39,060 research outputs found
Stochastic multi-period multi-product multi-objective Aggregate Production Planning model in multi-echelon supply chain
In this paper a multi-period multi-product multi-objective aggregate production planning (APP) model is proposed for an uncertain multi-echelon supply chain considering financial risk, customer satisfaction, and human resource training. Three conflictive objective functions and several sets of real constraints are considered concurrently in the proposed APP model. Some parameters of the proposed model are assumed to be uncertain and handled through a two-stage stochastic programming (TSSP) approach. The proposed TSSP is solved using three multi-objective solution procedures, i.e., the goal attainment technique, the modified ε-constraint method, and STEM method. The whole procedure is applied in an automotive resin and oil supply chain as a real case study wherein the efficacy and applicability of the proposed approaches are illustrated in comparison with existing experimental production planning method
A Practical Guide to Robust Optimization
Robust optimization is a young and active research field that has been mainly
developed in the last 15 years. Robust optimization is very useful for
practice, since it is tailored to the information at hand, and it leads to
computationally tractable formulations. It is therefore remarkable that
real-life applications of robust optimization are still lagging behind; there
is much more potential for real-life applications than has been exploited
hitherto. The aim of this paper is to help practitioners to understand robust
optimization and to successfully apply it in practice. We provide a brief
introduction to robust optimization, and also describe important do's and
don'ts for using it in practice. We use many small examples to illustrate our
discussions
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Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)
SP models combine the paradigm of dynamic linear programming with
modelling of random parameters, providing optimal decisions which hedge
against future uncertainties. Advances in hardware as well as software
techniques and solution methods have made SP a viable optimisation tool.
We identify a growing need for modelling systems which support the creation
and investigation of SP problems. Our SPInE system integrates a number of
components which include a flexible modelling tool (based on stochastic
extensions of the algebraic modelling languages AMPL and MPL), stochastic
solvers, as well as special purpose scenario generators and database tools.
We introduce an asset/liability management model and illustrate how SPInE
can be used to create and process this model as a multistage SP application
Robust optimization with incremental recourse
In this paper, we consider an adaptive approach to address optimization
problems with uncertain cost parameters. Here, the decision maker selects an
initial decision, observes the realization of the uncertain cost parameters,
and then is permitted to modify the initial decision. We treat the uncertainty
using the framework of robust optimization in which uncertain parameters lie
within a given set. The decision maker optimizes so as to develop the best cost
guarantee in terms of the worst-case analysis. The recourse decision is
``incremental"; that is, the decision maker is permitted to change the initial
solution by a small fixed amount. We refer to the resulting problem as the
robust incremental problem. We study robust incremental variants of several
optimization problems. We show that the robust incremental counterpart of a
linear program is itself a linear program if the uncertainty set is polyhedral.
Hence, it is solvable in polynomial time. We establish the NP-hardness for
robust incremental linear programming for the case of a discrete uncertainty
set. We show that the robust incremental shortest path problem is NP-complete
when costs are chosen from a polyhedral uncertainty set, even in the case that
only one new arc may be added to the initial path. We also address the
complexity of several special cases of the robust incremental shortest path
problem and the robust incremental minimum spanning tree problem
Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition
In this paper, we study chance constrained mixed integer program with
consideration of recourse decisions and their incurred cost, developed on a
finite discrete scenario set. Through studying a non-traditional bilinear mixed
integer formulation, we derive its linear counterparts and show that they could
be stronger than existing linear formulations. We also develop a variant of
Jensen's inequality that extends the one for stochastic program. To solve this
challenging problem, we present a variant of Benders decomposition method in
bilinear form, which actually provides an easy-to-use algorithm framework for
further improvements, along with a few enhancement strategies based on
structural properties or Jensen's inequality. Computational study shows that
the presented Benders decomposition method, jointly with appropriate
enhancement techniques, outperforms a commercial solver by an order of
magnitude on solving chance constrained program or detecting its infeasibility
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
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