In this paper, the strategic planning of a supply chain under a static chain-to-chain competition on the plane is addressed. It is assumed that each retailer has a coverage area called the radius of influence. The demand of each demand zone is divided equally between the retailers which can cover that market. However, the demand of distant customers who are not in the retailers’ radius of influ...

Multi-objective optimization is the simultaneous consideration of two or more objective functions that are completely or partially inconflict with each other. The optimality of such optimizations is largely defined through the Pareto optimality. Multiple objective integer linear programs (MOILP) are special cases of multiple criteria decision making problems. Numerous algorithms have been desig...

This paper presents a stochastic mixed-integer linear programming approach for solving the selfscheduling problem of a price-taker thermal and wind power producer taking part in a pool-based electricity market. Uncertainty on electricity price and wind power is considered through a set of scenarios. Thermal units are modelled by variable costs, start-up costs and technical operating constraints...

Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer programs. In particular, prior to this work, it was open whether some classical problems, like the minimum odd-cut problem, can be expressed by a compact mixe...

To increase their competitiveness, many industrial companies monitor their production process, collecting large amount of measurements. This paper describes a technique using this data to improve the performance of a monitored process. In particular we wish to find a set of rules, i.e. intervals on a reduced number of parameters, for which an output value is maximized. The model-free optimizati...

We propose a method for solving mixed-integer nonlinear programs (MINLPs) to global optimality by discretization of occuring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear program (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP we develope an iterative algorithm which solves MIP relaxat...

Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception with Charnes, Cooper and Rhodes work in 1978. The methodology behind the classical DEA method is to determine how much improvements in the outputs (inputs) dimensions is necessary in order to render them efficient. One of the underlying assumptions of this methodology is that the units consume and prod...

In this paper, we examine a mixed integer linear programming (MILP) reformulation for mixed integer bilinear problems where each bilinear term involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first replacing a general integer variable with its binary expansion and then using McCormick envelopes to linearize the resul...

The purpose of the paper is to present a hybrid algorithm to solve a transportation optimization model with random demand parameters and network design variables. At first, the classical deterministic linear transportation model with network design 0-1 variables is introduced. Then, randomness is considered for demand parameters and modeled by here-and-now approach. The obtained scenario-based ...

The classical 1962 Benders decomposition scheme is a traditional approach for solving mixed-integer problems such as the uncapacitated facility location problem. Subsequent research has been focused on finding better cutting-plane generation schemes to reduce the solution process time. Pareto-optimal cuts are typically preferred because no other cut can dominate them. However, the Pareto-optim...