需求随机依赖库存环境下的订货仿真优化模型

需求的随机性和依赖库存性是库存问题的特点之一,在需求以泊松分布的形式随机依赖库存的条件下讨论了（Q,T）型库存控制问题。为了评估库存控制策略的平均盈利水平,建立了该库存问题的离散事件系统仿真模型,设计了一种基于仿真的种群重叠、遗传操作非重叠的进化算法,用以优化库存控制策略,类似设计了基于仿真的模拟退火和粒子群优化算法进行比较。通过实例分析了不同参数的变化对模型最优解的影响,灵敏度分析表明需求依赖库存效应越明显时,利润水平越高,最优订货策略越倾向于高库存、短周期和现货销售。仿真实例说明了基于仿真的优化算法的可行性、有效性。     

横向整合战略下异质车辆库存路径优化模型

以实现供货商联盟期望物流成本最小化为目标,针对需求随机波动下的多供货商多产品库存路径问题（IRP）进行了研究。基于横向整合战略,设计了供货商联盟成员间车辆配送成本的合理分摊方式。考虑零售商配送软硬时间窗和库存服务水平要求,构建了多供货商多产品的异质车辆库存路径混合整数随机规划模型,并利用需求累积分布逆函数将其转化为确定型规划模型。然后设计改进遗传算法求解该确定型规划模型。算例分析结果显示,使用异质车辆配送可以比使用同质重型和轻型车辆分别降低供货商联盟总成本8.3%和11.92%,分别提升配送车辆装载率24%和17%。敏感性分析结果表明,无论供货商供货数量占联盟总供货数量比例和零售商商品需求变异系数如何变化,采用异质车辆配送的供货商联盟总成本都能得到有效降低;且需求变异系数越大,采用异质车辆配送的优势越明显。     

The distribution free continuous review inventory system with a service level constraint

The stochastic inventory models require the information on the lead time demand. However, the distributional information of the lead time demand is often limited in practice. We relax the assumption that the cumulative distribution function, say F, of the lead time demand is completely known and merely assume that the first two moments of F are known and finite. The distribution free approach for the inventory model consists of finding the most unfavorable distribution for each decision variable and then minimizing over the decision variable. We apply the distribution free approach to the continuous review inventory system with a service level constraint. We develop an iterative procedure to find the optimal order quantity and reorder level.     

Industrial cost modelling and multi-objective optimisation for decision support in production systems development

Recent developments in cost modelling, simulation-based multi-objective optimisation, and post-optimality analysis have enabled the integration of costing data and cost estimation into a new methodology for supporting economically sound decision-making in manufacturing enterprises. Within this methodology, the combination of production engineering and financial data with multi-objective optimisation and post-optimality analysis has been proven to provide the essential information to facilitate knowledge-driven decision-making in real-world production systems development. The focus of this paper is to present the incremental cost modelling technique specifically designed for the integration with discrete-event simulation models and multi-objective optimisation within this methodology. A complete example, using the simulation model and data modified from a previous real-world case study, is provided in this paper to illustrate how the methodology and cost modelling are applied for the optimal investment decision support.     

An integrated and dynamic optimisation model for the multi-level emergency logistics network in anti-bioterrorism system

Demand for emergency resources is usually uncertain and varies quickly in anti-bioterrorism system. Besides, emergency resources which had been allocated to the epidemic areas in the early rescue cycle will affect the demand later. In this article, an integrated and dynamic optimisation model with time-varying demand based on the epidemic diffusion rule is constructed. The heuristic algorithm coupled with the MATLAB mathematical programming solver is adopted to solve the optimisation model. In what follows, the application of the optimisation model as well as a short sensitivity analysis of the key parameters in the time-varying demand forecast model is presented. The results show that both the model and the solution algorithm are useful in practice, and both objectives of inventory level and emergency rescue cost can be controlled effectively. Thus, it can provide some guidelines for decision makers when coping with emergency rescue problem with uncertain demand, and offers an excellent reference when issues pertain to bioterrorism.     

Order overlapping: A practical approach for preventing shortages during screening

We develop an EOQ-type model with unreliable supply, where each order contains a random fraction of imperfect quality items with a known distribution. Upon receiving an order, a screening process is conducted to identify imperfect items. These imperfect items are salvaged as a single batch at the end of the screening process. To prevent shortages during the screening process, an order is placed when the inventory level is just enough to cover the demand during the screening period. Then, the demand during the screening period of an order is met from the inventory of the “previous” order. This represents an improvement in customer service level over earlier literature, where demand is assumed to be met during the screening period from the order being screened leading to potential shortages. We show that this improvement in service level comes at a modest cost. We further analytically and numerically study our model and draw useful insights.     

3级网状随机性库存控制策略的仿真优化

研究了多制造商,多分销商和多零售商的3级网状随机性库存系统的(r,Q)库存控制策略问题.由于该系统具有顾客到达时间服从泊松分布,随机顾客需求量,随机顾客购买行为,随机订货时间和制造商生产容量有限制等特点,使得解析方法很难描述系统中的多种复杂随机因素并无法求解有效的库存控制策略.为此建立了以总成本最小为目标的数学模型,运用了基于仿真的优化方法,通过将仿真方法与粒子群优化算法相结合对问题进行求解.最后通过仿真实例与比较,验证了模型和基于仿真的粒子群优化方法的可行性和有效性.也表明了基于仿真的优化方法在供应链管理中的适用性.     

A novel energy demand modelling approach for CNC machining based on function blocks

Energy efficiency remains one of the major issues in the machining domain. Today's machining systems are confronted with a number of new challenges, such as turbulent product demand and variations in production resources. Rapid and flexible energy modelling in a distributed and collaborative machining environment emerges as a new research area. Energy demand models in such an environment need to be practical, accurate, effective, scalable and reusable. Energy analysis and optimisation cannot be carried out once for all at the beginning. Instead, it is an on-going process. In this paper, the function block technique, i.e. IEC 61499, is used for the development of energy demand models as it brings advantages such as modularity, encapsulation, extensibility and reusability. A brief review on energy modelling and research on function blocks are given in the first part. A novel energy demand modelling approach based on function blocks is then proposed and elaborated. Three types of function blocks have been developed, i.e. machine tool dependent function blocks, state transition function blocks, and service interface function blocks. The first type, as the fundamental building blocks, is divided into two sub-types, machine component function block and machining state function block. Two case studies, based on a small 3-axis milling machine and an industrial production line respectively, are presented to demonstrate the possible applications using the function block-based model. Comprehensive discussions are given thereafter, including a pilot application of a distributed process planning system and a unique energy evaluation scheme. A confidence level associated energy rating system is proposed as the first step to turn energy consumption figures into useful indicators. The energy demand model based on function blocks developed here enhances the energy modelling and their practical implementations.     

Analyzing a lost-sale stochastic inventory model with Markov-modulated demands: A simulation-based optimization study

A consumer demand that presents auto-correlated components is a class of demand commonly found in competitive markets in which consumers may develop preferences for certain products which influence their willingness to purchase them again. This behavior may be observed in inventory systems whose products are subject to promotion plans in which mechanisms that incentivize the demand are implemented. Inventory systems that ignore these dependency components may severely impair their performance. This paper analyzes a stochastic inventory model where the control review system is periodic, is categorized as a lost-sale case, and is exposed to this class of auto-correlated demand pattern. The demand for products is characterized as a discrete Markov-modulated demand in which product quantities of the same item may relate to one another according to an empirical probability distribution. A simulation-based optimization that combines simulated annealing, pattern search, and ranking and selection (SAPS&RS) methods to approximate near-optimal solutions to this problem is employed. Lower and upper bounds for a range of near-optimal solutions are determined by the pattern search step enhanced by ranking and selection—indifferent zone. Results indicate that inventory performance significantly declines as the autocorrelation increases and is disregarded.     

A linear programming formulation for an inventory management decision problem with a service constraint

Inventory systems with uncertainty go hand in hand with the determination of a safety stock level. The decision on the safety stock level is based on a performance measure, for example the expected shortage per replenishment period or the probability of a stock-out per replenishment period. The performance measure assumes complete knowledge of the probability distribution during lead time, which might not be available. In case of incomplete information regarding the lead-time distribution of demand, no single figure for the safety stock can de determined in order to satisfy a performance measure. However, an optimisation model may be formulated in order to determine a safety stock level which guarantees the performance measure under the worst case of lead-time demand, of which the distribution is known in an incomplete way. It is shown that this optimisation problem can be formulated as a linear programming problem.     

Approximate dynamic programming for an inventory problem: Empirical comparison

This study investigates the application of learning-based and simulation-based Approximate Dynamic Programming (ADP) approaches to an inventory problem under the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. Specifically, we explore the robustness of a learning-based ADP method, Sarsa, with a GARCH(1,1) demand model, and provide empirical comparison between Sarsa and two simulation-based ADP methods: Rollout and Hindsight Optimization (HO). Our findings assuage a concern regarding the effect of GARCH(1,1) latent state variables on learning-based ADP and provide practical strategies to design an appropriate ADP method for inventory problems. In addition, we expose a relationship between ADP parameters and conservative behavior. Our empirical results are based on a variety of problem settings, including demand correlations, demand variances, and cost structures.     

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.     

Dynamic reorder point replenishment strategies for a capacitated supply chain with seasonal demand

Managing inventory and service levels in a capacitated supply chain environment with seasonal demand requires appropriate selection and readjustment of replenishment decision variables. This study focuses on the dynamic adjustment of decision variables within supply chains using continuous-review reorder point (ROP) replenishment. A framework is proposed to adjust reorder points and lot sizes based on optimal settings within different regions of a seasonal demand cycle. This framework also includes the optimal timing of adjustments defining these regions. A discrete-event simulation model of a simple, capacity-constrained supply chain is developed and simulation–optimization experiments are performed, the objective being to minimize the total supply chain inventory subject to a target delivery service level. The performance of ROP systems with optimal static and optimal dynamic decision variable settings are compared using two different seasonal demand patterns. The results confirm that performance with dynamic decision variable adjustment is better. For a given delivery service level, average work-in-process inventory levels are almost the same for both systems. However average finished goods inventory levels decrease significantly and are more stable under dynamic adjustment. The practical implication is that both finished goods holding costs and maximum storage capacity requirements are reduced.     

随机需求下的选址一库存配送系统集成规划模型及算法

研究了随机需求条件下由单供应商、候选分拨中心和分销点构成的选址-库存问题,分销点、分拨中心分别基于周期检查(R,s,Q)和连续检查(s,S)库存控制策略．综合考虑库存成本、运输成本和设施成本之间的均衡关系,建立了二级库存与无能力约束选址集成规划模型．给出了适合求解实际规模问题的拉格朗日松弛算法,提出了求解子问题的有效启发式方法,改进了次梯度优化方法．通过仿真试验验证了模型的正确性和算法的有效性．最后讨论了相对于传统规划方法,需求方差、服务水平、持有成本、提前期等关键库存控制参数对系统运营成本节约的影响规律．     

随机需求下的选址-库存配送系统集成规划模型及算法

研究了随机需求条件下由单供应商、候选分拨中心和分销点构成的选址－库存问题, 分销点、分拨中心分别基于周期检查(R, s,Q)和连续检查(s, S)库存控制策略. 综合考虑库存成本、运输成本和设施成本之间的均衡关系, 建立了二级库存与无能力约束选址集成规划模型. 给出了适合求解实际规模问题的拉格朗日松弛算法, 提出了求解子问题的有效启发式方法, 改进了次梯度优化方法. 通过仿真试验验证了模型的正确性和算法的有效性. 最后讨论了相对于传统规划方法, 需求方差、服务水平、持有成本、提前期等关键库存控制参数对系统运营成本节约的影响规律.     

A coordinated approach to hedge the risks in stochastic inventory-routing problem

The inventory routing problem (IRP) studied in this research involves repeated delivery of products from a depot to a set of retailers that face stochastic demands over a long period. The main objective in the IRP is to design the set of routes and delivery quantities that minimize transportation cost while controlling inventory costs. Traditional IRP focuses on risk-neutral decision makers, i.e., characterizing replenishment policies that maximize expected total net present value, or equivalently, minimize expected total cost over a planning horizon. In this research, for incorporating risk aversion, a hedge-based stochastic inventory-routing system (HSIRS) integrated with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and Forward Option Pricing (FOP)model based on Black-Scholes model, from hedge point of view, is proposed to solve the multi-product multi-period inventory routing problem with stochastic demand. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to maximize the net present value at an acceptable service level. As a result, an optimal portfolio (R, s, S) system of product group can be generated to maximize the net present value under an acceptable service level in a given planning horizon. Meanwhile, the target group needed to be served and the relative transportation policy also can be determined accordingly based on the time required to be served as a priori partition to minimize the average transportation costs; hence, the routing assignment problem can be successfully optimized through a Predicting Particle Swarm Optimization algorithm.     

Spare parts inventory control considering stochastic growth of an installed base

Installed base is a measure describing the number of units of a particular system actually in use. To maintain the performance of the installed units, spare parts inventory control is extremely important and becomes very challenging when the installed base changes over time. This problem is often encountered when a manufacturer starts to deliver a new product to customers and agrees to provide spare parts to replace failed units in the future. To cope with the resulting non-stationary stochastic maintenance demand, a spare parts control strategy needs to be carefully developed. The goal is to ensure that timely replacements can be provided to customers while minimizing the overall cost for spare parts inventory control. This paper provides a model for the aggregate maintenance demand generated by a product whose installed base grows according to a homogeneous Poisson process. Under a special case where the product’s failure time follows the exponential distribution, the closed form solutions for the mean and variance of the aggregate maintenance demand are obtained. Based on the model, a dynamic (Q, r) restocking policy is formulated and solved using a multi-resolution approach. Two numerical examples are provided to demonstrate the application of the proposed method in controlling spare parts inventory under a service level constraint. Simulation is utilized to explore the effectiveness of the multi-resolution approach.     

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

We study the rationing policy in an inventory system with two demand classes and different service criteria for backorders. Due to the difference of customer values, system performance sometimes has to be measured with a mixture of penalty cost and service level in managing inventory. With a continuous review (r,Q) system, we develop a critical level rationing policy in which a threshold mechanism is adopted to allocate backorders when multiple outstanding orders exist. Due to the complexity of the problem, a heuristic is developed based on the principle that both demand classes are served with respective target service levels. We also introduce bounds so that the search ranges of decision variables become restrictive. The numerical examples indicate an excellent performance of our heuristic. In addition, when ordering cost is medium or high, the threshold clearing mechanism has the same results as the optimal one. When ordering cost is small (set to zero), different clearing mechanisms should be used depending on the priorities of demand classes. Further analysis indicates that transforming the service constraint into a cost parameter and then applying the existing algorithm will not be a good approach for this problem with mixed performance criteria. It either increases the costs or violates the service constraint. This study also shows the importance of applying rationing policy when high priority class has a low demand volume, target service levels between two classes have a large gap, or replenishment lead time is long. The results of this study should enhance our understanding of how to implement rationing policies in practice.     

Computing optimal base-stock levels for an inventory system with imperfect supply

We study a single-item, single-site, periodic-review inventory system with negligible fixed ordering costs. The supplier to this system is not entirely reliable, such that each order is a Bernoulli trial, meaning that, with a given probability, the supplier delivers the current order and any accumulated backorders at the end of the current period, resulting in a Geometric distribution for the actual resupply lead time. We develop a recursive expression for the steady-state probability vector of a discrete-time Markov process (DTMP) model of this imperfect-supply inventory system. We use this recursive expression to prove the convexity of the inventory system objective function, and also to prove the optimality of our computational procedure for finding the optimal base-stock level. We present a service-constrained version of the problem and show how the computation of the optimal base-stock level using our DTMP method, incorporating the explicit distribution of demand over the lead time plus review (LTR) period, compares to approaches in the literature that approximate this distribution. We also show that the version of the problem employing an explicit penalty cost can be solved in closed-form for the optimal base-stock level for two specific period demand distributions, and we explore the behavior of the optimal base-stock level and the corresponding optimal service level under various values of the problem parameters.     

Inventory management with log-normal demand per unit time

This paper examines optimal policies in a continuous review inventory management system when demand in each time period follows a log-normal distribution. In this scenario, the distribution for demand during the entire lead time period has no known form. The proposed procedure uses the Fenton-Wilkinson method to estimate the parameters for a single log-normal distribution that approximates the probability density function (PDF) for lead time demand, conditional on a specific lead time. Once these parameters are determined, a mixture of truncated exponentials (MTE) function that approximates the lead time demand distribution is constructed. The objective is to include the log-normal distribution in a robust decision support system where the PDF that best fits the historical period demand data is used to construct the lead time demand distribution. Experimental results indicate that when the log-normal distribution is the best fit, the model presented in this paper reduces expected inventory costs by improving optimal policies, as compared to other potential approximations.