An Open-Pit Production scheduling (OPPS) problem focuses on specifying block Production scheduling to achieve the highest possible Net Present Value (NPV). This paper presents a new mathematical model for OPPS under uncertainty. To this end, a robust box and ellipsoidal counterpart approach was used. The proposed method was implemented in a hypothetical model. A Genetic Algorithm (GA) and an exact mathematical modeling approach were used to solve the model. It was shown that the scheduling of deterministic and robust models in various conditions is different. Considering the type of robust counterparts, different Production plans under various conditions were scheduled. Furthermore, the price of robustness was determined for various levels of conservation.

Many supply chains lack flexibility and adaptability in today's competitive market, resulting in customer dissatisfaction, backorders, and several extra costs for the business. Additionally, the inability to quickly meet the customer's demands andthe unnecessary transportation costs is also one of the significant challenges facedby the fixed facilities' supply chain. To address these challenges, this study analyzedthe mobile facilities supply chain and the Production, distribution, and delivery ofgoods conducted by trucks based on customer preferences. This study proposes abi-objective mixed-integer linear programming model to ensure the mobilefacilities' routing and manufacturing schedules are optimized to meet the customer's needs. Furthermore, this model minimizes Production and distribution costs in the shortest amount of time. An exact decomposition algorithm based on Bendersdecomposition is used to find high-quality solutions in a reasonable amount of timeto tackle the problem efficiently. We present several acceleration strategies forincreasing the convergence rate of Benders' decomposition algorithm, includingPareto optimality cut and warm-up start. The warm-up start acceleration strategyitself is a meta-heuristic based on particle swarm optimization (PSO). Using theBenders decomposition, we demonstrate the superior accuracy of our solutionmethodology for large-scale cases with 10 kinds of products ordered by 30customers using 10 mobile facilities.

With increasing competition in the business world and the emergence and development of new technologies, many companies have turned to integrated Production and distribution for timely Production and delivery at the lowest cost of Production and distribution and with the least delay in delivery. By increasing human population and the increase in greenhouse gas emissions and industrial waste, in recent years the pressures of global environmental organizations have prompted private and public organizations to take action to reduce environmental pollutants. This paper presents a nonlinear mixed integer model for the Production and distribution of goods with specified shipping capacity and specific delivery time for customers. The proposed model is applicable to flexible Production systems; it also provides routing for the means of transportation of products, as well as the reduction of emissions from Production and distribution. The model is presented, and then by mathematical linearization is transformed into a mixed integer linear model. The data of a furniture company is used to solve the linear model, and then the linear model with the company data is solved by CPLEX software. The numerical results show that as costs increase, delays are reduced and consequently, customer satisfaction increases, and as costs increase the air pollution decreases.

A three-stage Production system is considered in this paper. There are two stages to fabricate and provide the parts and an assembly stage to assemble the parts and complete the products in this system. Suppose that a number of products of different kinds are ordered. Each product is assembled with a set of several parts. At first the parts are produced in the first stage with parallel machines and then they are controlled and provided in the second stage and finally the parts are assembled in an assembly stage to complete the products. Two objective functions are considered: (1) minimizing the completion time of all products (makespan), and (2) minimizing the sum of earliness and tardiness of all products (Si(Ei/Ti). Since this type of problem is NP-hard, a new multi-objective algorithm is designed for searching local Pareto-optimal frontier for the problem. To validate the performance of the proposed algorithm, various test problems are designed and the reliability of the proposed algorithm, based on some comparison metrics, is compared with two prominent multi-objective genetic algorithms, i.e. NSGA-II and SPEA-II. The computational results show that the performance of the proposed algorithms is good in both efficiency and effectiveness criteria.

In an Open-Pit Production scheduling (OPPS) problem, the goal is to determine the mining sequence of an orebody as a block model. In this paper, linear programing formulation is used to aim this goal. OPPS problem is known as an NP-hard problem, so an exact mathematical model cannot be applied to solve in the real state. Genetic Algorithm (GA) is a well-known member of evolutionary algorithms that widely are utilized to solve NP-hard problems. Herein, GA is implemented in a hypothetical Two-Dimensional (2D) copper orebody model. The orebody is featured as two-dimensional (2D) array of blocks. Likewise, counterpart 2D GA array was used to represent the solution space of an OPPS problem. Thereupon, the fitness function is defined according to the OPPS problem objective function to assess the solution domain. Also, new normalization method was used to handle the block sequencing constraint. A numerical study is performed to compare the solutions of the exact and GA-based methods. It is shown that the gap between GA and the optimal solution by the exact method is less than % 5; hereupon GA is found to be efficient in solving OPPS problem.

In today's manufacturing processes, Production optimization is very important to increase the competitive edge, so Production managers are hardly trying to increase their Production output (without increasing resources) by using different manufacturing processes and different fields of industrial engineering. These methods are used in productivity and decrease the cost of goods sold, which managers favor in all companies. This paper investigated the optimization problem in a flow shop Production line with the probable time and the other constraints such as limited equipment, manufacturing process limit, by using scheduling techniques and creating a learning system by simulating. We use a simulation-based optimization approach that combines simulation and exact methods to solve the Flow Shop scheduling problem. simulation software used to reduce the constraints and exact model used for optimizing answers that can be efficient and effective. Implementing this model with all its probable components in a high-tech pharmaceutical company with many different products increases utilization and largely to those outputs have increased by 12%.

Machine maintenance is performed in Production to prevent machine failure in order to maintain Production efficiency and reduce failure costs. Due to the importance of maintenance in Production, it is necessary to consider an integrated schedule for Production and maintenance. Most of the literature on machine scheduling assumes that machines are always available. However, this assumption is unrealistic in many industrial applications. Preventive maintenance (PM) is often performed in a Production system to prevent premature machine failure in order to maintain Production efficiency. However, this assumption is inappropriate in real industrial cases. Machine maintenance plan is often performed in a Production system to prevent premature machine failure in order to maintain Production efficiency. Parallel machine layout is very common in modern Production systems. Its performance sometime has a key impact on overall productivity. In this paper, a parallel machine scheduling problem with individual maintenance operations is considered. Then, a mathematical model is formulated including scheduling and maintenance operation optimization. The objective is to assign all jobs to machines so that the completion time and the average cost are minimized, jointly. Maintenance is considered in time intervals. To solve the proposed problem, a branch and bound (B&B) algorithm is adapted and proposed. The results show the applicability of the mathematical model in Production systems and efficiency of the adapted B&B in comparison with Gams optimization software.