We study the mixed-integer rounding (MIR) closures of polyhedral sets. The MIR closure of a polyhedral set is equal to its split closure and the associated separation problem is NP-hard. We describe a mixed-integer programming (MIP) model with linear constraints and a non-linear objective for separating an arbitrary point from the MIR closure of a given mixed-integer set. We linearize the objec...

This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source co...

    In this paper, a new revenue efficiency data envelopment analysis (RE-DEA) approach is considered for finding the most revenue efficient unit with price uncertainty in both optimistic and pessimistic perspectives. The optimistic and pessimistic perspectives use efficient frontier and inefficient frontier, respectively. An integrated model is introduced to find decision making units (DMUs) t...

Combinatorial optimization over continuous and integer variables was proposed recently as an useful tool for solving complex optimal control problems for linear hybrid dynamical systems formulated in discretetime. Current approaches are based on mixed-integer linear/quadratic programming (MIP), which provides the solution after solving a sequence of relaxed standard linear (or quadratic) progra...

In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The generalized model is formulated as a mixed integer quadratic programming (MIP) problem. The purpose of this paper is to investigate a continuous approach base...

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...

Recently, we compared the performance of mixed-integer programming (MIP), constraint programming (CP), and constraint integer programming (CIP) to a state-of-the-art logic-based Benders manual decomposition (LBBD) for a resource allocation/scheduling problem. For a simple linear relaxation, the LBBD and CIP models deliver comparable performance with MIP also performing well. Here we show that a...

in this paper, a new revenue efficiency data envelopment analysis (re-dea) approach is considered for finding the most revenue efficient unit with price uncertainty in both optimistic and pessimistic perspectives. the optimistic and pessimistic perspectives use efficient frontier and inefficient frontier, respectively. an integrated model is introduced to find decision making units (dmus) that ...

In this paper, a robust reconfiguration approach based on Mixed Integer Programming (MIP) is proposed to minimize loss in distribution systems. A Depth-First Search (DFS) algorithm to enumerate possible loops provides radiality constraint. This provides a general solution to the radiality constraint for distribution system reconfiguration/expansion problems. Still, imprecision and ambiguity in ...

This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP...