mixed-integer nonlinear programming

The issue of international trade and economic sanctions has been one of the important issues for every country, especially developing countries and those under sanctions. Since ancient times, countries traded with other countries to meet their needs through international trade. Some countries impose sanctions on a number of countries to achieve their political and economic goals. Studying these sanctions and reducing their effects is very important for boycotting countries. We also know that exchange rate fluctuations are one of the main challenges export and import agents face in sanction settings, including public or private agents. Therefore, it is important to deal with the exchange rate debate and its volatility in the business section. Although numerous studies in this field have been done, few studies have been done by mathematical modeling. In this paper, we attempt to present a mathematical model for the optimization of Iran's trade exchange with its important partners during trade sanctions. Two objective functions, which are to accurately represent the effect of trade sanctions and minimize the standard deviation of the logarithm of exchange rate difference between the two following years, are applied to achieve a robust solution. Therefore, the problem is modeled as a mixed integer non-linear programming for selecting countries and the amount of goods exchanged. To evaluate the performance of the proposed model, the solution is compared with the commercial data of the years 1395 to 1398. The results show improved trade balance because of changing the country of origin of goods or the destination of export of goods and exploitation of conversion industries to improve export value added. The solution obtained from the model to curb the effects of commercial sanctions is available. The model results indicate reducing the effect of sanctions if the appropriate program is used according to the exchange rate fluctuation

With the increase in environmental pollution due to the disposal of used products in the environment, recovery of such products at the end of their life cycle has become one of the important issues in the field of reverse logistics and sustainable production. Remanufacturing is one of the options for used products recovery with high economic advantages and the least harmful environmental effects. The simultaneous planning of the production of new products and remanufacturing of used ones forms a combined manufacturing/remanufacturing system, which is among the complex issues in the field of production systems planning. The combined pricing, warranty, and competition considerations has so far not been seriously investigated in this field. The aim of this research is to create an optimal production plan for a multi-period hybrid manufacturing/remanufacturing system, where the producer decides on the price, the amount of production and the warranty period for both new and remanufactuted products. To achieve this goal, a multi-period mixed integer non-linear programming (MINLP) model is built. Only new products are produced and sold in the first period, then the used products (cores), in different quality levels, are purchased from customers in the following periods, and hence, remanufacturing is added to the model. Both types of products are sold in the same market, so there is competition between them to gain more market share. Due to the complexity of the developed model, particle swarm optimization (PSO), and simulated annealing (SA) algorithms are used for its solution. Numerical results show the efficiency and effectiveness of the proposed model and solution approaches.

The increasing importance of customer's trust and demand diversification has turned the attention to warranty policy and supplying a family of products. In this respect, while retaining the benefits of mass production and flexibility each member shows to a specific segment of demand, appropriate models have not been sufficiently developed. This paper presents a maximization profit model by simultaneously optimizing the price and warranty length for products in a family of products through application of Markov chains. A continuous Markov model was used to calculate the steady state probabilities that the products need for warranty services. Then, the optimal prices and warranty lengths for all products were determined using a mathematical model to maximize the profitability of the products. The problem was formulated in two scenarios of fixed time and renewable warranty policies. Given the integer warranty length, the problem was a mixed nonlinear integer programming. Numerical samples for the problems solved by GAMS software and sensitivity analysis for the important parameters were also investigated. The results showed that the model was sensitive mostly in the case of price and warranty length elasticity. Moreover, the share of each product in total production did not change much under the influence of capacity change. This study can help manufacturers optimize the main variables of a product including reliability, price, and warranty period simultaneously at the product development stage (design and engineering). The proposed model can be operationally used by the managers for decision-making on the price and warranty length for a family product.

Production planning problems are generally modeled as mixed integer programming problems; and solved through heuristic algorithms، because of their innate high computational complexity. In this paper، a mixed integer nonlinear programming (MINLP) model is designed for multi-item، multi-period production planning to replenish orders of the buyer and minimizing the supplier’s costs. It is supposed that the order quantity is constant، and ordering occurs at once. This model has been developed according to the realistic assumptions of SAPCO Company، which is a major supplier of automotive parts in Iran، and one of its partner companies. In addition، an efficient heuristic algorithm based on A* search has been proposed to solve this mathematical model. The proposed search algorithm does not need an initial solution; also، it can overcome the memory overhead through bounding the stored states in its open-list. Actually، in spite of the simplicity of the proposed algorithm، which is established based on the simple inventory management equations; it is able to generate efficiently optimal or near-optimal solutions in comparison with an exact solution method، a greedy search algorithm، and simulated annealing algorithm as a metaheuristic algorithm.

In this paper a new method is proposed for path planning of planar manipulators amid obstacles through mathematical programming in a way that the robot’s links avoid collision with obstacles throughout their motion from an initial to a goal configuration. After inputting the workspace geometry، the shortest feasible path for the robot’s end-effector is planned toward its goal position using Generalized Visibility Graph، which is then interpolated into subgoal points that should be sequentially reached by the end-effector. Next، a Mixed Integer Nonlinear Programming (MINLP) model with the objective of minimizing the distance between the end-effector and the subgoals is successively solved and the angle of each link is determined such that it does not intersect obstacles. In order to enhance the safety of clearance from obstacles، they are enlarged by an offset. Also، the proposed method has been modified and tuned aiming to reduce the number of constraints and 0-1 variables، which led to reduced runtimes.