the factory, which is classified into two groups; self-owned areas and contracted areas, the decisions of aromatic coconuts flow in the plant, and addressing a question of which warehouse will be in use. The problem is formulated as a mixed-integer linear programming model within supply chain management framework. The objective function seeks to minimize the total cost including the harvesting, labor and inventory costs. Constraints on the system include the production activities in the company and demand requirements. Numerical results are presented to demonstrate the feasibility of coconuts supply chain model compared with base case.

**Keywords:**
Aromatic coconut,
supply chain management,
production planning,
mixed-integer linear programming.

##### 1624 Mathematical Rescheduling Models for Railway Services

**Authors:**
Zuraida Alwadood,
Adibah Shuib,
Norlida Abd Hamid

**Abstract:**

This paper presents the review of past studies concerning mathematical models for rescheduling passenger railway services, as part of delay management in the occurrence of railway disruption. Many past mathematical models highlighted were aimed at minimizing the service delays experienced by passengers during service disruptions. Integer programming (IP) and mixed-integer programming (MIP) models are critically discussed, focusing on the model approach, decision variables, sets and parameters. Some of them have been tested on real-life data of railway companies worldwide, while a few have been validated on fictive data. Based on selected literatures on train rescheduling, this paper is able to assist researchers in the model formulation by providing comprehensive analyses towards the model building. These analyses would be able to help in the development of new approaches in rescheduling strategies or perhaps to enhance the existing rescheduling models and make them more powerful or more applicable with shorter computing time.

**Keywords:**
Mathematical modelling,
Mixed-integer
programming,
Railway rescheduling,
Service delays.

##### 1623 A Bi-Objective Preventive Healthcare Facility Network Design with Incorporating Cost and Time Saving

**Authors:**
Mehdi Seifbarghy,
Keyvan Roshan

**Abstract:**

**Keywords:**
Preventive healthcare problems,
Non-linear integer
programming models,
Multi-objective decision making techniques

##### 1622 On Optimum Stratification

**Authors:**
M. G. M. Khan,
V. D. Prasad,
D. K. Rao

**Abstract:**

In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

**Keywords:**
Auxiliary variable,
Dynamic programming technique,
Nonlinear programming problem,
Optimum stratification,
Uniform distribution.

##### 1621 A Multi-Objective Model for Supply Chain Network Design under Stochastic Demand

**Authors:**
F. Alborzi,
H. Vafaei,
M.H. Gholami,
M.M. S. Esfahani

**Abstract:**

**Keywords:**
Mixed Integer Programming,
Multi-objective
Optimization,
Stochastic Demand,
Supply Chain Design,
Two Stage
Programming

##### 1620 Solving the Teacher Assignment-Course Scheduling Problem by a Hybrid Algorithm

**Authors:**
Aldy Gunawan,
Kien Ming Ng,
Kim Leng Poh

**Abstract:**

This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.

**Keywords:**
Timetabling problem,
mathematical programming
model,
hybrid algorithm,
simulated annealing.

##### 1619 Optimal Planning of Waste-to-Energy through Mixed Integer Linear Programming

**Authors:**
S. T. Tan,
H. Hashim,
W. S. Ho,
C. T. Lee

**Abstract:**

**Keywords:**
Mixed Integer Linear Programming (MILP),
optimization,
solid waste management (SWM),
Waste-to-energy (WTE).

##### 1618 A Fuzzy Mixed Integer Multi-Scenario Portfolio Optimization Model

**Authors:**
M. S. Osman,
A. A. Tharwat,
I. A. El-Khodary,
A. G. Chalabi

**Abstract:**

In this paper, we propose a multiple objective optimization model with respect to portfolio selection problem for investors looking forward to diversify their equity investments in a number of equity markets. Based on Markowitz-s M-V model we developed a Fuzzy Mixed Integer Multi-Objective Nonlinear Programming Problem (FMIMONLP) to maximize the investors- future gains on equity markets, reach the optimal proportion of the budget to be invested in different equities. A numerical example with a comprehensive analysis on artificial data from several equity markets is presented in order to illustrate the proposed model and its solution method. The model performed well compared with the deterministic version of the model.

**Keywords:**
Equity Markets,
Future Scenarios,
PortfolioSelection,
Multiple Criteria Fuzzy Optimization

##### 1617 Determining Optimum Time Multiplier Setting of Overcurrent Relays Using Mixed Integer Linear Programming

**Authors:**
P. N. Korde,
P. P. Bedekar

**Abstract:**

The time coordination of overcurrent relays (OCR) in a power distribution network is of great importance, as it reduces the power outages by avoiding the mal-operation of the backup relays. For this, the optimum value of the time multiplier setting (TMS) of OCRs should be chosen. The problem of determining the optimum value of TMS of OCRs in power distribution networks is formulated as a constrained optimization problem. The objective is to find the optimum value of TMS of OCRs to minimize the time of operation of relays under the constraint of maintaining the coordination of relays. A power distribution network can have a combination of numerical and electromechanical relays. The TMS of numerical relays can be set to any real value (which satisfies the constraints of the problem), whereas the TMS of electromechanical relays can be set in fixed step (0 to 1 in steps of 0.05). The main contribution of this paper is a formulation of the problem as a mixed-integer linear programming (MILP) problem and application of Gomory's cutting plane method to find the optimum value of TMS of OCRs. The TMS of electromechanical relays are taken as integers in the range 1 to 20 in the step of 1, and these values are mapped to 0.05 to 1 in the step of 0.05. The results obtained are compared with those obtained using a simplex method and its variants. It has been shown that the mixed-integer linear programming method outperforms the simplex method (and its variants) in the case of a system having a combination of numerical and electromechanical relays.

**Keywords:**
Backup protection,
constrained optimization,
Gomory's cutting plane method,
mixed-integer linear programming,
overcurrent relay coordination,
simplex method.

##### 1616 Determining Optimal Demand Rate and Production Decisions: A Geometric Programming Approach

**Authors:**
Farnaz G. Nezami,
Mir B. Aryanezhad,
Seyed J. Sadjadi

**Abstract:**

**Keywords:**
Geometric programming,
marketing,
nonlinear
optimization,
production.

##### 1615 Study on Optimal Control Strategy of PM2.5 in Wuhan, China

**Authors:**
Qiuling Xie,
Shanliang Zhu,
Zongdi Sun

**Abstract:**

In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

**Keywords:**
Grey relational degree,
multiple linear regression,
membership function,
nonlinear programming.

##### 1614 Supplier Selection by Considering Cost and Reliability

**Authors:**
K. -H. Yang

**Abstract:**

**Keywords:**
Mixed integer programming,
quantitative approach,
supplier’s reliability,
supplier selection.

##### 1613 Use of Linear Programming for Optimal Production in a Production Line in Saudi Food Co.

**Authors:**
Qasim M. Kriri

**Abstract:**

Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

**Keywords:**
Parameter linear programming,
objective function,
sensitivity analysis,
optimize profit.

##### 1612 Optimization of Petroleum Refinery Configuration Design with Logic Propositions

**Authors:**
Cheng Seong Khor,
Xiao Qi Yeoh

**Abstract:**

**Keywords:**
Mixed-integer linear programming (MILP),
petroleum refinery,
process synthesis,
superstructure.

##### 1611 Discrete Time Optimal Solution for the Connection Admission Control Problem

**Authors:**
C. Bruni,
F. Delli Priscoli,
G. Koch,
I. Marchetti

**Abstract:**

The Connection Admission Control (CAC) problem is formulated in this paper as a discrete time optimal control problem. The control variables account for the acceptance/ rejection of new connections and forced dropping of in-progress connections. These variables are constrained to meet suitable conditions which account for the QoS requirements (Link Availability, Blocking Probability, Dropping Probability). The performance index evaluates the total throughput. At each discrete time, the problem is solved as an integer-valued linear programming one. The proposed procedure was successfully tested against suitably simulated data.

**Keywords:**
Connection Admission Control,
Optimal Control,
Integer valued Linear Programming,
Quality of Service Requirements,
Robust Control.

##### 1610 Mathematical Model and Solution Algorithm for Containership Operation/Maintenance Scheduling

**Authors:**
Hun Go,
Ji-Su Kim,
Dong-Ho Lee

**Abstract:**

**Keywords:**
Containerships,
operation and preventive maintenance
schedules,
integer programming,
heuristic