A new MIP model for mine equipment scheduling by minimizing maintenance cost

Mining investment has been recognized as capital intensive due mainly to the cost of large equipment. Equipment capital costs for a given operation are usually within the order of hundreds of million dollars but may reach to billion dollars for large companies operating multiple mines. Such large investments require the optimum usage of equipment in a manner that the operating costs are minimized and the utilization of equipment is maximized through optimal scheduling. This optimum usage is required to ensure that the business remains sustainable and financially stable. Most mining operations utilize trucks to haul the mined material. Maintenance is one of the major operating cost items for these fleets as it can reach approximately one hundred million dollars yearly. There is no method or application in the literature that optimizes the utilization for truck fleet over the life of mine. A new approach based on mixed integer programming (MIP) techniques is used for annually scheduling a fixed fleet of mining trucks in a given operation, over a multi-year time horizon to minimize maintenance cost. The model uses the truck age (total hours of usage), maintenance cost and required operating hours to achieve annual production targets to produce an optimum truck schedule. While this paper focuses on scheduling trucks for mining operation, concept can be used in most businesses using equipment with significant maintenance costs. A case study for a large scale gold mine showed an annual discounted (10% rate) maintenance cost saving of over $2M and more than 16% ($21M) of overall maintenance cost reduction over 10 years of mine life, compared with the spreadsheet based approach used currently at the operation.     

A critical condition for the cost density in the circular city model

Two inequalities in Ref. 1 are modified.     

A critical condition for the cost density in the circular city model

In regard to the problem of determining minimal-cost routes in a region with variable cost density, it has been shown elsewhere that, for a radially symmetric cost density which is inversely proportional to the distance from a central point O, the minimal cost between two pointsP ₁ andP ₂ which are equidistant from O is attained along a circular arc. This is not true in general for an arbitrary, radially symmetric cost density. In the present paper, critical conditions for determining when a circular arc will be a relative minimal-cost path are derived. These criteria are then employed to examine a class of special cases in which the cost density is constant outside the city limits.The author would like to express his appreciation to Professor J. B. Keller for calling his attention to the work of R. K. Luneberg and to Professor K. A. Brakke for some helpful advice.     

A new mixed integer linear programming model for the multi level uncapacitated facility location problem

This paper considers the multi level uncapacitated facility location problem (MLUFLP). A new mixed integer linear programming (MILP) formulation is presented and validity of this formulation is given. Experimental results are performed on instances known from literature. The results achieved by CPLEX and Gurobi solvers, based on the proposed MILP formulation, are compared to the results obtained by the same solvers on the already known formulations. The results show that CPLEX and Gurobi can optimally solve all small and medium sized instances and even some large-scale instances using the new formulation.     

求解排课表问题的一个启发式数值算法

为了便于建立与排课表问题有关的决策支持系统,本文给出一个求解排课表问题的启发式数值算法,证明了算法的正确性,并举例说明算法的应用.该算法具有易于编程实现、收敛性好等优点,大量数值实值表明该算法能求得问题的最优解.     

A coefficient identification problem for a mathematical model related to ductal carcinoma in situ

We consider a coefficient identification problem for a mathematical model with free boundary related to ductal carcinoma in situ (DCIS). This inverse problem aims to determine the nutrient consumption rate from additional measurement data at a boundary point. We first obtain a global‐in‐time uniqueness of our inverse problem. Then based on the optimization method, we present a regularization algorithm to recover the nutrient consumption rate. Finally, our numerical experiment shows the effectiveness of the proposed numerical method.     

A new mixed integer programming model for curriculum balancing: Application to a Turkish university

Curriculum design is a highly important activity for the academic institutions. It is discussed in literature as a balancing academic curriculum problem (BACP). The BACP schedules courses to different semesters, while balancing the total workload per period. BACP model involves precedence relations, but the related courses are not necessarily assigned to closest periods.     

A new hybrid iterative method for mixed equilibrium problems and variational inequality problem for relaxed cocoercive mappings with application to optimization problems

In this paper, we introduce and study a new hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for a ξ-Lipschitz continuous and relaxed (m,v)-cocoercive mappings in Hilbert spaces. Then, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm which solves some optimization problems under some suitable conditions. Our results extend and improve the recent results of Yao et al. [Y. Yao, M.A. Noor, S. Zainab and Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl (2009). doi:10.1016/j.jmaa.2008.12.005] and Gao and Guo [X. Gao and Y. Guo, Strong convergence theorem of a modified iterative algorithm for Mixed equilibrium problems in Hilbert spaces, J. Inequal. Appl. (2008). doi:10.1155/2008/454181] and many others.