Optimal dispatching control of an AGV in a JIT production system

This paper deals with an FMS (Flexible Manufacturing System) in a JIT (Just-In-Time) production system. The FMS consists of m workstations, one dispatching station and a single AGV (Automated Guided Vehicle). Each workstation has an input buffer of limited capacity and its processing times are distributed stochastically. When the processing of a new component starts at the workstation, a withdrawal Kanban attached to it is sent to the dispatching station. The AGV chooses one from workstations whose withdrawal Kanbans are accumulated at the dispatching station, and conveys a component with a withdrawal Kanban from the dispatching station to the workstation. The main purpose of this paper is to find an optimal dispatching policy of the AGV that maximizes the long-run expected average reward per unit time. The problem is formulated as a semi-Markov decision process and an optimal dispatching policy is computed. Numerical experiments are performed to make several comparisons.     

An algorithm to dynamically adjust the number of Kanbans in stochastic processing times and variable demand environment

In a real-life environment, the just-in-time JIT system is subjected to various types of uncertainties such as stochastic processing times and variable demand. Since, JIT was only meant to operate in a deterministic environment, its performance is seriously affected by variations in processing times and demand. In this paper, a newly developed Kanban system is presented which uses an algorithm to dynamically and systematically manipulate the number of Kanbans in order to offset the blocking and starvation caused by the said uncertainties during a production cycle. The new system is termed a flexible Kanban system FKS . The steps of the algorithm are detailed and the effectiveness of FKS is demonstrated using an example model. For the example model, the solution procedure, results and a discussion are presented.     

Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost

In this paper, an economic order quantity inventory model is analyzed, considering that the unit cumulative holding cost has two significant components: a fixed cost which represents the cost of accommodating the item in the warehouse and a variable cost given by a potential function of the length of time over which the item is held in stock. Shortages are allowed and, during the stockout period, only a fraction of demand is partially backordered. The backordering cost includes a fixed cost and a cost linearly dependent on the length of time for which backorder exists. A solution procedure is developed for determining the optimal inventory policy. Moreover, to illustrate the effects of some parameters on the optimal policy and the minimum total inventory cost, a numerical study is developed.     

提前期、构建成本和短缺量拖后率均可控的EOQ模型

传统库存模型通常将提前期和构建成本视为不可控制。事实上可以通过追加投资缩短提前期和降低构建成本。缺货期间,为减少订单丢失量和补偿顾客的损失,供应商会给予一定的价格折扣。现实库存系统中,容易得到需求的期望值和标准差,但较难得到其分布规律。基于此,考虑短缺量拖后率与价格折扣和缺货期间库存水平相关,提出了一种需求为任意分布且提前期和构建成本均可控的EOQ模型,证明了模型存在唯一最优解,给出了一种寻优算法。数值仿真分析表明,一般情况下,压缩提前期和降低构建成本能降低订购批量和安全库存,降低库存总成本;短缺量拖后系数和缺货概率对库存总成本影响较大,企业应尽量降低缺货概率,尤其在短缺量拖后系数较小时。     

Optimal Inventory Control with Dual‐Sourcing,Heterogeneous Ordering Costs and Order Size Constraints

We consider a dual‐sourcing inventory system, where procuring from one supplier involves a high variable cost but negligible fixed cost whereas procuring from the other supplier involves a low variable cost but high fixed cost, as well as an order size constraint. We show that the problem can be reduced to an equivalent single‐sourcing problem. However, the corresponding ordering cost is neither concave nor convex. Using the notion of quasi‐convexity, we partially characterize the structure of the optimal policy and show that it can be specified by multiple thresholds which determine when to order from each supplier and how much. In contrast to previous research, which does not consider order size constraints, we show that it is optimal to simultaneously source from both suppliers when the beginning inventory level is sufficiently low. We also show that the decision to source from the low‐cost supplier is not monotonic in the inventory level. Our results require that the variable costs satisfy a certain condition which guarantees quasi‐convexity. However, extensive numerical results suggest that our policy is almost always optimal when the condition is not satisfied. We also show how the results can be extended to systems with multiple capacitated suppliers.     

一种考虑原材料库存成本的变质物品EPQ模型

在库存管理研究中,单独实现产成品或原材料库存成本最小,往往无法获得整个库存系统的最优控制策略.本文提出了一种同时考虑产成品和原材料库存成本的变质物品EPQ集成模型.运用迭代寻优法得到模型最优解,得出计划期内最优原材料订购次数,原材料订购周期内的最优生产次数和最优服务水平,并对主要参数进行了灵敏度分析,为生产制造企业的库存管理提供了决策依据.     

Inventory Control with a Fixed Cost and a Piecewise Linear Convex Cost

This paper studies the optimal policy for a periodic‐review inventory system in which the production costs consist of a fixed cost and a piecewise linear convex variable cost. Such a cost function can arise from alternate sources of supply or from the use of overtime production. We fully characterize the structure of the optimal policy for the single‐period problem. For the multi‐period problem, the optimal policy can have disconnected production regions and complicated optimal produce‐up‐to levels, which implies that implementation of the optimal policy may not be practical. Fortunately, careful investigation shows that the optimal policy has some interesting properties. The structure of the optimal policy outlined by these properties leads to a practical and close‐to‐optimal heuristic policy. In an extensive numerical study, the average gap is only 0.02% and the worst gap is 1.37%.     

Dynamic performance of a hybrid inventory system with a Kanban policy in remanufacturing process

In this paper we study a hybrid system with both manufacturing and remanufacturing. The inventory control strategy we use in the manufacturing loop is an automatic pipeline, inventory and order based production control system (APIOBPCS). In the remanufacturing loop we employ a Kanban policy to represent a typical pull system. The methodology adopted uses control theory and simulation. The aim of the research is to analyse the dynamic (as distinct from the static) performance of the specified hybrid system. Dynamics have implications on total costs in terms of inventory holding, capacity utilisation and customer service failures. We analyse the parameter settings to find preferred “nominal”, “fast” and “slow” values in terms of system dynamics performance criteria such as rise time, settling time and overshoot. Based on these parameter settings, we investigate the robustness of the system to changes in return yield and the manufacturing/remanufacturing lead time. Our results clearly show that the system is robust with respect to the system dynamics performance and the remanufacturing process can help to improve system dynamics performance. Thus, the perceived benefits of remanufacturing of products, both environmentally and economically, as quoted in the literature are found not to be detrimental to system dynamics performance when a Kanban policy is used to control the remanufacturing process.     

库存成本变化的VMI供应链协调

提出了库存成本变化的经济订货批量(EOQ)模型，基于该模型研究了库存成本变化时供应商管理库存(VMI)系统的最优协议问题。在该系统中，订货商和供应商达成缺货成本共担协议：当缺货发生时，供应商需要向订货商支付缺货补偿。订货商和供应商分散决策，订货商通过设计协议来减少其成本，而供应商通过制定补货决策来缩小自身成本。通过与传统系统和整合系统的比较，得出了库存成本变化时VMI系统的最优补货决策和缺货成本共担协议。采用数值算例验证了分析结果。结果表明，当且仅当供应商预期成本等于整合系统的最小总成本与固定缺货罚金之和时，VMI系统与整合系统具有相同的补货决策和系统绩效，即能够实现供应链协调。     

基于可控提前期的随机寄售库存模型

本文通过假定需求提前期为随机且可控的,将寄售库存（Consignment Stock,CS）模型拓展到随机情形。本文首先将库存成本分为与财务相关的成本和与储存相关的成本两部分,得出CS方式下买卖双方的联合期望总成本公式,然后将订货量、订货点、提前期、运送次数作为决策变量,求得系统的最优参数设置及最小总成本。文章最后提出一个算法,并通过仿真的形式表明无论在确定还是随机环境中,CS方式的总成本都可能优于集成化库存方式。     

Optimum number of Kanbans between two adjacent stations

A model and solution strategies are developed for determining the optimum number of Kanbans between two adjacent workstations. The total cost is expressed as a function of the number of Kanbans, and the parameters, shortage cost of materials and holding cost of containers. Since the number of Kanbans obtained has to be an integer, an incremental search procedure is used, which leads to the construction of a strong bound on the optimal number of Kanbans required.     

Inventory‐Based Dynamic Pricing with Costly Price Adjustment

We study an average‐cost stochastic inventory control problem in which the firm can replenish inventory and adjust the price at anytime. We establish the optimality to change the price from low to high in each replenishment cycle as inventory is depleted. With costly price adjustment, scale economies of inventory replenishment are reflected in the cycle time instead of lot size—An increased fixed ordering cost leads to an extended replenishment cycle but does not necessarily increase the order quantity. A reduced marginal cost of ordering calls for an increased order quantity, as well as speeding up product selling within a cycle. We derive useful properties of the profit function that allows for reducing computational complexity of the problem. For systems requiring short replenishment cycles, the optimal solution can be easily computed by applying these properties. For systems requiring long replenishment cycles, we further consider a relaxed problem that is computational tractable. Under this relaxation, the sum of fixed ordering cost and price adjustment cost is equal to (greater than, less than) the total inventory holding cost within a replenishment cycle when the inventory holding cost is linear (convex, concave) in the stock level. Moreover, under the optimal solution, the time‐average profit is the same across all price segments when the inventory holding cost is accounted properly. Through a numerical study, we demonstrate that inventory‐based dynamic pricing can lead to significant profit improvement compared with static pricing and limited price adjustment can yield a benefit that is close to unlimited price adjustment. To be able to enjoy the benefit of dynamic pricing, however, it is important to appropriately choose inventory levels at which the price is revised.     

Inventory Rationing for Multiple Class Demand under Continuous Review

We consider how a firm should ration inventory to multiple classes in a stochastic demand environment with partial, class‐dependent backlogging where the firm incurs a fixed setup cost when ordering from its supplier. We present an infinite‐horizon, average cost criterion Markov decision problem formulation for the case with zero lead times. We provide an algorithm that determines the optimal rationing policy, and show how to find the optimal base‐stock reorder policy. Numerical studies indicate that the optimal policy is similar to that given by the equivalent deterministic problem and relies on tracking both the current inventory and the rate that backorder costs are accumulating. Our study of the case of non‐zero lead time shows that a heuristic combining the optimal, zero lead time policy with an allocation policy based on a single‐period profit management problem is effective.     

Trade-off between quoted lead time and price

In a make-to-order environment, lead time and price can play a crucial role in determining the financial success of a firm. Their importance increases when demand is sensitive to the quoted lead time and price. A model is presented which uses the quoted lead time and price as a mechanism to determine the optimal demand level. The relationships between the model parameters and their impacts on the firm's profit is also analysed. In addition, the effect of the number of job requests, and the mean processing time are examined. Based on the results presented in this paper, there is clear indication that the firm's profit is sensitive to the inventory holding rate, and that the inventory holding cost component is redundant in the presence of a tardiness cost component.     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

带学习效应的双渠道供应链库存策略研究

针对具有学习行为的双渠道供应链问题,本文研究了两种分销渠道并存下的最优库存策略。有限计划期内,分销商通过传统销售和在线销售来满足下游顾客的需求。两种分销渠道下的销售单价为时变不减线性函数,当系统中各周期的生产订购固定成本以一定的概率具有学习效应行为时,分别建立了非变质产品生产存贮问题的混合整数约束优化模型以及易变质产品存贮问题的无约束混合整数优化模型,所建立模型的目标为极大化分销商总利润函数。对于这两类模型,通过分析其最优解的性质,利用将生产订购次数松弛为连续变量的技巧证明了最优解存在的唯一性。给出了最优策略的求解方法并比较了两类模型最优利润函数值的大小。最后通过数值算例对上述模型进行了验证,数值结果表明当供应链系统中存在学习效应行为时,该系统能够获得更多的利润。     

Analysis of Local Decision Rules in a Dual-Kanban Flow Shop

A recent article reported the results of a study on the effects of two kanban policy variables—the length of withdrawal cycle and the type of priority rule—on average customer wait time and total inventory. This study extends that work by adding two kanban policy variables and two performance criteria. It reports the results of simulation experiments that were conducted to determine how four policy variables—withdrawal cycle, priority rule, status of waiting withdrawal kanbans, and number of kanbans influence four performance criteria—average customer wait-time, total inventory, and average number of full containers in the input and output stock points of stations. It was found that the information about waiting withdrawal kanbans in sequencing decisions results in the simultaneous improvement in two conflicting objectives—customer wait time and total inventory. Also, the effects of including the information regarding the status of waiting withdrawal kanbans on system performance are larger than the effects associated with the type of priority rule. The results provide insights into determining the level of each policy variable while fully considering the possible interactions among the variables and the levels of other policy variables to improve system performance. These insights allow for setting the levels of policy variables to make the improvement process smooth.     

Optimal ordering time interval taking account of time value

In this paper, the optimal inventory policies for an infinite lime span taking account of time value is discussed. First, bounds for the optimal ordering time interval are derived. Second, with these bounds, a simple algorithm to compute die optimal ordering time interval is developed. Numerical examples are given to illustrate the algorithm.     

Integrating Kanban principles in a pharmaceutical campaign production system

Centralised planned campaign production is the predominant production system in process industries. In this study, we investigate whether a decentralised Kanban control system, which has proven to offer advantages in other industries, can be successfully integrated in a campaign production environment. The used research methodology combines model-based and case-study-based elements. Using the example of a pharmaceutical internal five-stage supply chain, we conceive a Kanban concept that integrates campaign formation, develop a discrete-event simulation model and conduct a range of explorative simulation experiments. We find that a Kanban campaign production system is not merely feasible but would also be favourable: throughput times can be reduced without increasing customer lead times. Sensitivity analysis shows that the system’s performance is relatively robust to changes in Kanban key configuration parameters such as number of Kanban cards or campaign size. We conclude by discussing our findings and formulating three propositions that might stimulate future research.