Cost-based domain filtering for stochastic constraint programming

Cost-based filtering is a novel approach that combines techniques from Operations Research and Constraint Programming to filter from decision variable domains values that do not lead to better solutions [7]. Stochastic Constraint Programming is a framework for modeling combinatorial optimization problems that involve uncertainty [9]. In this work, we show how to perform cost-based filtering for certain classes of stochastic constraint programs. Our approach is based on a set of known inequalities borrowed from Stochastic Programming ¿ a branch of OR concerned with modeling and solving problems involving uncertainty. We discuss bound generation and cost-based domain filtering procedures for a well-known problem in the Stochastic Programming literature, the static stochastic knapsack problem. We also apply our technique to a stochastic sequencing problem. Our results clearly show the value of the proposed approach over a pure scenario-based Stochastic Constraint Programming formulation both in terms of explored nodes and run time

Filtering algorithms for global chance constraints

Stochastic Constraint Satisfaction Problems (SCSPs) are a powerful modeling framework for problems under uncertainty. To solve them is a PSPACE task. The only complete solution approach to date — scenario-based stochastic constraint programming — compiles SCSPs down into classical CSPs. This allows the reuse of classical constraint solvers to solve SCSPs, but at the cost of increased space requirements and weak constraint propagation. This paper tries to overcome these drawbacks by automatically synthesizing filtering algorithms for global chance constraints. These filtering algorithms are parameterized by propagators for the deterministic version of the chance constraints. This approach allows the reuse of existing propagators in current constraint solvers and it has the potential to enhance constraint propagation. Our results show that, for the test bed considered in this work, our approach is superior to scenario-based stochastic constraint programming. For these instances, our approach is more scalable, it produces more compact formulations, it is more efficient in terms of run time and more effective in terms of pruning for both stochastic constraint satisfaction and optimization problems

Genetic algorithms for the scheduling of multiproduct batch plants within uncertain environment

This study addresses the problem of batch plant scheduling. In addition uncertainty on product demands is considered through probabilistic-based methods. In the resulting two-stage stochastic programming problem, the objective is to maximize an Expected Profit Value (EPV) while respecting a constraint forcing the makespan to be lower than a time horizon. A Genetic Algorithm (GA) is proposed for the solution of a multiproduct example. The variable encoding requires special attention. Computational tests are first carried out with a deterministic model to validate the GA efficiency. Then, different runs with different scenario sets highlight the existence of various solution classes, characterized by specific numbers of batches manufactured for each product. Further analysis finally enables to discuss if each schedule is really the best-fitted to the scenario set for which it has been determined

A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return

A closed-loop supply chain (CLSC) network consists of both forward and reverse supply chains. In this paper, a CLSC network is investigated which includes multiple plants, collection centres, demand markets, and products. To this aim, a mixed-integer linear programming model is proposed that minimizes the total cost. Besides, two test problems are examined. The model is extended to consider environmental factors by weighed sums and ε-constraint methods. In addition, we investigate the impact of demand and return uncertainties on the network configuration by stochastic programming (scenario-based). Computational results show that the model can handle demand and return uncertainties, simultaneously

Stochastic Constraint Programming with And-Or Branch-and-Bound

Complex multi-stage decision making problems often involve uncertainty, for example, regarding demand or processing times. Stochastic constraint programming was proposed as a way to formulate and solve such decision problems, involving arbitrary constraints over both decision and random variables. What stochastic constraint programming currently lacks is support for the use of factorized probabilistic models that are popular in the graphical model community. We show how a state-ofthe-art probabilistic inference engine can be integrated into standard constraint solvers. The resulting approach searches over the And-Or search tree directly, and we investigate tight bounds on the expected utility objective. This significantly improves search efficiency and outperforms scenario-based methods that ground out the possible worlds.status: publishe

Comparison between Multistage Stochastic Optimization Programming and Monte Carlo Simulations for the Operation of Local Energy Systems

The paper deals with the day-ahead optimization of the operation of a local energy system consisting of photovoltaic units, energy storage systems and loads aimed to minimize the electricity procurement cost. The local energy system may refer either to a small industrial site or to a residential neighborhood. Two mixed integer linear programming models are adopted, each for a different representation of the battery: A simple energy balance constraint and the Kinetic Battery Model. The paper describes the generation of the scenarios, the construction of the scenario tree and the intraday decision-making procedure based on the solution of the multistage stochastic programming. Moreover, the daily energy procurement costs calculated by using the stochastic programming approach are compared with those calculated by using the Monte Carlo method. The comparison is repeated for two different sizes of the battery and for two load profiles

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