We discuss a mixed-integer nonlinear programming formulation for the problem of covering a set of points with a given number of slabs of minimum width, known as the bottleneck variant of the hyperplane clustering problem. We derive several linear approximations, which we solve using a standard mixed-integer linear programming solver. A computational comparison of the performance of the differen...

The concept of a forecast horizon has been widely studied in the operations management/research literature in the context of evaluating the impact of future data on current decisions in a multi-period decision making environment. As a solution approach for computing forecast horizons, integer programming has been largely ignored by the research community. However, the modelling and structural a...

The heterogeneous fixed fleet open vehicle routing problem (HFFOVRP) is one of the most significant extension problems of the open vehicle routing problem (OVRP). The HFFOVRP is the problem of designing collection routes to a number of predefined nodes by a fixed fleet number of vehicles with various capacities and related costs. In this problem, the vehicle doesn’t return to the depot after se...

Abstract In this paper, we study the recently introduced time-constrained maximal covering routing problem. problem, are given a central depot, set of facilities, and customers. Each customer is associated with subset facilities which can cover it. A feasible solution consists k Hamiltonian cycles on subsets depot. cycle must contain depot respect distance limit. The goal to maximize number cus...

A famous travelling salesman problem, appearing simple to state but complex solve, has been widely investigated and various algorithms have proposed. In this article, mixed integer linear programming of python (MIP) is used model problem with varying input data. The result shows that small data the modelling code MIP executing quickly converging optimal value, while large scale require plenty c...

In this research, a single batch processing machine scheduling problem with minimization of total earliness and tardiness as the objective function is investigated.We first formulate the problem as a mixed integer linear programming model. Since the research problem is shown to be NP-hard, an improved memetic algorithmis proposed to efficiently solve the problem. To further enhance the memetic ...