We give multi-stage stochastic programming formulations for lot-sizing problems where costs, demands and order lead times follow a general discrete-time stochastic process with finite support. We characterize the properties of an optimal solution and give a dynamic programming algorithm, polynomial in input size, when orders do not cross in time.

Multi-stage stochastic programming problems arise in many practical situations, such as production and manpower planning, portfolio selections and so on. In general, the deterministic equivalences of these problems can be very large, and may not be solvable directly by general-purpose optimization approaches. Sequential quadratic programming methods are very effective for solving medium-size no...

The field of multi-stage stochastic programming provides a rich modelling framework to tackle a broad range of real-world decision problems. In order to numerically solve such programs once they get reasonably large the infinite-dimensional optimization problem has to be discretized. The stochastic optimization program generally consists of an optimization model and a stochastic model. In the m...

in today’s competitive business environment, the design and management of supply chainnetwork is one of the most important challenges that managers encounter. the supply chain network shouldbe designed for satisfying of customer demands as well as minizing the total system costs. this paper presentsa multi-period multi-stage supply chain network design problem under demand uncertainty. the prob...

In this paper we develop and test scenario generation methods for asset liability management models. We propose a multi-stage stochastic programming model for a Dutch pension fund. Both randomly sampled event trees and event trees tting the mean and the covariance of the return distribution are used for generating the coeecients of the stochastic program. In order to investigate the performance...

In the context of public transportation system, improving the service quality and robustness through minimizing the average passengers waiting time is a real challenge. This study provides robust stochastic programming models for train timetabling problem in urban rail transit systems. The objective is minimization of the weighted summation of the expected cost of passenger waiting time, its va...

In this article, the design of a Supply Chain Network (SCN) consisting of several suppliers, production plants, distribution centers and retailers, is considered. Demands of retailers are considered stochastic parameters, so we generate amounts of data via simulation to extract a few demand scenarios. Then a mixed integer two-stage programming model is developed to optimize simultaneously two o...

A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, governs the prices of fuels, the availability of electricity, and the demand for chemicals. A key difficulty in optimization under uncertainty is in dealing with an uncertainty space ...

How to make decisions while the future is full of uncertainties is a major problem shared virtually by every human being including housewives, firm managers, as well as politicians. In this paper we introduce a mathematical programming resolution to the problem, namely multi-stage stochastic programming. An advantage of that approach is obviously that we will be working with a precise, tangible...