The (<Emphasis Type="Italic">p</Emphasis>, <Emphasis Type="Italic">q</Emphasis>, <Emphasis Type="Italic">r</Emphasis>, <Emphasis Type="Italic">l</Emphasis>) model for stochastic demand under Intuitionistic fuzzy aggregation with Bonferroni mean

This paper investigates a hill type economic production-inventory quantity (EPIQ) model with variable lead-time, order size and reorder point for uncertain demand. The average expected cost function is formulated by trading off costs of lead-time, inventory, lost sale and partial backordering. Due to the nature of the demand function, the frequent peak (maximum) and valley (minimum) of the expected cost function occur within a specific range of lead time. The aim of this paper is to search the lowest valley of all the valley points (minimum objective values) under fuzzy stochastic demand rate. We consider Intuitionistic fuzzy sets for the parameters and used Intuitionistic Fuzzy Aggregation Bonferroni mean for the defuzzification of the hill type EPIQ model. Finally, numerical examples and graphical illustrations are made to justify the model.     

价格波动下的生产-库存控制研究

研究原材料价格波动下多级生产-库存系统的控制问题.所有的原材料价格、半成品加工成本、成品的生产成本、库存费用率和产品的需求率都随时间变动,为此,分析了最优采购、加工、生产决策的必要和充分条件,得到了在某些假设条件下的最优生产-库存策略为JIT(Just-in-time)采购、加工、生产策略,或者为在最开始阶段以最大能力进行采购、加工、生产活动的Bang-Bang策略.     

DYNAMICS AND CONTROL OF INTEGRATED PRODUCTION-INVENTORY-SHIPPING SYSTEMS

Abstract

In this paper, multivariable system theory is used to synthesize piecewise-constant control policies for production-inventory systems which incorporate unfilled-order backlogs. The state variables of the systems are the actual production rate, the inventory level discrepancy, and the unfilled-order backlog respectively. The control inputs are the desired production rate and the desired shipping rate, and the disturbance input is the demand for finished parts. It is shown that the original multi-input system can be decoupled into a set of single-input sub-systems in the modal domain by using a suitably chosen generalised modal matrix. The required policies for the original system are then readily obtained by considering each of the decoupled sub-systems separately. The behaviour of the controlled production-inventory system is illustrated by the presentation of the results of computer simulation studies showing typical transient and steady state response characteristics.     

Kalman filter based production control of a failure-prone single-machine single-product manufacturing system with imprecise demand and inventory information

An adaptive production control structure for failure-prone manufacturing systems under inventory and demand uncertainty is proposed. It contains estimation and forecasting modules incorporated into a control loop. The customer demand is unknown and its rate is composed of ramp-type, seasonal and random components. Information available to decision maker consists of imprecise inventory records, and the Kalman filter technique is used for estimating the inventory level and demand rate online from noisy inventory measurements. Estimates obtained are shown to converge to the actual values in stochastic sense. They are subsequently used for demand component forecasting, once the estimation errors become sufficiently small. A forecasting algorithm allows estimating ramp-type and seasonal demand components, together with their potential errors. Obtained estimates are incorporated into production control procedures, recently developed for manufacturing systems under variable and uncertain demand. Optimality conditions in the form of Hamilton-Jacobi-Bellman equations are obtained. A constructive numerical method for computing sub-optimal production policies is proposed and validated through numerical simulations.     

Particle Swarm Optimization and Pure Adaptive Search in Finish Goods’ Inventory Management

Abstract

Inventory management deals with a tradeoff between the benefits of keeping stocks of goods that allows fulfillment of the customer’s demand, and the cost of carrying inventory. Inventory control techniques are very important components and the most organizations can substantially reduce their costs associated with the flow of materials. This paper presents new inventory management model based on particle swarm optimization and pure adaptive search global optimization algorithm in production-inventory system. The proposed model is focusing on planned level of demand for finished goods, production and raw materials cost, production capacity as the norm, change of the production cost and inventory capital cost, all of which are typical factors in automobile manufacture industry. The model determines different factors such as the minimizing inventory quantity, minimizing inventory value, and minimizing production cost based on demand for production items. The model is tested with original real-world dataset obtained from the automotive company Lear from US and its factory in Novi Sad, Serbia.     

Calculating target inventory levels for constrained production: A fast simulation-based approximation

An accurate model for the inventory shortfall distribution is necessary to calculate the target level required to give a desired service level in manufacturing systems under stochastic demand and production capacity constraint. Existing methods for modelling the inventory shortfall require that the demand distribution be expressible in functional form and that the coefficient of demand variation be small. When these conditions cannot be met, the only recourse to a practitioner is to set target levels using simulation-based optimisation, which is computationally intensive and time consuming. By contrast, this paper presents a model in which the inventory shortfall is approximated by sampling from a single simulation run of the inventory process. The target level required for a given service level can then be calculated efficiently, to a high degree of reliability, using an iterative search. This new model is thus an efficient alternative to conventional simulation-based optimisation. Because the shortfall distribution is generated by simulating demand directly, the model makes no assumptions about the form of the demand distribution. By requiring no user modelling of the functional form or parameters of the demand distribution, this new method is easily used by inventory managers in practice or implemented in software.     

Infinitesimal Perturbation Analysis and Optimization for Make-to-Stock Manufacturing Systems Based on Stochastic Fluid Models

In this paper we study Make-To-Stock manufacturing systems and seek on-line algorithms for determining optimal or near optimal buffer capacities (hedging points) that balance inventory against stockout costs. Using a zStochastic Fluid Model (SFM), we derive sample derivatives (sensitivities) which, under very weak structural assumptions on the defining demand and service processes, are shown to be unbiased estimators of the sensitivities of a cost function with respect to these capacities. When evaluated based on the sample path of discrete-part systems, we show that these estimators are greatly simplified. Thus, they can be easily implemented and evaluated on line. Though the implementation on discrete-part systems does not necessarily preserve the unbiasedness property, simulation results show that stochastic approximation algorithms that use such estimates do converge to optimal or near optimal hedging points. Supported in part by the National Science Foundation under Grants EEC-0088073 and DMI-0330171, by AFOSR under contract F49620-01-0056, and by ARO under grant DAAD19-01-0610.     

一种利用切比雪夫逼近求解库存最优控制的方法

针对供应链中库存随着需求的变化可能导致的积压和对生产(或采购)产生的不利影响,为更好地协调生产(或采购)并减少产品库存,研究了一类基于库存约束和动态时变需求下的多品种、多周期、多循环的生产与库存的最优控制模型.结合最优控制理论,给出一种采用切比雪夫多项式逼近和高斯-切比雪夫数值积分对库存最优控制问题进行数值求解的方法.实例分析表明该方法是可行的.     

Inventory control with general demand and lead time distributions

This paper extends an earlier paper in this journal by Murphy (1975) by presenting practical approaches for determining the expected lost sales for a reorder level system of inventory control. First, a set of formulas are derived for computing the first four moments (f.f.m.) of the lead time demand, these formulas are applicable to any distribution forms of daily demand and lead time. By fitting the lead time demand's f.f.m. to either a beta or a Schmeiser-Deutsch distribution, this paper then demonstrates how the expected lost sales can be easily computed. The approaches presented provide accurate modelling for diversified situations and the computations can be easily performed manually.     

A newsboy problem with reactive production

This paper extends the classic newsboy problem by introducing reactive production. Production occurs in two stages, a anticipatory stage and a reactive stage. In the anticipatory stage, one determines a production level that anticipates the demand, all of which occurs in the reactive stage. There production takes place with full knowledge of the actual demand and, thus, can react to it. The reactive stage contains multiple sources of capacitated production. Demand is continuous and stochastic, and production, holding, and shortage costs are proportional. There are no fixed costs. Shortages are lost. Our model reduces to a single-period model with piecewise-linear convex costs. We obtain an analogue of the well-known critical fractile formula of the classic newsboy model. We also undertake a numerical study that compares our model with (i) the classic newsboy model, and (ii) a model which employs reactive production but uses classic newsboy formulas. Extensive computational experiments with normal demand problems suggest that the costs under our model can be substantially less than the costs under (i) and (ii).Scope and purposeConsider a seasonal product with a long-selling season and a highly volatile stochastic demand. The classic newsboy formulation of this problem assumes that all unsold goods be salvaged at a price that is often far below the production cost. This could lead to unacceptably low service levels since it tends to discourage high stock levels. On the other hand, were management to raise the service level to an acceptable level, the cost of the safety stock might be too great because of the highly volatile demand. To address this difficulty, we modify the classic newsboy problem by allowing management to schedule production in reaction to the demand during the selling period. Such production is possible when the selling period encompasses a long time interval. Our results indicate that this modification can significantly improve both costs and service levels.     

Optimal production control in a discrete manufacturing system withunreliable machines and random demands

We consider a production control problem in a manufacturing system with a failure-prone machine and a stochastic demand. The objective is to minimize a discounted inventory holding and backlog cost over an infinite planning horizon. The optimal production control of continuous, stochastic manufacturing systems with a failure-prone machine and a constant demand has been considered in Akella and Kumar (1986). However, the problem of optimal production control for discrete stochastic manufacturing systems with uncertain demands remains open. In this paper, we investigate a case where the exogenous demand forms a homogeneous Poisson flow. Primarily, we show that the optimal production control for such a system is of the threshold control type. In addition, the explicit form of production control policy and the objective functions are provided. Numerical examples are included to demonstrate the results obtained in the paper and to compare with the one in Akella and Kumar     

Fuzzy production control with limited resources and response delay

This paper attempts to study the possibility of using fuzzy control in production-inventory systems that contain variable processes with fixed capacity. The average processing rate that builds up the inventory is equal to the average delivery rate that consumes the inventory so that the system needs no-control action on the basis of averages. However, the inherent randomness in both consumption and replenishment of inventory gives rise to random variations in inventory level that needs to be controlled. Attempt is thus made to develop a fuzzy control system (FCS) to control the effects of randomness in such production systems. Effects of various parameters of the FCS on various performance measures are investigated so that a FCS may be developed for specific situations. It is shown how limited resources on production capacity and the delay due to processing time frustrate the efforts of designing an effective FCS although some benefits can still be achieved. The question of how frequently the fuzzy inference engine (FIE) should observe the system and process the inputs is also studied. Finally it is shown how a little extra production capacity makes the FCS very effective. The investigations provide an understanding and methodology that can be used to design FCS for any situation and, although we have considered two products, it can easily be extended to more than two products.     

Disruption management in a constrained multi-product imperfect production system

Over several decades, production and inventory systems have been widely studied in different aspects, but only a few studies have considered the production disruption problem. In production systems, the production may be disrupted by priorly unknown disturbance and the entire manufacturing plan can be distorted. This research introduces a production-disruption model for a multi-product single-stage production-inventory system. First, a mathematical model for the multi-item production-inventory system is developed to maximize the total profit for a single-disruption recovery-time window. The main objective of the proposed model is to obtain the optimal manufacturing batch size for multi-item in the recovery time window so that the total profit is maximized. To maintain the matter of multi-product, budget and space constraints are used. A genetic algorithm and pattern search techniques are employed to solve this model and all randomly generated test results are compared. Some numerical examples and sensitivity analysis are given to explain the effectiveness and advantages of the proposed model. This proposed model offers a recovery plan for managers and decision-makers to make accurate and effective decisions in real time during the production disruption problems.     

模糊需求和模糊能力约束的集约生产计划

通过对模糊需求量和模糊等式及模糊需求环境下生产-库存平衡方程两种等价的描述方法的基础上,建立了具有模糊需求量和模糊能力约束集约生产计划问题的最佳平衡模型(BAPP)、交互式集约计划模型(IAPP)和交互式求解方法.     

Minimum settling-time control policies for cascaded production-inventory systems

In this paper, the technique of entire eigenstructure assignment is used to derive minimum settling-time control policies for a class of production—inventory systems which can be described by linear multivariate discrete-time state equations. It is shown that this technique can be readily used to derive minimum settling-time control policies for production-inventory systems which consist of a set of production-inventory sub-systems connected in cascade. The advantage obtained by using control policies derived in this way, compared with control policies derived by consideration of each sub-system in isolation, is clearly demonstrated.     

Unreliable production-inventory model with a two-phase erlang demand arrival process

A production-inventory system is studied in which an unreliable machine is susceptible to failure following which it must be repaired to make it operative again. The demand for the product is governed by a two-phase Erlang process and demand sizes are independent and identically distributed random variables. A two-critical-number policy (m, M) is used to control a machine's setups and shutdowns, namely, the machine is shut down whenever the inventory level reaches M, and is resumed to operate only when the inventory level falls below the critical number m (m ≤ M). We obtain the steady-state distribution of the inventory process and some performance measures of the process.     

按单装配系统中组件生产和库存分配控制策略研究

针对由两种组件、三类顾客需求组成的按单装配系统, 本文研究了其中的组件生产控制与库存分配问题. 在各类顾客需 求是泊松到达过程, 各种组件加工时间服从指数分布的假设下, 我们运用马尔科夫决策理论建立了无限期折扣总成本模型, 根据Lippman转换得到了相应归一化后的离散最优方程, 在此基础之上分析了生产和库存分配联合最优控制策略的结构性质. 本文证明了最优策略是依赖于系统状态的动态策略. 组件的最优生产策略是动态基库存策略, 其中基库存水平是关于系统中其他组件库存水平的非减函数. 而最优的分配策略是动态的阈值策略, 对于只需一种组件构成的顾客需求, 组件的分配阈值是系统中另一组件库存水平的增函数; 而对于同时需要两种组件组成的顾客需求, 其各组件的分配阈值是另一组件库存水平的减函数. 最后通过数值试验给出了各个参数对联合最优控制策略的影响, 并得到了相应的管理启示.     

Joint management of finished goods inventory and demand process for a make-to-stock product: a computational approach

In this paper, we consider the joint management of finished goods inventory and demand for a product in a make-to-stock production system. The production process is random with controllable mean rate, and the demand process is stochastic with changeable mean rate dependent on the sale price being high or low. The management issue is how to dynamically adjust the production rate and the sale price to maximize the long run total discounted profit. We show that: 1) the optimal management of the finished goods inventory follows a base stock policy: when the inventory is above certain base stock level, the production is halted; otherwise the maximum production rate is deployed to raise the inventory to the base stock level; and 2) the optimal management of the demand process follows a price switch threshold policy: when the inventory is above the threshold, the low sale price is chosen to sell the product; and below it the high price is chosen to reduce the demand. We provide an algorithm to compute the base stock level and price switch threshold. Extension to multiple price choices is given with proofs highlighted.     

Cost benefits from standardization of the packaging glass bottles

This study deals with a recycling system with two competing brewers. It is assumed that they coordinate their manufacturing operations through standardization of their glass bottles for easy implementation of extended producer responsibility (EPR). Immediate benefits from the standardization are three folds. Firstly, the sorting and exchange processes of the bottles collected for reuse by each brewer become no longer necessary. Secondly, cost reduction is achieved through streamlining of collection and reuse processes. Finally, under the stochastic demand of glass bottles their inventory holding costs and lost sales cost are reduced via inventory pooling. Through the development of the mathematical models we determine an optimal operation policy of the two brewers that maximizes the sum of benefits obtained from standardization. Numerical examples are solved to show the validity of the model. Sensitivity tests are also performed to examine the effects of system parameters on the objective function value and decision variables.     

需求和回收品均随机的制造-再制造系统生产控制

需求及回收品数量和时间的不确定性, 导致制造-再制造系统的库存管理非常困难. 为控制库存尽可能位于某一合理区间内, 在假设库存水平变化由无负跳跃Lévy 过程描述条件下, 利用更新过程和鞅理论, 构建了系统期望折扣总费用模型, 并采用交叉熵法确定最优的生产速率和调整阈值. 最后, 通过仿真实验分析了回收品、需求和系统参数对最优控制策略和期望折扣费用的影响.