(s, S) Inventory Systems with Correlated Demands

Abstract

Most inventory models in the literature assume that demands are independent among different time periods. However, a number of recent studies suggest that demands are often correlated over different time periods, which motivates our work here. In this paper, we study a class of periodic review (s, S) inventory systems in which demands are correlated and modeled as a Markov-modulated process. Using a Maclaurin series analysis and a Pade approximation, as well as an infinite system of linear equations, we develop algorithms to calculate the moments of the inventory level based on which various performance measures of the system can also be evaluated. Numerical experiments show that our approach is quite efficient and provides accurate estimates for the moments of the inventory level and other related performance measures.

Regression Monte Carlo for Impulse Control

“…The most well known sub-case is when the state (X t ) is one dimensional and is expected to be a renewal process when optimally controlled. The so-called (s, S) strategies focus on determining an impulse threshold s and a target level S and reduce computation of optimal strategy to a two-dimensional optimization over the two constants s, S. (s, S) strategies have been studied in Operations Research for over 20 years, formulations similar to the one I discuss have appeared in optimal inventory [10,14,26] and dividend payout problems [7,11,18].…”

Regression Monte Carlo for Impulse Control

“…The most well known sub-case is when the state (X t ) is one dimensional and is expected to be a renewal process when optimally controlled. The so-called (s, S) strategies focus on determining an impulse threshold s and a target level S and reduce computation of optimal strategy to a two-dimensional optimization over the two constants s, S. (s, S) strategies have been studied in Operations Research for over 20 years, formulations similar to the one I discuss have appeared in optimal inventory [11,14,26] and dividend payout problems [7,10,18].…”

Stochastic premarshalling of block stacking warehouses

“…To obtain the expected cost, we must fit the appropriate statistical distribution on historic pickup frequency data. If we consider day-long intervals, pickings could be modeled by a Poisson distribution: the number of times a specific SKU is picked in a day is discrete, pickings of different SKU are often independent of one another (for a discussion on this, see [24]), the rate at which picking orders are issued is constant, thus the probability of a picking in an interval is proportional to the length of the interval. To get to this, we first propose a Bernoulli model of the process, and then generalize it to a Poisson model, under the assumption of independence of SKU requests in the picking lists.…”