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发信人: Christy (诗意的信仰), 信区: Matlab
标  题: An Example of Monte Carlo Simulation
发信站: 哈工大紫丁香 (2001年11月06日18:46:37 星期二), 站内信件

我把我的一个Monte-Carlo Simulation的介绍和结论给你贴出来，希望有
所帮助.

                             Introduction

The aim of this assignment is to establish the minimum cost policy (the comb
ination between a re-order point and a number of order quantities for the mi
nimum cost) in an inventory system for an item which historically has been s
ubject to both variable demand (in units per week) and variable lead time (i
n weeks from order to delivery). This will be performed by means of a Monte
Carlo Simulation using Turboc2.0 in which the syntax of loops and conditiona
l judgement is essential[1]. The inventory system will be simulated with a c
ertain number of repetitions and a certain length of time measured by weeks
(simulation weeks). The repetitions and the simulation weeks will be varied
independently to minimise any possible negative effects of using computer-ge
nerated random numbers and to find the optimal policy with the cost paramete
rs associated with the system, i.e., order placement cost, holding cost and
stockout cost. Furthermore, the confidence interval for the cost from each c
ombination will be constructed. Finally, the effects on the optimal policy b
y changing the cost parameters will be investigated.

A Monte Carlo Simulation is a probabilistic type of simulation that approxim
ates the solution to a problem by sampling from a random process. Some known
probability distributions of certain key variables (the demand and the lead
time in this system) will be defined firstly and then converted to cumulati
ve probability distributions in order to determine specific variable values
used in the simulation. Note that sufficient repetitions and numbers of simu
lation weeks should be used (up to 10,000 repetitions and 5200 weeks in this
system), since computers are deterministic, and as a result computer-genera
ted numbers are not really random[3]. In addition, the variance of the resul
ts will be reduced.

*****************************************************************************

                              Conclusion

Monte Carlo Simulation techniques can be used to establish the optimal opera
ting policy for an inventory system. In the inventory system, because of the
stochastic nature of the variables, deterministic mathematical methods are
invalid, and statistic methods should be used instead. Note that in this inv
entory system, the most important result is not detailed values but the poli
cies behind them.
For this system, the optimal policy is the combination between a re-order po
int and order quantities for the minimum cost, and is related to some cost p
arameters. Note that due the properties of the random number generators in p
rogramming languages, the reliability and validity of pseudo-random numbers
should be considered. Therefore, sufficiently large repetitions and long len
gth of simulation time are necessary, which is also dedicated to the reducti
on of the variances.
With the initial values of the three cost parameters, 100 repetitions and 52
simulation weeks, the simulation shows that setting the re-order point to b
e 0 units and the order quantities to be 5 units will be probably the optima
l policy for the item. Then after using larger number of repetition as well
as longer length of simulation time, the optimal policy is stabilised to be
the combination above. In addition, confidence intervals are constructed aim
ing to estimate the existing ranges of the true cost from each combination w
ith 95% probability.
In order to study the effects of the three cost parameters on the optimal po
licy of the system, they are changed independently in three series of simula
tions, and the changes of the optimal policy caused by the different paramet
ers are investigated. The results show that a large order placement cost mak
es the optimal policy lead to a large number of order quantities and a small
re-order point. A large holding cost causes the optimal policy to change to
have both a small re-order point and a small number of order quantities. Th
e optimal policy tends to be both a large re-order point and a large number
of order quantities when a large stockout cost is introduced. The change of
the optimal policy is more sensitive to the change of stockout cost than to
that of the holding cost and to that of the order placement cost. Finally, i
f significant large values of the cost parameters are introduced, the curren
t model of the system will not be suitable any more and as a result, models
with different range of re-order point and order quantities are required ins
tead.

--
屈原既黜，披发行吟泽畔，颜色憔悴，形容枯槁。渔父见而问之曰：“子非
三闾大夫耶？何以至此？”屈原曰：“举世浑浊而我独清，众人皆醉而我独
醒，是以见放。”渔父曰：“吾闻夫圣人者，不凝滞于物，而与世推移。举
世浑浊，何不逐其流而荡其波；众人皆醉，何不哺其糟而啜其螭，何故怀瑾
握瑜，而自令见放为？”屈原曰：“吾闻新沐者必弹冠，新浴者必振衣。人
又能向之察察，而受物之汶汶者乎？"......�

※ 来源:·哈工大紫丁香 bbs.hit.edu.cn·[FROM: 天外飞仙]

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