We study the performance of Empirical Revenue Maximizing (ERM) mechanism in a single-item, single-seller, single-buyer setting. assume buyer’s valuation is drawn from regular distribution F and that seller has access to two independently samples F. By solving family mixed-integer linear programs (MILPs), ERM proven guarantee at least .5914 times optimal revenue expectation. Using solutions thes...

Usually, in make-to-order environments which work only in response to the customer’s orders, manufacturers for maximizing the profits should offer the best price and delivery time for an order considering the existing capacity and the customer’s sensitivity to both the factors. In this paper, an integrated approach for pricing, delivery time setting and scheduling of new arrival orders are prop...

We present a Mixed Integer Non-Linear Programming (MINLP) model capable of choosing the best design considering economic profit, availability, and safety. The takes into account probability suffering failure in year operation, as well revenue generated process units being non-functional state. inclusion programmed maintenances specified duration is considered model, assuming an equal distributi...

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some o...

We present an overview of noncommercial software tools for the solution of mixed-integer linear programs (MILPs). We first review solution methodologies for MILPs and then present an overview of the available software, including detailed descriptions of eight software packages available under open-source or other noncommercial licenses. Each package is categorized as a black-box solver, a calla...

The aim of this work is to propose a mathematical programming model for the Economic Lot Scheduling Problem (ELSP) with performance decay. The main difficulties related to this model are the nonlinearities and/or nonconvexities associated with the dynamic behavior of the system with time. Firstly, the problem is formulated as a Mixed Integer Non Linear Program (MINLP), which is found to be nonc...

In the rst part of the paper we present a framework for describing basic tech niques to improve the representation of a mixed integer programming problem We elaborate on identi cation of infeasibility and redundancy improvement of bounds and coe cients and xing of binary variables In the second part of the paper we discuss recent extensions to these basic techniques and elaborate on the investi...

This survey presents tools from polyhedral theory that are used in integer programming. It applies them to the study of valid inequalities for mixed integer linear sets, such as Gomory’s mixed integer cuts.

A wide range of problems can be modeled as Mixed Integer Linear Programming (MILP) problems using standard formulation techniques. However, in some cases the resulting MILP can be either too weak or to large to be effectively solved by state of the art solvers. In this survey we review advanced MILP formulation techniques that result in stronger and/or smaller formulations for a wide class of p...