2005年优博：物流系统的库存控制模型与方法研究

作者姓名：周永务
论文题目：物流系统的库存控制模型与方法研究
作者简介：周永务，男，1964年9月出生，1999年9月师从于合肥工业大学杨善林教授，于2002年12月获博士学位。

中文摘要

研究物流系统的根本目标之一是降低物流总成本，物资的库存成本在物流总成本中占据着相当大的比重，因此，研究库存控制的相关理论与方法对降低物流总成本具有重要的实际意义，这也是库存控制理论研究成为物流系统理论研究一个热点问题的原因之一。

近几十年来，尽管传统库存控制理论的研究取得了较大的进展，但由于库存控制系统所处环境的复杂性与多变性，其理论成果与实际应用的要求还有相当大的差距。本文从应用已有的库存控制理论进行实际的库存决策时遇到的具体问题入手，从多个方面对传统的库存控制理论进行了进一步的拓展研究，具体的研究内容如下：

1、EOQ公式的推广。针对经典的EOQ公式忽略每个需求被服务的时间，而实际上每个需求到达时都要经历一个服务过程这一状况，本文首先将经典的EOQ公式推广到了有限服务率的情形，这使得EOQ公式能适用于电子商务；其次将备运期的控制问题引入库存模型，在备运期―费用函数为指数函数的假定下，进一步提出了服务率有限的库存系统选择合理备运期和订货策略的联合决策模型；第三，分析了供货方就某一变质性物品提供临时价格折扣对库存系统原先的正常订货策略的影响，证明了当临时折价期含于正常的订货周期内时，如果在临时折价期内的某一时刻作一次临时订货能从折扣的价格中获得实惠，那么该时刻必定是折价期的终止时刻，并为库存系统提供了在临时折价期内进行临时订货的最优订货决策方法。

2、时变需求库存控制模型的进一步研究。（1）本文通过利用折扣现金流方法，率先研究了资金时值变化对库存系统订货策略的影响，针对一般时变需求提出了考虑资金时值变化的库存控制模型，这使得传统的库存控制模型能适用于通货膨胀的经济环境；（2）在库存管理实践中，库存系统所订购物品的到达与其购买资金的投入有时并非是同时的，本文将购买费用的滞后支付问题首次引入到带有时变需求的库存系统，提出了该系统在三种不同的滞后支付规则下寻求最优订货策略的库存控制模型；（3）通过将订货费看成是一部分固定费用与另一部分正比于订货量的可变费用之和，并放松了等补充周期的假定，而将带有时变需求的库存控制模型作了进一步拓展，针对一般时变需求，建立了库存系统在有限计划期内的库存控制模型，并就线性需求情形，证明了该模型整体最优解的存在性与唯一性，设计了寻求模型最优解的简便算法；（4）本文还研究了带有多个有限容量货栈的库存系统的库存控制问题，在利用一种特别的指数增加函数去逼近产品在其增长期内需求的情形下，为库存系统提出了一个多货栈库存控制模型，证明了模型唯一最优解的存在性，并设计了确定该最优解的一维算法；（5）根据产品在其"寿命期"内需求变化特征，本文利用一种特别的m次多项式函数去逼近产品在其"寿命期"内的需求，提出了一个在产品的整个"寿命期"寻求最优订货策略的动态规划模型，运用贝尔曼最优化原理，为库存系统设计了一个寻求最优订货策略的简易算法，该模型克服了现有时变需求的库存模型仅适用于产品的"增长期"或"衰退期"的不足。

3、生产库存控制模型的进一步研究：（1）将预防性性维修中断计划和原材料订货问题同时引入到传统的生产库存控制模型，建立了寻求最优生产批量和相应的原材料订货策略、预防性维修中断策略的联合决策模型；（2）将生产率作为决策变量、单位产品生产费用看成是生产率的函数，提出了允许短缺发生的柔性制造系统的最优生产批量模型，提供了寻求模型整体最优解的简单算法。研究结果表明，当制造系统的柔性增强时，该系统的最优生产率应减少，而相应的最优生产批量则应增大；（3）通过利用D.
Jong的学习曲线，分析了人类学习现象对制造系统生产策略的影响，提出了允许短缺发生的制造系统在考虑人类学习现象时的生产库存控制模型，并证明了该模型最优解的存在性与唯一性，设计了求解算法；（4）采用了逐步调整生产率以适应市场需求变化的思想，为连续生产的柔性制造系统提供了一类新的连续生产的生产库存控制模型。
首先在相继调整周期长度减小幅度相同的假定下，就线性需求模式，给出了在有限计划期内调整生产率的简单方法；其次通过放松相继调整周期长度减小幅度相同的假定，针对一般时变需求，进一步发展了生产变质性产品的生产系统在有限计划期内的生产率最优调整模型，并将这类模型又进一步拓展到了缺货要补的情形以及生产率的调整费用依赖于生产率的调整幅度的情形。这类模型克服了传统生产库存模型仅提供间隙性生产策略的缺陷。

4、从两个方面将经典的Newsboy
问题进行了拓展：（1）针对某些带有"节日"消费性质的易变质商品，厂家为了减少库存往往提供提前订购价格折扣的实际情况，将供货方常常提供提前订购价格折扣的实际现象加入Newsboy问题，提出了带有提前购买价格折扣的变质性物品的随机库存模型；（2）将广告宣传引进了经典的Newsboy
模型，在分析广告宣传对商品市场需求的影响的基础上，假定商品的期望需求是广告投入的增加凹函数，以期望总利润为目标，建立了一个联合确定最优广告投入与订货策略的随机库存模型，证明了市场需求的不确定性的增加将导致经销商减少在广告上的投入。

5、本文将需求率依赖于库存水平的库存控制模型进一步拓展到了考虑随等待时间变化的拖后短缺情形，通过利用等待时间的下降函数来逼近短缺期内短缺拖后的比例，提出了需求率线性依赖于库存水平的变质性物品的一个库存控制模型。和已有的相关模型不同，该模型以销售利润为目标，它不需要决策者去估计实际中难以估计的短缺损失费或短缺拖后费；其次将该类模型拓展到适用于具有固定保质期的物品，按照后进先出的实际销售策略（这反映了顾客总挑选最新鲜物品的购买心理），建立了寻求该类物品进货策略的一个简单决策模型。

6、具有链结构的物流系统的库存控制模型研究。本文研究了由一个制造商和许多个不同的销售商组成的两层供应链间的协调问题，在制造商的补充计划独立于每个销售商订货批量的假定下，为供应单一产品给许多不同销售商的制造商设计了诱使销售商们协调运作的两种不同方法：独立量折扣和公共量折扣，并进一步研究了供应多个产品个许多不同销售商的制造商如何促使销售商们进行协作问题，提出了一个相应的独立量折扣模型。

上述研究成果不仅丰富了库存控制理论的内容，也拓展了传统库存控制模型的应用范围，为决策者进行实际的库存决策提供了更充分的科学依据。

关键词：EOQ 模型；生产库存控制模型；Newsboy 模型；多货栈库存控制方法；供应链管理

Research on inventory control models and methods of the logistics system

Zhou Yong-Wu

ABSTRACT

One of the fundamental objectives of studying the logistics
system is to reduce the total cost of logistics. But much more
proportion of the total cost of logistics is the inventory cost of
items. Therefore, studying the theory and methods of inventory control
is very significant for reducing the total cost of logistics. This is
also one of the reasons why it is a hot spot of logistics theory
research.

During recent several decades, although the research on the
traditional inventory control theory has made much more progress,
there is still a considerable big gap between the acquired theoretical
results and the requirement of practical application due to the
complexity and variation of environment. This dissertation starts with
the concrete problems that decision makers may encounter while they
use the existing inventory theory to make practical inventory
decisions, and makes further extensive study on the traditional
inventory control theory from various aspects. The details are given
as follows.

1. Extensions for EOQ formula. First, noting that the classical EOQ
formula does not consider the served time of each demand but each
demand actually has a served process, this dissertation extends the
classical EOQ formula to the situation with a finite service rate. It
makes EOQ formula be suitable for electric business. Second, the
control problem of lead-time is incorporated into inventory model.
Under the assumption that the lead-time-cost function is an
exponential one, an integrated decision model is offered to the
inventory system with the finite service rate to choose rational
lead-time and order policy. Third, we analyze the effect of the
supplier providing a temporary price discount for a deteriorating item
on the original order policy of the inventory system. We prove that if
placing a temporary order at some time in the temporary price discount
period can get benefits from the discounted price, the time of placing
this order must be at the ending time of the temporary price discount
period, while the temporary price discount period is included in the
normal order cycle. Also, we provide an optimal decision method for
the inventory system to place a temporary order during the temporary
price discount period.

2. The further research on inventory control models with time-varying
demand. (1) By employing discounted cash flow approach, the
dissertation studies the effect of the time value of money on the
order policy of the inventory system, and presents an inventory
control model considering the time value of money for the general
time-varying demand. This makes the traditional inventory control
model be suitable for the economic environment of inflation. (2) The
dissertation is probably the first to integrate the problem of paying
the purchasing cost in delay to the inventory system with time-varying
demand. It proposes inventory control models for finding the optimal
order policy under three rules of the delayed payment. (3) Inventory
control models with time-varying demand is further extended by
relaxing the assumption of equal replenishment cycle and considering
the order cost as the sum of one portion of fixed cost and the other
portion of flexible cost proportioned to the order quantity. An
inventory control model is developed for the inventory system with
general time-varying demand in the finite planning period. The
existence and uniqueness of the global optimal solution of this model
is proved for a linearly time-varying demand. A simple algorithm is
provided for finding this optimal solution. (4) Inventory control
problems are also studied for an inventory system with multiple
warehouses of finite volume. By using a special exponential increasing
function to approach the demand of the product in its growth phase, a
multi-warehouse inventory control model is proposed for the inventory
system. The existence of this model's unique optimal solution is
proved. A one-dimensional algorithm is designed for determining this
optimal solution. (5) By using a special polynomial of degree m to
approach the demand of the product in its lifetime, a dynamic
programming model is provided for finding the optimal order policy in
the whole lifetime of the product. According to Bellman's optimization
principle, a simple algorithm is designed to find the optimal order
policy over the whole lifetime. This model overcomes the flaws that
the existing inventory models appear to be only fit for the growth
phase or the declining phase of the product.

3. The further study on the traditional production-inventory control
models. (1) The preventive-maintain interruption schedule and the
order problem of materials are simultaneously incorporated into the
traditional production-inventory control models. An integrated
decision model is built for determining the optimal production lot
size, its corresponding preventive maintain interruption policy and
order policy of materials. (2) An optimal production lot size model
for the volume flexible manufacturing system with shortages permitted
is presented by considering the production rate as decision variable
and the production cost per unit product as a function of the
production rate. A simple algorithm is proposed to determine the
global optimal solution of this model. The research results indicate
that as the flexibility of the manufacturing system increases, the
optimal production rate of the system decreases but the corresponding
optimal production lot-size increases. (3) The effect of the human
learning phenomenon on the production policy of the manufacturing
system is analyzed by using D. Jong learning curve. A
production-inventory control model is presented for the manufacturing
system considering the human learning phenomenon and shortages. (4) By
adopting an idea of adjusting gradually the production rate to meet
the change of the market demand, we propose a sort of new
production-inventory control models for the volume flexible
manufacturing system producing continuously. First, under the
assumption that the reducing scopes of the successive adjustment cycle
lengths are the same, a simple method of adjusting the production rate
over the finite planning period is shown for a linear trend in demand.
Second, by relaxing the above assumption, an optimal adjustment model
of the production rate is developed for the manufacturing system that
produces a deteriorating item with general time-varying demand during
the finite planning period. Third, this sort of models are further
extended to cover the situation with shortages allowed to backlog and
the case with the adjustment cost of the production rate dependent
upon the adjustment scope of the production rate. This sort of models
covers the shortcoming that the traditional production-inventory
control models only show intermittent production policy.

4. The classical Newsboy problem is extended in the following two
aspects. (1) The price discount for early purchase is added to Newsboy
problem. A random inventory model is presented for deteriorating items
with a price discount for early purchase. (2) Advertisement propaganda
is incorporated into Newsboy models. Based on analyzing the effect of
advertisement propaganda on the market demand of the merchandise, it
is assumed that the expected demand of the merchandise is an
increasing concave function of advertisement investment cost. A random
inventory model is built for integratedly determining the optimal
advertisement investment cost and order policy to keep the total
expected profit to be maximum.

5. Inventory control models with stock-dependent demand rate are
firstly extended by considering waiting-time-dependent backlogged
shortages. Using a decreasing function of waiting time to approach the
fraction of backlogged shortages, an inventory control model is
proposed for deteriorating items with linearly stock-dependent demand
rate. Unlike the existing relative models, this model takes the sale
profit as the objective. It does not require the decision-maker
estimating the opportunity cost due to the lost sale or the backorder
cost, which is difficult to estimate in practice. Next, inventory
models with stock-dependent demand rate are further extended to the
situation of considering items with fixed lifetime. According to the
LIFO (last-in-first-out) sale policy, which reflects customers'
purchase psychology: always picking out the most fresh goods, a simple
decision model is built for finding the order policy of this type of
items.

6. Study on inventory control models for the chain-structured
logistics system. This dissertation studies the coordinated problem of
the two-echelon supply chain that consists of a manufacturer and many
different retailers. Under the assumption that the manufacturer's
replenishment planning is independent on the order lot size of every
retailer, two different methods (independent quantity discount and
common quantity discount) that induce the retailers to cooperate are
designed for the manufacturer who supplies a single product to the
retailers. Further discussed is the problem of how the manufacturer
who supplies multiple products to the retailers induces the retailers
to cooperate. A corresponding independent quantity discount model is
developed.

The research results presented above not only enrich the content of
inventory control theory but also widen the applied areas of the
traditional inventory control models, and provide more sufficient
scientific evidence for decision makers making inventory decision.

Keywords: EOQ model; Production-inventory control model; Newsboy
model; Multi-warehouse inventory control method; Supply chain
management.