Optimization of warehousing and transportation costs, in a multi-product multi-level supply chain system, under a stochastic demand

The centralized management approach provides a general view to set a better coordination between the elements of the supply chain, and look for the equilibrium between the stock and the shipped quantities. This paper describes a stochastic model predictive control algorithm to optimize the warehousing cost and the shipping cost on the same time. We consider a multi-level and multi-product supply chain dealing with a stochastic demand. We solve the stochastic model predictive control problem by a dynamic programming to determine the optimal policies to minimize the costs of shipping and warehousing products

Using duality to solve generalized fractional programming problems

In this paper we explore the relations between the standard dual problem of a convex generalized fractional programming problem and the “partial” dual problem proposed by Barros et al. (1994). Taking into account the similarities between these dual problems and using basic duality results we propose a new algorithm to directly solve the standard dual of a convex generalized fractional programming problem, and hence the original primal problem, if strong duality holds. This new algorithm works in a similar way as the algorithm proposed in Barros et al. (1994) to solve the “partial” dual problem. Although the convergence rates of both algorithms are similar, the new algorithm requires slightly more restrictive assumptions to ensure a superlinear convergence rate. An important characteristic of the new algorithm is that it extends to the nonlinear case the Dinkelbach-type algorithm of Crouzeix et al. (1985) applied to the standard dual problem of a generalized linear fractional program. Moreover, the general duality results derived for the nonlinear case, yield an alternative way to derive the standard dual of a generalized linear fractional program. The numerical results, in case of quadratic-linear ratios and linear constraints, show that solving the standard dual via the new algorithm is in most cases more efficient than applying directly the Dinkelbach-type algorithm to the original generalized fractional programming problem. However, the numerical results also indicate that solving the alternative dual (Barros et al., 1994) is in general more efficient than solving the standard dual