Multi-choice mixed integer goal programming optimization for real problems in a sugar and ethanol milling company

Goal Programming (GP) is an important analytical approach devised to solve many realworld problems. The first GP model is known as Weighted Goal Programming (WGP). However, Multi-Choice Aspirations Level (MCAL) problems cannot be solved by current GP techniques. In this paper, we propose a Multi-Choice Mixed Integer Goal Programming model (MCMI-GP) for the aggregate production planning of a Brazilian sugar and ethanol milling company. The MC-MIGP model was based on traditional selection and process methods for the design of lots, representing the production system of sugar, alcohol, molasses and derivatives. The research covers decisions on the agricultural and cutting stages, sugarcane loading and transportation by suppliers and, especially, energy cogeneration decisions; that is, the choice of production process, including storage stages and distribution. The MCMIGP allows decision-makers to set multiple aspiration levels for their problems in which the more/higher, the better and the less/lower, the better in the aspiration levels are addressed. An application of the proposed model for real problems in a Brazilian sugar and ethanol mill was conducted; producing interesting results that are herein reported and commented upon. Also, it was made a comparison between MCMI GP and WGP models using these real cases. © 2013 Elsevier Inc.

Hydrocarbon field size distributions: a case study in mixed integer nonlinear programming

Of key importance to oil and gas companies is the size distribution of fields in the areas that they are drilling. Recent arguments suggest that there are many more fields yet to be discovered in mature provinces than had previously been thought because the underlying distribution is monotonic not peaked. According to this view the peaked nature of the distribution for discovered fields reflects not the underlying distribution but the effect of economic truncation. This paper contributes to the discussion by analysing up-to-date exploration and discovery data for two mature provinces using the discovery-process model, based on sampling without replacement and implicitly including economic truncation effects. The maximum likelihood estimation involved generates a high-dimensional mixed-integer nonlinear optimization problem. A highly efficient solution strategy is tested, exploiting the separable structure and handling the integer constraints by treating the problem as a masked allocation problem in dynamic programming.

Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming

In the energy management of the isolated operation of small power system, the economic scheduling of the generation units is a crucial problem. Applying right timing can maximize the performance of the supply. The optimal operation of a wind turbine, a solar unit, a fuel cell and a storage battery is searched by a mixed-integer linear programming implemented in General Algebraic Modeling Systems (GAMS). A Virtual Power Producer (VPP) can optimal operate the generation units, assured the good functioning of equipment, including the maintenance, operation cost and the generation measurement and control. A central control at system allows a VPP to manage the optimal generation and their load control. The application of methodology to a real case study in Budapest Tech, demonstrates the effectiveness of this method to solve the optimal isolated dispatch of the DC micro-grid renewable energy park. The problem has been converged in 0.09 s and 30 iterations.

A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems

This paper presents a mixed-integer linear programming approach to solving the problem of optimal type, size and allocation of distributed generators (DGs) in radial distribution systems. In the proposed formulation, (a) the steady-state operation of the radial distribution system, considering different load levels, is modeled through linear expressions; (b) different types of DGs are represented by their capability curves; (c) the short-circuit current capacity of the circuits is modeled through linear expressions; and (d) different topologies of the radial distribution system are considered. The objective function minimizes the annualized investment and operation costs. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. The results of one test system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique.© 2012 Elsevier B.V. All rights reserved.

Bilevel approach for optimal location and contract pricing of distributed generation in radial distribution systems using mixed-integer linear programming

In this study, a novel approach for the optimal location and contract pricing of distributed generation (DG) is presented. Such an approach is designed for a market environment in which the distribution company (DisCo) can buy energy either from the wholesale energy market or from the DG units within its network. The location and contract pricing of DG is determined by the interaction between the DisCo and the owner of the distributed generators. The DisCo intends to minimise the payments incurred in meeting the expected demand, whereas the owner of the DG intends to maximise the profits obtained from the energy sold to the DisCo. This two-agent relationship is modelled in a bilevel scheme. The upper-level optimisation is for determining the allocation and contract prices of the DG units, whereas the lower-level optimisation is for modelling the reaction of the DisCo. The bilevel programming problem is turned into an equivalent single-level mixed-integer linear optimisation problem using duality properties, which is then solved using commercially available software. Results show the robustness and efficiency of the proposed model compared with other existing models. As regards to contract pricing, the proposed approach allowed to find better solutions than those reported in previous works. © The Institution of Engineering and Technology 2013.

Short-term expansion planning of radial electrical distribution systems using mixed-integer linear programming

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector

This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.

A Mixed Integer Quadratic Programming Model for the Low Autocorrelation Binary Sequence Problem

In this paper the low autocorrelation binary sequence problem (LABSP) is modeled as a mixed integer quadratic programming (MIQP) problem and proof of the model’s validity is given. Since the MIQP model is semidefinite, general optimization solvers can be used, and converge in a finite number of iterations. The experimental results show that IQP solvers, based on this MIQP formulation, are capable of optimally solving general/skew-symmetric LABSP instances of up to 30/51 elements in a moderate time. ACM Computing Classification System (1998): G.1.6, I.2.8.

A mixed-integer LP model for the optimal allocation of voltage regulators and capacitors in radial distribution systems

This paper presents a mixed-integer linear programming model to solve the problem of allocating voltage regulators and fixed or switched capacitors (VRCs) in radial distribution systems. The use of a mixed-integer linear model guarantees convergence to optimality using existing optimization software. In the proposed model, the steady-state operation of the radial distribution system is modeled through linear expressions. The results of one test system and one real distribution system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique. An heuristic to obtain the Pareto front for the multiobjective VRCs allocation problem is also presented. © 2012 Elsevier Ltd. All rights reserved.

Optimal conductor size selection and reconductoring in radial distribution systems using a mixed-integer LP approach

This paper presents a mixed-integer linear programming model to solve the conductor size selection and reconductoring problem in radial distribution systems. In the proposed model, the steady-state operation of the radial distribution system is modeled through linear expressions. The use of a mixed-integer linear model guarantees convergence to optimality using existing optimization software. The proposed model and a heuristic are used to obtain the Pareto front of the conductor size selection and reconductoring problem considering two different objective functions. The results of one test system and two real distribution systems are presented in order to show the accuracy as well as the efficiency of the proposed solution technique. © 1969-2012 IEEE.