Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4+T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.

Fuzzy linear model for production optimization of mining systems with multiple entities

Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

Strategic mining options optimization:Open pit mining, underground mining or both

Near-surface deposits that extend to considerable depths are often amenable to both open pit mining and/or underground mining. This paper investigates the strategy of mining options for an orebody using a Mixed Integer Linear Programming(MILP) optimization framework. The MILP formulation maximizes the Net Present Value(NPV) of the reserve when extracted with(i) open pit mining,(ii) underground mining, and(iii) concurrent open pit and underground mining. Comparatively, implementing open pit mining generates a higher NPV than underground mining. However considering the investment required for these mining options, underground mining generates a better return on investment than open pit mining. Also, in the concurrent open pit and underground mining scenario, the optimizer prefers extracting blocks using open pit mining. Although the underground mine could access ore sooner, the mining cost differential for open pit mining is more than compensated for by the discounting benefits associated with earlier underground mining.

Supply-based optimal scheduling of oil product pipelines

Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model was established for a single-source multi-distribution oil pro- duct pipeline, and scheduling plans were made based on supply. In the model, time node constraints, oil offloading plan constraints, and migration of batch constraints were taken into consideration. The minimum deviation between the demanded oil volumes and the actual offloading volumes was chosen as the objective function, and a linear programming model was established on the basis of known time nodes＇ sequence. The ant colony optimization algo- rithm and simplex method were used to solve the model. The model was applied to a real pipeline and it performed well.

MILP Optimization Model for Assessing the Participation of Distributed Residential PV-battery Systems in Ancillary Services Market

A novel non-linear stochastic method based on a Mixed-Integer Linear Programming(MILP)optimization model is proposed to optimally manage a high number of photovoltaic(PV)-battery systems for the provision of up and down regulation in the ancillary services market.This method,considers both the technical constraints of the power system,and those of the equipment used by all the prosumers.This allows an aggregator of many residential prosumers endowed with photovoltaic(PV)-battery systems to evaluate the baseline of the aggregate by minimizing the costs related to the electrical energy absorbed from the grid and then to assess the up and down flexibility curves with relative offer prices.As confirmed by simulation results carried out considering different realistic case studies,the method can effectively be used by an aggregator to evaluate the economic impact of its participation in the ancillary services market,both for the aggregator and for its prosumers.

SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.