The main optimized objects in underground mines include: stope layout, access layout and production scheduling. It is common to optimize each component sequentially, where optimal results from one phase are regarded as the input data for the next phase. Numerous methods have been developed and implemented to achieve the optimal solution for each component. In fact, the interaction between different phases is ignored in the tradition optimization models which only get the suboptimal solution compared to the integrated optimization model. This paper proposes a simultaneous integrated optimization model to optimize the three components at the same time. The model not only optimizes the mining layout to maximize the Net Present Value (NPV), but also considers the extension sequence of stope extraction and access excavation. The production capacity and ore quality requirement are also taken into account to keep the mining process stable in all mine life. The model is validated to a gold deposit in China. A two-dimensional block model is built to do the resource estimation due to the clear boundary of the hanging wall and footwall. The thickness and accumulation of each block is estimated by Ordinary Kriging (OK). In addition, the conditional simulation method is utilized to generate a series of orebodies with equal possibility. The optimal solution of optimization model is carried out on each simulated orebody to evaluate the influence of geological uncertainty on the optimal mining design and production scheduling. The risk of grade uncertainty is quantified by the possibility of obtaining the expected NPV. The results indicate that the optimization model has the ability to produce an optimal solution that has a good performance under the uncertainty of grade variability.
The paper refers to planning deliveries of food products (especially those available in certain seasons) to the recipients: supermarket networks. The paper presents two approaches to solving problems of simultaneous selection of suppliers and transportation modes and construction of product flow schedules with these transportation modes. Linear mathematical models have been built for the presented solution approaches. The cost criterion has been taken into consideration in them. The following costs have been taken into account: purchase of products by individual recipients, transport services, storing of products supplied before the planned deadlines and penalties for delays in supply of products. Two solution approaches (used for transportation planning and selection of suppliers and selection of transportation modes) have been compared. The monolithic approach calls for simultaneous solutions for the problems of supplier selection and selection of transportation modes. In the alternative (hierarchical) solution approach, suppliers are selected first, and then transportation companies and their relevant transportation modes are selected. The results of computational experiments are used for comparison of the hierarchical and monolithic solution approaches.
In the paper, we present a coordinated production planning and scheduling problem for three major shops in a typical alloy casting foundry, i.e. a melting shop, molding shop with automatic line and a core shop. The castings, prepared from different metal, have different weight and different number of cores. Although core preparation does not required as strict coordination with molding plan as metal preparation in furnaces, some cores may have limited shelf life, depending on the material used, or at least it is usually not the best organizational practice to prepare them long in advance. Core shop have limited capacity, so the cores for castings that require multiple cores should be prepared earlier. We present a mixed integer programming model for the coordinated production planning and scheduling problem of the shops. Then we propose a simple Lagrangian relaxation heuristic and evolutionary based heuristic to solve the coordinated problem. The applicability of the proposed solution in industrial practice is verified on large instances of the problem with the data simulating actual production parameters in one of the medium size foundry.
In a rectilinear route, a moving sink is restricted to travel either horizontally or vertically along the connecting edges. We present a new algorithm that finds the shortest round trip rectilinear route covering the specified nodes in a grid based Wireless Sensor Network. The proposed algorithm determines the shortest round trip travelling salesman path in a two-dimensional grid graph. A special additional feature of the new path discovery technique is that it selects that path which has the least number of corners (bends) when more than one equal length shortest round trip paths are available. This feature makes the path more suitable for moving objects like Robots, drones and other types of vehicles which carry the moving sink. In the prosed scheme, the grid points are the vertices of the graph and the lines joining the grid points are the edges of the graph. The optimal edge set that forms the target path is determined using the binary integer programming.