On two-echelon inventory systems with Poisson demand and lost sales

We derive approximations for the service levels of two-echelon inventory systems with lost sales and Poisson demand. Our method is simple and accurate for a very broad range of problem instances, including cases with both high and low service levels. In contrast, existing methods only perform well for limited problem settings, or under restrictive assumptions.\u

Computing (R, S) policies with correlated demand

This paper considers the single-item single-stocking non-stationary stochastic lot-sizing problem under correlated demand. By operating under a nonstationary (R, S) policy, in which R denote the reorder period and S the associated order-up-to-level, we introduce a mixed integer linear programming (MILP) model which can be easily implemented by using off-theshelf optimisation software. Our modelling strategy can tackle a wide range of time-seriesbased demand processes, such as autoregressive (AR), moving average(MA), autoregressive moving average(ARMA), and autoregressive with autoregressive conditional heteroskedasticity process(AR-ARCH). In an extensive computational study, we compare the performance of our model against the optimal policy obtained via stochastic dynamic programming. Our results demonstrate that the optimality gap of our approach averages 2.28% and that computational performance is good

Measuring the variability in supply chains with the peakedness

This paper introduces a novel way to measure the variability of order flows in supply chains, the peakedness. The peakedness can be used to measure the variability assuming the order flow is a general point pro- cess. We show basic properties of the peakedness, and demonstrate its computation from real-time continuous demand processes, and cumulative demand collected at fixed time intervals as well. We also show that the peakedness can be used to characterize demand, forecast, and inventory variables, to effectively manage the variability. Our results hold for both single stage and multistage inventory systems, and can further be extended to a tree-structured supply chain with a single supplier and multiple retailers. Furthermore, the peakedness can be applied to study traditional inventory problems such as quantifying bullwhip effects and determining safety stock levels. Finally, a numerical study based on real life Belgian supermarket data verifies the effectiveness of the peakedness for measuring the order flow variability, as well as estimating the bullwhip effects.variability, peakedness, supply chain

Evolutionary multiobjective optimization of the multi-location transshipment problem

We consider a multi-location inventory system where inventory choices at each location are centrally coordinated. Lateral transshipments are allowed as recourse actions within the same echelon in the inventory system to reduce costs and improve service level. However, this transshipment process usually causes undesirable lead times. In this paper, we propose a multiobjective model of the multi-location transshipment problem which addresses optimizing three conflicting objectives: (1) minimizing the aggregate expected cost, (2) maximizing the expected fill rate, and (3) minimizing the expected transshipment lead times. We apply an evolutionary multiobjective optimization approach using the strength Pareto evolutionary algorithm (SPEA2), to approximate the optimal Pareto front. Simulation with a wide choice of model parameters shows the different trades-off between the conflicting objectives

The influence of demand variability on the performance of a make-to-stock queue

Variability, in general, has a deteriorating effect on the performance of stochastic inventory systems. In particular, previous results indicate that demand variability causes a performance degradation in terms of inventory related costs when production capacity is unlimited. In order to investigate the effects of demand variability in capacitated production settings, we analyze a make-to-stock queue with general demand arrival times operated according to a basestock policy. We show that when demand inter-arrival distributions are ordered in a stochastic sense, increased arrival time variability indeed leads to an augmentation of optimal base-stock levels and to a corresponding increase in optimal inventory related costs. We quantify these effects through several numerical examplesproduction/inventory; make-to-stock; base-stock; stochastic comparisons; GI/M/1, POLICIES; COSTS; SYSTEMS; LEAD

Approximation Algorithms for Stochastic Inventory Control Models

Approximation Algorithms for Stochastic Inventory Control Model