To deal with optimal design problem of manufacturing/remanufacturing (M/R) logistics network under uncertain circumstance, a two-stage stochastic-fuzzy programming model is developed, which involves continuous distrib...
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ISBN:
(纸本)9781424439706
To deal with optimal design problem of manufacturing/remanufacturing (M/R) logistics network under uncertain circumstance, a two-stage stochastic-fuzzy programming model is developed, which involves continuous distribution stochastic parameters and fuzzy triangle or tolerance parameters. With the help of the model, the following items can be computed such as the optimal sites and numbers of M/R factory, integrated center, distribution center and collection center, the quantities of logistics flow in the network and the minimum fee in the planning horizon. Applying the fuzzy chance-constrained programming approach, the proposed model is transformed into a pure stochastic programming model. To solve this model, a hybrid genetic algorithm is presented, the sample average approximation method is introduced, the optimal objective value approaching technique is presented, and the optimal design steps are summarized. Besides, the application of the proposed model is showed with an example.
In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved wi...
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In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.
In this paper, we propose an adapted version of the progressive hedging algorithm (PHA) (Rockafellar and Wets, 1991;Lokketangen and Woodruff, 1996;Watson and Woodruff, 2011) for the two-stage stochastic traveling sale...
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ISBN:
(纸本)9789897582189
In this paper, we propose an adapted version of the progressive hedging algorithm (PHA) (Rockafellar and Wets, 1991;Lokketangen and Woodruff, 1996;Watson and Woodruff, 2011) for the two-stage stochastic traveling salesman problem (STSP) introduced in (Adasme et al., 2016). Thus, we compute feasible solutions for small, medium and large size instances of the problem. Additionally, we compare the PHA method with the sampleaverageapproximation (SAA) method for all the randomly generated instances and compute statistical lower and upper bounds. For this purpose, we use the compact polynomial formulation extended from (Miller et al., 1960) in (Adasme et al., 2016) as it is the one that allows us to solve large size instances of the problem in short CPU time with CPLEX. Our preliminary numerical results show that the results obtained with the PHA algorithm are tight when compared to the optimal solutions of small and medium size instances. Moreover, we obtain significantly better feasible solutions than CPLEX for large size instances with up to 100 nodes and 10 scenarios in significantly low CPU time. Finally, the bounds obtained with SAA method provide an average reference interval for the stochastic problem.
A novel fourth-party logistics (4PL) network design problem under uncertainty environment is studied in the current work. Demand uncertainty and two types of disruptions, facility and third-party logistics (3PL) disru...
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A novel fourth-party logistics (4PL) network design problem under uncertainty environment is studied in the current work. Demand uncertainty and two types of disruptions, facility and third-party logistics (3PL) disruptions, are simultaneously considered. To minimize the total cost, a two-stage stochastic programming model is presented, which is further approximated as a mixed-integer linear programming model using the sampleaverageapproximation (SAA) method. As a large number of disruption and demand scenarios generated in the approximation process lead to challenges in model solving, the scenario reduction (SR), SAA, dual decomposition and Lagrangian relaxation (DDLR) approaches are integrated to present an SR-DDLRSAA algorithm. The effectiveness of our model and algorithm is illustrated by adopting numerical instances and real-life cases. A comparative analysis indicates that the impact of disruptions on the 4PL network is closely related to the values of the disruption probability and the fluctuation degree of uncertain demand. Furthermore, we extend the proposed basic model by considering demand uncertainty and three types of disruptions, namely supply, facility, and 3PL disruptions, and analyze the impact of supply disruption on the 4PL network.
To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC) have drawn much attention in the recent literature. Our concern is the detailed ...
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To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC) have drawn much attention in the recent literature. Our concern is the detailed analysis of convergence properties of a regularization sampleaverageapproximation (SAA) method for solving a stochastic mathematical program with complementarity constraints (SMPCC). The analysis of this regularization method is carried out in three steps: First, the almost sure convergence of optimal solutions of the regularized SAA problem to that of the true problem is established by the notion of epiconvergence in variational analysis. Second, under MPCC-MFCQ, which is weaker than MPCC-LICQ, we show that any accumulation point of Karash-Kuhn-Tucker points of the regularized SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Finally, some numerical results are reported to show the efficiency of the method proposed.
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