In this paper we extend the generalized surrogate optimization approaches and the stochastic comparison so as to tackle the lot-sizing problem in manufacturing system. In practice, with the surrogate methodology, the lot sizes are continuously adjusted on-line by the gradient-based approaches. The lot sizing determines the number of parts batched together for production. We utilize the queueing...

Considering the competition in today’s business environment, tactical planning of a supply chain becomes more complex than before. In many multi-product inventory systems, substitution flexibility can improve profits. This paper aims to prepare a comprehensive substitution inventory model, where an inventory system with two substitute products with ignorable lead time has been considered, and e...

In this paper, we derive a parabolic partial differential equation for the expected exit time of non-autonomous time-periodic non-degenerate stochastic equations. This establishes Feynman–Kac duality between equations and solutions Casting solution as fixed point problem convex optimisation problem, give sufficient conditions in which is well-posed weak classical sense. With no known closed for...

Abstract. We present a simple dynamical model to address the question of introducing a stochastic nature in a time variable. This model includes noise in the time variable but not in the “space" variable, which is opposite to the normal description of stochastic dynamics. The notable feature is that these models can induce a “resonance" with varying noise strength in the time variable. Thus, th...

Patient preferences have a social welfare interpretation consonant with a belief that the society affected by present decisions will last for a very long time. In stochastic settings, these preferences lead to justifications for variants of the precautionary principle.

It is known that a stochastic differential equation (SDE) induces two probabilistic objects, namely a difusion process and a stochastic flow. While the diffusion process is determined by the innitesimal mean and variance given by the coefficients of the SDE, this is not the case for the stochastic flow induced by the SDE. In order to characterize the stochastic flow uniquely the innitesimal cov...

In literature, most papers examine several stochastic demand processes where order lead times are constant. In reality, manufacturing firms use inventory management software, especially MRP, which ignored lead time uncertainty. It is true that in certain special cases, lead time uncertainty has essentially no effect and can be ignored. Nevertheless more often, lead time fluctuations strongly de...