Linear Programming Mathematical Model Research Articles

DESIGN OF SPRINKLER IRRIGATION TAPERED MAIN LINE BY LINEAR PROGRAMMING

A mathematical linear programming model based on Microsoft Excel spreadsheet was developed to design mainline of sprinkler irrigation system. The line considered has a length of 522 m combined with five different nominal diameters of 3', 3-1/2, 4, 5 and (internal diameter of 73.7, 85.4, 97.2, 122.3and 149.3 mm) which are commercially available in the Egyptian markets. The objective function was to minimize the cost of the mainline pipe; and the constraints considered were commercial availability of diameters. The head loss calculations are based on four different head loss formulas. These are the Hazen-Williams, Manning, Scobey, and Darcy-Weisbach equations. The model estimates the number of pipe unit according to the available manufacturer length. ( taken as 6 meter long). The lowest cost of 7924 US$ was found by the Darcy Wiesbach equation followed by Manning as 8030, Hazen–Williams as 8051 and Scobey as 8385. Validity and sensitivity of the model were confirmed. The effect of land slope and inlet pressure to the system was studied. The results indicated that increasing in inlet pressure decreases the cost of the mainline. Meanwhile, the cost of the mainline is proportionally increased by increasing the up slope of the land, and inversely increases by increasing the down slope of the land.

A Resource-Constrained Project Scheduling Problem with Fuzzy Activity Times

This paper is about the Resource-Constrained Project Scheduling Problem) RCPSP) which is one of the most important problems in last three decades and many researchers have paid attention to it and have reached useful results. In this paper, to cope with uncertainty issue, the RCPSP is studied under fuzzy environment where activity times are assumed to be fuzzy numbers. For this problem with fuzzy numbers as activity times, a linear mathematical programming model is presented. The objective function of the model is minimizing the completion time of project. Since the activity times are fuzzy numbers, finish time is also a fuzzy number. Hence, the model is transformed to a crisp multi-objective linear programming model. To illustrate the solution method, a numerical example is solved under both fuzzy and crisp environment and the results are compared. To prove the efficiency of the proposed method the results of the proposed solution method, some benchmark problems obtained from PSPLIB are utilized.

Relative Concentration-Based Mathematical Optimization for the Fluctuant Analysis of Multi-Impurity Hydrogen Networks

Hydrogen is a crucial and expensive resource for refineries. Hydrogen network integration is an effective way to conserve fresh hydrogen. On the basis of relative concentration analysis, a mixed integer linear programming (MILP) mathematical model is established to synthesize refinery multi-impurity hydrogen networks. By correlating the hydrogen consumption of a sink with its oil processing throughputs, this model reveals the fresh hydrogen variation tendency caused by fluctuation of each capacity, and determines the key sink(s) of a hydrogen network with multiple impurities on the premise of minimum fresh hydrogen consumption. With a structure matrix variable, practical hydrogen networks can be analyzed through the proposed model. The results show that the novel method in this paper is superior to traditional absolute concentration-based methods in fresh hydrogen conservation under cases of static, fluctuant throughputs, and fluctuant throughputs with restricted network structure. Two cases are employed ...

Mathematical modeling in municipal solid waste management: case study of Tehran.

BackgroundSolid Waste Management (SWM) in metropolises with systematic methods and following environmental issues, is one of the most important subjects in the area of urban management. In this regard, it is regarded as a legal entity so that its activities are not overshadowed by other urban activities. In this paper, a linear mathematical programming model has been designed for integrated SWM. Using Lingo software and required data from Tehran, the proposed model has been applied for Tehran SWM system as a case study.ResultsTo determine the optimal status of the available system for Tehran’s Solid Waste Management System (SWMS), a novel linear programming model is applied. Tehran has 22 municipal regions with 11 transfer stations and 10 processing units. By running of the model, the transfer stations and processing units are decreased to 10 and 6 units, respectively.ConclusionsThe proposed model is an alternative method for improvement the SWMS by decreasing the transfer stations and processing units.

Study of Some Agricultural Crop Production Planning Condition through Fuzzy Multi-Objective Linear Programming Mathematical Model

Study of Some Agricultural Crop Production Planning Condition through Fuzzy Multi-Objective Linear Programming Mathematical Model

Linear Programming in the economic estimate of livestock-crop integration: application to a Brazilian dairy farm

A linear programming mathematical model was applied to a representative dairy farm located in Brazil. The results showed that optimization models are relevant tools to assist in the planning and management of agricultural production, as well as to assist in estimating potential gains from the use of integrated systems. Diversification was a necessary condition for economic viability. A total cost reduction potential of about 30% was revealed when a scenario of lower levels of diversification was contrasted to one of higher levels. Technical complementarities proved to be important sources of economies. The possibility of reusing nitrogen, phosphorus, and potassium present in animal waste could be increased to 167%, while water reuse could be increased up to 150%. In addition to economic gains, integrated systems bring benefits to the environment, especially with reference to the reuse of resources. The cost dilution of fixed production factors can help economies of scope to be achieved. However, this does not seem to have been the main source of these benefits. Still, the percentage of land use could increase up to 30.7% when the lowest and the highest diversification scenarios were compared. The labor coefficient could have a 4.3 percent increase. Diversification also leads to drastic transaction cost reductions.

A generic method for energy-efficient and energy-cost-effective production at the unit process level

Generally, industry includes various sectors like manufacturing, energy, materials & mining, and transportation. Industry consumes about one half of the world's total delivered energy, and manufacturing is one of the energy-intensive industrial sectors. With the rising energy price, the energy cost is becoming a controllable expenditure in manufacturing. In this paper, a generic method has been proposed to minimize the energy cost and improve the energy efficiency of manufacturing unit processes. Finite state machines have been used to build the transitional state-based energy model of a single machine. A mixed-integer linear programming mathematical model has been formulated for energy-cost-aware job order scheduling on a single machine. A generic algorithm has been implemented to search for an energy-cost-effective schedule at volatile energy prices with the constraint of due dates. As a result, plant managers can have an energy-cost-effective job order schedule which is associated with machine energy states along time, and can also get time-indexed energy simulation of the schedule. In comparison to most of the static scheduling approaches, stochasticity has been further handled through a cyclic interaction between the scheduler and the energy model, which facilitates to investigate how stochasticity on a shop floor affects the performance of energy-cost-aware scheduling. Empirical data have been used in the case study, including the power measured from a grinding machine, and the real-time pricing and time-of-use pricing tariffs. The proposed method has been demonstrated to be both energy-efficient and energy-cost-efficient even at the presence of stochasticity. As a joint effort of energy efficiency and demand response within demand side management, this method shows its effectiveness for contributing to the reduction of greenhouse gas emissions during peak periods, and for leading to energy-efficient, demand-responsive, and cost-effective manufacturing processes.

A decision model for selecting parts feeding policies in assembly lines

Purpose – The purpose of this paper is to develop an optimization model allowing the choice of parts feeding policy to assembly lines in order to minimize total cost. Design/methodology/approach – An integer linear programming mathematical model is developed to assign the optimal material feeding policy to each part type. The model allows choice between kitting, line stocking and just in time delivery policies. Findings – The choice of assembly lines feeding policy is not trivial and requires a thorough economic comparison of alternatives. It is found that a proper mix of parts feeding policies may be better that adopting a single material delivery policy for all parts. Research limitations/implications – The model is aimed at single-model assembly lines operating in a deterministic environment, but can be extended to the multi-model line case. While relevant quantitative cost drivers are included, some context-related qualitative factors are not included yet. The model assumes that information about product structure and part requirements are known and that a preliminary design of the assembly system has been carried out. Practical implications – Production managers are given a quantitative-decision tool to determine the optimal mix of material supply policies at an early decision stage. Originality/value – Respect previous simplified literature models, this approach allows to quantify a number of additional factors which are critical for successful implementation of cost-effective parts feeding systems, allowing comparison of alternative policies on a consistent basis.

An energy management approach for renewable energy integration with power generation and water desalination

The share of the renewable energy sources (RES) in the global electricity market is substantially increasing as a result of the commitment of many countries to increase the contribution of the RES to their energy mix. However, the integration of RES in the electricity grid increases the complexity of the grid management due to the variability and the intermittent nature of these energy sources. Energy storage solutions such as batteries offer either short-term storage that is not sufficient or longer period storage that is significantly expensive. This paper introduces an energy management approach which can be applied in the case of power and desalinated water generation. The approach is based on mathematical optimization model which accounts for random variations in demands and energy supply. The approach allows using desalination plants as a deferrable load to mitigate for the variability of the renewable energy supply and water and/or electricity demands. A mathematical linear programming model is developed to show the applicability of this idea and its effectiveness in reducing the impact of the uncertainty in the environment. The model is solved for the real world case of Saudi Arabia. The optimal solution accounts for random variations in the renewable energy supply and water and/or electricity demands while minimizing the total costs for generating water and power.

Globally Optimal Superconducting Homogeneous Magnet Design for an Asymmetric 3.0 T Head MRI Scanner

This paper describes a hybrid numerical method with a combination of linear programming (LP) and nonlinear programming to design an asymmetric magnetic resonance imaging (MRI) system for head imaging. The method was successfully employed to a 0.7 T open-style MRI. Recently, we have updated the LP mathematical model in the hybrid optimization strategy by adding maximum axial and radial magnetic field strength limitation to make the magnet safe. The whole magnet consists of eight coaxial coils asymmetry about the z-axis. The six innermost coils are the main coils with positive current direction and the two outermost coils are shielding coils with negative current direction. All coils contribute their efforts to produce a central magnetic field strength of 3.0 T over a 20 cm diameter of spherical volume, and the peak to peak homogeneity is 12 ppm. The temperature bore for the magnet is formed with two different diameters cylindrical bores which makes head and shoulder access to the imaging volume easier. A 5 Gauss footprint area is restricted larger than an elliptical region with the sizes of 3.5 m in radial and 4.0 m in axial direction. The results show that the methodology is very flexible and efficient for asymmetric MRI magnet design.

Fuzzy optimization of a waste-to-energy network system in an eco-industrial park

The Ulsan Eco-Industrial Park (EIP) in South Korea houses as many as 1,000 companies, which generate about 524,000 t/year of organic waste. Of this total, 34 % is recycled, 8 % is incinerated with energy recovery, and the rest (58 %) is disposed of by ocean dumping (45 %), landfilling (11 %), or incineration without energy recovery (2 %). Although 42 % of the total waste generated at Ulsan EIP is recycled for material and energy recovery, additional opportunities to recover energy from improperly disposed of or incompletely utilized waste are possible through existing waste-to-energy (WTE) networks. To find an optimal WTE network in the Ulsan EIP, a fuzzy mixed integer linear programming mathematical model was developed to meet energy supply and demand (in terms of both quantity and grade) while considering the satisfaction level of potential stakeholders (e.g., the EIP initiator and tenants). The developed model was applied to two different scenarios that considered the requirements of EIP tenants for waste treatment and energy recovery. Based on the satisfaction level of the stakeholders, the WTE networks were analyzed to establish an optimal WTE network with maximum energy production and a minimal payback period.

Minimizing the total weighted late work in scheduling of identical parallel processors with communication delays

This paper addresses a certain type of scheduling problem that arises when a parallel computation is to be executed on a set of identical parallel processors. It is assumed that if two precedence-related tasks are processed on two different processors, due to the information transferring, there will be a task-dependent communication delay between them. For each task, a processing time, a due date and a weight is given while the goal is to minimize the total weighted late work. An integer linear mathematical programming model and a branch-and-bound algorithm have been developed for the proposed problem. Comparing the results obtained by the proposed branch-and-bound algorithm with those obtained by CPLEX, indicates the effectiveness of the method.

Rational Analysis of Sewage Treatment

Sewage treatment problem is a typical linear programming problem, and can be solved by method of linear programming. In order to reflect the principle of fairness and make full use of self-purification capacity of environment, this paper gives rational analysis of the sewage disposal problems in 2007 Chinese Undergraduate Mathematical Modeling Contest. The mathematical model of linear programming is established, and solved by lingo optimization software. The results show that: by the principle of fairness, investment funds increased; by the principle of self-purification capacity of environment, investment funds decreased. The results can provide guidance for decision makers to choose different scheme.

A multi-step approach to long-term open-pit production planning

The objective of this paper is to develop, verify, and present a multi–step methodology for three interrelated key components of open–pit mine planning: controlled optimal phase–design, characterisation of selective mining–units, and long–term production scheduling optimisation. A hybrid solution methodology for open–pit phase–design using integer programming and a local search heuristic is presented. Next, a hierarchical clustering approach with size and shape control, which aggregates blocks into minable polygons constrained within the pushback boundaries, is presented; and finally, a mixed integer linear programming mathematical model, which uses the generated pushbacks and aggregates as the planning units to provide near–optimal practical life–of–mine schedules, is introduced. In addition, the model inherently solves the cut–off grade optimisation problem. Two case–studies of real–size deposits are presented to illustrate practicality of the developed methodologies, and also to compare the results against industrial conventional practices to assess validity, performance, strengths, and limitations of the developed methodologies.

Modeling and solving mixed-model assembly line balancing problem with setups. Part I: A mixed integer linear programming model

This paper is the first one of the two papers entitled “modeling and solving mixed-model assembly line balancing problem with setups”, which has the aim of developing the mathematical programming formulation of the problem and solving it with a hybrid meta-heuristic approach. In this current part, a mixed-integer linear mathematical programming (MILP) model for mixed-model assembly line balancing problem with setups is developed. The proposed MILP model considers some particular features of the real world problems such as parallel workstations, zoning constraints, and sequence dependent setup times between tasks, which is an actual framework in assembly line balancing problems. The main endeavor of Part-I is to formulate the sequence dependent setup times between tasks in type-I mixed-model assembly line balancing problem. The proposed model considers the setups between the tasks of the same model and the setups because of the model switches in any workstation. The capability of our MILP is tested through a set of computational experiments. Part-II tackles the problem with a multiple colony hybrid bees algorithm. A set of computational experiments is also carried out for the proposed approach in Part-II.

A hybrid cGA applied to the MLCLSP with overtime

A hybrid version of a compact genetic algorithm (cGA) is presented as approach to solve the Multi-Level Capacitated Lot Sizing Problem. The present paper extends results reported in [18]. The hybrid method combines a fix and optimize heuristic with cGA aiming to improve solutions generated by cGA. Also a linear mathematical programming model is solved to first evaluated solution provided by cGA. The performance of the hybrid compact genetic algorithm (HcGA) is evaluated over two sets of benchmark instances. The results are compared against methods from literature recently proposed for the same problem: two time-oriented decomposition heuristics and a hybrid multi-population genetic algorithm. A superior performance of HcGA is reported mainly for instances dealing with setup times and against time-oriented decomposition heuristics.

Optimization in day-ahead planning of energy trading

In the twentieth century electricity was produced and transmitted by and between monopolistic public electric power companies. Over the last twenty years, electricity markets have been deregulated allowing customers to choose from a number of competing suppliers and producers. On one hand electricity market participants try to first satisfy their own country’s demand and, on the other hand, to transmit electricity across borders into neighborhood markets. Cross-border transmission is part of a competition where market participants have non-discriminatory access to interconnected transmission lines. This paper examines the problem of day-ahead planning at trading sections of electricity companies. The underlying assumption is that the demand and supply are known in advance. Available transmission capacities are also known as well as additional transmission capacities that can be purchased. The prices and amounts of trading and transmission are subjects of auctions. The problem of day-ahead planning is here discussed from the perspective of a decision maker of an energy trading company (ETC). Decisions to be made are: where and how much electricity should the ETC buy and sell, and which transmission capacity will be used in order to maximize daily profit. The problem is formulated according to real-life experience of a Serbian ETC which trades in Central and South-East Europe. It is further modeled as a directed multiple-source and multiple-sink network and then represented by linear programming (LP) mathematical model in which the total daily profit is maximized subject to market constraints and flow capacities. The main goal of this model is to provide a useful tool for preparing auction bids. Numerical examples are given in order to illustrate possible applications of the model.

Fuzzy earthwork dynamic allocation and optimization for construction of high concrete face Rockfill dam

Due to the complexity of earthwork allocation system for the construction of high concrete face rockfill dam, traditional allocation and planning are not able to function properly in the construction process with strong randomness. In this paper, the working mechanism of earthwork dynamic allocation system is analyzed comprehensively and a solution to fuzzy earthwork dynamic allocation is proposed on the basis of uncertain factors in the earthwork allocation of a hydropower project. Under the premise of actual situation and the experience of the construction site, an all-coefficient-fuzzy linear programming mathematical model with fuzzy parameters and constraints for earthwork allocation is established according to the structure unit weighted ranking criteria. In this way, the deficiency of certain allocation model can be overcome. The application results indicate that the proposed method is more rational compared with traditional earthwork allocation.

Determining the Optimum Time Quantum Value in Round Robin Process Scheduling Method

The process scheduling, is one of the most important tasks of the operating system. One of the most common scheduling algorithms used by the most operating systems is the Round Robin method in which, the ready processes waiting in ready queue, seize the processor for a short period of time known as the quantum (or time slice) circularly. In this paper, a non- linear programming mathematical model is developed to determine the optimum value of the time quantum, in order to minimize the average waiting time of the processes. The model is implemented and solved by Lingo 8.0 software on four selected problems from the literature.

A multi-period model for managing used product returns

During the last decades there has been a consistent need for companies to manufacture ‘green’ products in order to contribute to environmental protection. The utilisation of used products (literally, the extension of their useful life cycle) is an excellent, indirect way for companies to conform to this requirement and, at the same time, increase their profit. In this paper a mixed integer linear programming mathematical model is proposed, which can be used for the optimisation of procurement, remanufacturing, stocking and salvaging decisions. The model is flexible enough to incorporate multiple suppliers, several quality levels of returned products and multiple periods of time. The applicability of the model is demonstrated through the optimisation of alternative scenarios, the optimal solutions of which reveal the potential profitability of used products exploitation.