Modified Normal Demand Distributions in (R,S)-Inventory Models

To model demand, the normal distribution is by far the most popular; the disadvantage that it takes negative values is taken for granted.This paper proposes two modi.cations of the normal distribution, both taking non-negative values only.Safety factors and order-up-to-levels for the familiar (R, S)-control system are derived and compared with the standard values corresponding with the original normal distribution.demand;inventory control

Simulating an (R,s,S) Inventory System

inventory control;simulation models;reorder point;fill rate

New proposals for the validation of trace-driven simulations

simulation;simulation models;operations research

Two-Step Sequential Sampling for Gamma Distributions

estimation bias;extended sampling;sample extension;stochastic sample size;two-step sampling;statistical distribution

Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand

For the familiar (R; s; S) inventory control system only approximate expressions exist for the fill rate, i.e. the fraction of demand that can be satisfied from stock.Best-known are the approximations derived from renewal theory by Tijms & Groenevelt (1984), holding under specific conditions; in particular, S ¡ s should be reasonably large.They considered, more specifically, the cases of normally and gamma distributed demand.Here, an exact expression for the fill rate is derived, holding generally in the situation that demand has a gamma distribution with known integer-valued parameters, while lead time is constant.This formula is checked through extensive simulations; besides, detailed comparisons are made with Tijms & Groenevelt's approximation.demand;inventory control;simulation

Comparison of bias-reducing methods for estimating the parameter in dilution series

Estimation;mathematische statistiek

Investigating several alternatives for estimating the compound lead time demand in an (s,Q) inventory model

Inventory Models;management science

How to Determine the Order-up-to Level When Demand is Gamma Distributed with Unknown Parameters

Inventory models need information about the demand distribution. In practice, this information is not known with certainty and has to be estimated with often relatively few historical demand observations. Using these estimates leads to underperformance. This paper focuses on gamma distributed demand and a periodic review, order-up-to inventory control policy, where the order-up-to level satisfies a service equation. Under this policy the underperformance is quantified analytically under strong assumptions and with help of simulation if these assumptions are relaxed. The analytical results can be used to improve the attained service level, such that it approaches the desired service level more closely, even if the assumptions are not met. With help of simulation we show that in some cases this improvement results in reaching the desired service level. For the remaining cases, i.e., the cases in which the desired service level is not reached, the underperformance decreases; improvements range from almost 17% up to over 90%. Moreover, with help of simulation and linear regression further improvements can be obtained. The desired service level is reached in more cases and the underperformance in the other cases is decreased even more compared to using only the first improvement. These improvements range from 57% up to 99% compared to the base case (i.e., do not use analytical results) and from 35% up to over 90% compared to using the analytical results, except for a few cases in which the service hardly improved, but in those cases the attained service level was already very close to the desired one. Finally, the method developed in this paper is applied to real demand data using simulation. The total improvements in this case study range from 53% up to 96%.Unknown Demand Parameters;Inventory Control;Gamma Distribution;Ser- vice Level Criterion;Case Study

Assessing the Effects of using Demand Parameters Estimates in Inventory Control

Inventory models need some specification of the distribution of demand in order to find the optimal order-up-to level or reorder point.This distribution is unknown in real life and there are several solutions to overcome this problem.One approach is to assume a distribution, estimate its parameters and replace the unknown demand parameters by these estimates in the theoretically correct model.Earlier research suggests that this approach will lead to underperformance, even if the true demand distribution is indeed the assumed one.This paper directs the cause of the underperformance and quantifies it in case of normally distributed demand.Furthermore the formulae for the order-up-to levels are corrected analytically where possible and otherwise by use of simulation and linear regression.Simulation shows that these corrections improve the attained performance.Unknown Demand Parameters;Inventory Control;Normal Distribution;Service Level Criterion