integer programming

Warehousing is very important in the economies of countries, because a significant percentage of assets are stored in the warehouse. Proper warehouse design and layout has a great role in reducing costs, reducing lead time and delivery time, improving resource utilization and customer service. One type of warehouse that has become widely used recently is cross dock warehouses, which differ from traditional warehouses in terms of the number of products stored and their storage time. The main purpose of this research is modeling and solving a problem that is compatible with real world conditions that have received less attention from researchers.

Multi-Objective Gray Wolf Optimization (MOGWO) algorithm is used to solve the problem and Parameters are adjusted using the Taguchi method.

Using the mean ideal distance, spacing, number of pareto solutions and diversification metric, the best possible level for the algorithm parameters is determined by the signal-to-noise ratio diagram. By solving 10 examples in different sizes and reviewing the results and their solution time, it has been determined that with increasing the size of the problem, the solution time also increases.

Originality/Value: 

In this study, in addition to considering the distance traveled in the warehouse, which most studies have done in the field of warehouse design, more use of available space in the warehouse and the satisfaction of retailers has also been considered. For this purpose, a mixed integer programing model is proposed to design a cross dock warehouse to minimize distances, minimize the vacant space of the warehouse, and maximize retailer’s satisfaction.

Cancer, one of the leading causes of death in the world, has been on the rise in recent years and is expected to continue in the coming years. Therefore, the importance of developing a cancer control program and the need to provide effective methods is very important. Given that radiation therapy is an effective way to treat cancer, studies on this method of treatment are important and significant. The main purpose of this paper is to provide a mathematical model for the latest method of radiotherapy called volumetric modulated arc therapy. In most studies in this field, due to the complexity of the model, the purpose of the problem is to maximize the dose received in the target area or to minimize the dose received in the area organs at risk. In this study, both objectives are considered together and a bi-objective model is presented. The results of the 8 studied instances show that the dose received in the target area is significantly higher than the dose received in the area around the tumor. In addition to increasing the dose received in the target area and decreasing the dose received in the cells around the target, the distribution of the dose in the voxels is very important, so the dose was examined with the coefficient of variation. The results show that the proposed model with a coefficient of variation of less than 10% has a conformal dose distribution in all tissues (cancerous tissue and healthy tissue).

Production scheduling is the most important and influential issue in open pit and underground mining design and planning. The main purpose of mine production planning is time scheduling and determination of mine activities sequencing under some technical and extraction constraints in order to achieve one of the following goals: maximizing Net Present Value (NPV), the amount of ore extraction or mine life. Underground mine planning optimization which is used to determine the sequence of stopes extraction, is difficult due to the complexity of decision making and the interaction between existing constraints. Since, mathematical programming techniques are capable for solving complex and multi-limiting problems, they can be used for optimization purposes. In this study, after reviewing previous studies on the design and planning of underground mine production, the step by step explanation of a proposed model based on Integer Programming (IP) has been addressed. In order to validate proposed model, an example of 9 stopes was considered. First, the sequence of extraction was carried out using manual design and then using extended mathematical model in GAMS/CPLEX software. The current NPV obtained by manual production scheduling was 8.211 million dollars. While, this value for mathematical model was 8.331 million dollars. In other words, NPV value in mathematical model was 1.46% higher than manual method which indicate the power of mathematical programming for solving complex problems.

Stope layout and production scheduling are two main areas of underground mine planning that have a close relationship with each other such a way that optimization results of each of them have important effects on the other one. Hence, separately optimization of these two areas cannot guarantee the true optimum. Because, in isolated optimization approach often ignores the effects of different planning areas on each other, this is not able to manage issues among different areas. To tackle this problem, simultaneous optimization approaches are developed in recent years which simultaneously optimize the different areas of the mine planning process and lead to more profitable mine plans. In the present research, a mathematical IP model has been developed to simultaneously optimize stope layout and production schedules for sublevel stoping (SLS). Then, the developed model is applied on iron ore operations and obtained results from simultaneous optimization were compared with those of isolated approach. It has been concluded that the simultaneous optimization approach is able to produce the globally optimal scheduling result for the stope layout optimization and scheduling by taking into account all constraints related to both areas. Application of the simultanous optimization method in iron ore operation resulted in a 16 per cent increase in final NPV over the isolated approach.