Simple expressions for finding recovery system inventory control parameter values

In recent years considerable effort has been devoted to the development of inventory control models for joint manufacturing and remanufacturing. Optimality of control policies is analyzed and algorithms for the determination of parameter values have been developed. However, there is still a lack of formulae or algorithms that allow for an easy computation of optimal or near optimal policy parameter values. This paper addresses the problem of computing the produce-up-to level S and the remanufacture-up-to level M in a periodic review inventory control model. We provide simple formulae for the policy parameter values, which can easily be implemented within spreadsheet applications. The approach is to derive news-vendor-type formulae that are based on underage and overage cost considerations. We propose different formulae depending on whether lead times for production and remanufacturing are identical or not. A numerical study shows that the obtained solutions provide relatively small cost deviations compared to the optimal solution within the investigated class of inventory control policies.     

Inventory control with fixed cost and price optimization in continuous time

We continue to study the problem of inventory control, with simultaneous pricing optimization in continuous time. In our previous paper [8], we considered the case without set up cost, and established the optimality of the base stock-list price (BSLP) policy. In this paper we consider the situation of fixed price. We prove that the discrete time optimal strategy (see [11]), i.e., the (s, S, p) policy can be extended to the continuous time case using the framework of quasi-variational inequalities (QVIs) involving the value function. In the process we show that an associated second order, nonlinear two-point boundary value problem for the value function has a unique solution yielding the triplet (s, S, p). For application purposes the explicit knowledge of this solution is needed to specify the optimal inventory and pricing strategy. Se- lecting a particular demand function we are able to formulate and implement a numerical algorithm to obtain good approximations for the optimal strategy.     

Optimal control of a finite-capacity inventory system with setup cost and lost sales

One of the most fundamental results in inventory theoryis the optimality of (s, S) policy for inventory systems withsetup cost. This result is established based on a key assumptionof infinite production/ordering capacity. Several studies haveshown that, when there is a finite production/ordering capacity,the optimal policy for the inventory system is very complicatedand indeed, only partial characterization for the optimal policyis possible. In this paper, we consider a continuous reviewinventory system with finite production/ordering capacity andsetup cost, and show that the optimal control policy for thissystem has a very simple structure. We also develop efficientalgorithms to compute the optimal control parameters.     

Optimal control of a dual service rate M/M/1 production-inventory model

We analyse a dual-source, production-inventory model in which the processing times at a primary manufacturing resource and a second, contingent resource are exponentially distributed. We interpret the contingent source to be a subcontractor, although it could also be overtime production. We treat the inventory and contingent sourcing policies as decision variables in an analytical study and, additionally, allow the primary manufacturing capacity to be a decision variable in a subsequent numerical study. Our goal is to gain insight into the use of subcontracting as a contingent source of goods and whether it can fulfill real-world managers' expectations for improved performance. We prove that a stationary, non-randomised inventory and subcontracting policy is optimal for our M/M/1 dual-source model and, moreover, that a dual base-stock policy is optimal. We then derive an exact closed-form expression for one of the optimal base stocks, which to our knowledge is the first closed-form solution for a dual-source model. We use that closed-form result to advantage in a numerical study from which we gain insight into how optimal capacity, subcontracting, and inventory policies are set, and how effectively a contingent source can reduce total cost, capacity cost, and inventory cost. We find that (i) the contingent source can reduce total cost effectively even when contingent sourcing is expensive and (ii) contingent sourcing reduces capacity cost more effectively than it does inventory cost.     

Analysis of deteriorating inventory/production systems using a linear quadratic regulator

We consider an inventory-production system where items deteriorate at a constant rate. The objective is to develop an optimal production policy that minimizes the cost associated with inventory and production rate. The inventory problem is first modeled as a linear optimal control problem. Then linear quadratic regulator (LQR) technique is applied to the control problem in order to determine the optimal production policy. Examples are solved for three different demand functions. Sensitivity analysis is then conducted to study the effect of changing the cost parameters on the objective function.     

VMCI下考虑顾客退货的供应链联合促销与协调

在允许顾客退货的环境下,以供应商管理寄售库存(VMCI)的供应链为对象,探讨了供应链的促销决策及协调问题。研究发现,集中情景下最优的寄售库存量与促销水平均高于分散情景下的对应值;根据在供应链运营过程中双方成员承担的不同风险设计的滞销补贴-双向促销成本分担契约可以实现供应链协调;期望退货费用不超过某一阈值时,全额退货策略优于不允许退货策略。此外,通过数值仿真揭示了顾客评估风险对利润及协调契约的影响。     

基于随机动态规划的有限库存ATO系统优化控制

本文研究n维组件单一产品,有限库存的ATO系统。通过建立马尔可夫决策过程模型(MDP),构造优化算法,研究组件生产与库存的最优控制策略。最优策路可以表示为状态依赖型库存阈值,系统内任一组件的控制策略受其它组件库存状态的影响。利用最优控制理论动态规划方法和数值计算方法对最优控制策略的存在性、最优值的数值计算进行研究,建立更符合实际生产的ATO系统决策模型,进行相应的理论和实验验证,研究系统参数对最优策略的影响。     

Monotonicity properties of a class of stochastic inventory systems

We consider inventory systems which are governed by an (r,q) or (r,nq) policy. We derive general conditions for monotonicity of the three optimal policy parameters, i.e., the optimal reorder level, order quantity and order-up-to level, as well as the optimal cost value, as a function of the various model primitives, be it cost parameters or complete cost rate functions or characteristics of the demand and leadtime processes. These results are obtained as corollaries from a few general theorems, with separate treatment given to the case where the policy parameters are continuous variables and that where they need to be restricted to integer values. The results are applied both to standard inventory models and to those with general shelf age and delay dependent inventory costs.     

Optimal policies for inventory systems with discretionary sales, random yield and lost sales

We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions are known. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand may be lost. Our objective is to minimize the total discounted cost over the problem horizon by choosing an optimal replenishment and discretionary sales policy. We obtain the structure of the optimal replenishment and discretionary sales policy and show that the optimal policy for finite horizon problem converges to that of the infinite horizon problem. Moreover, we compare the optimal policy under random yield with that under certain yield, and show that the optimal order quantity （sales quantity） under random yield is more （less） than that under certain yield.     

Optimal Solutions in the Multi-location Inventory System with Transshipments

We consider a single-period multi-location inventory system where inventory choices at each location are centrally coordinated. Transshipments are allowed as recourse actions in order to reduce the cost of shortage or surplus inventory after demands are realized. This problem has not been solved to optimality before for more than two locations with general cost parameters. In this paper we present a simple and intuitive model that enables us to characterize optimal inventory and transshipment policies for three and four locations as well. The insight gained from these analytical results leads us to examine the optimality conditions of a greedy transshipment policy. We show that this policy will be optimal for two and three locations. For the n location model we characterize the necessary and sufficient conditions on the cost structure for which the greedy transshipment policy will be optimal.      

An inventory model where backordered demand ratio is exponentially decreasing with the waiting time

We analyze an inventory system with a mixture of backorders and lost sales, where the backordered demand rate is an exponential function of time the customers wait before receiving the item. Stockout costs (backorder cost and lost sales cost) include a fixed cost and a cost proportional to the length of the shortage period. A procedure for determining the optimal policy and the maximum inventory profit is presented. This work extends several inventory models of the existing literature.     

具有定价和开机成本的生产-库存系统的最优(s,d,S)策略

考虑一个具有有限容量和开机成本的连续盘点生产-库存系统, 其控制策略为(s,d,S)策略. 未被满足的需求都会丢失. 当机器处于关闭状态时,库存产品可以两个不同的价格进行销售. 当机器处于开机状态时,库存只能以较高的价格进行销售. 研究了如何发现该系统下的最优(s,d,S)策略,并开发了用于计算最优控制参数的有效算法.     

An inventory model for slow moving items subject to obsolescence

In this paper, we consider a continuous review inventory system of a slow moving item for which the demand rate drops to a lower level at a known future time instance. The inventory system is controlled according to a one-for-one replenishment policy with a fixed lead time. Adapting to lower demand is achieved by changing the control policy in advance and letting the demand take away the excess stocks. We show that the timing of the control policy change primarily determines the tradeoff between backordering penalties and obsolescence costs. We propose an approximate solution for the optimal time to shift to the new control policy minimizing the expected total cost during the transient period. We find that the advance policy change results in significant cost savings and the approximation yields near optimal expected total costs.     

Optimality of Base-Stock and (s, S) Policies for Inventory Problems with Information Delays

Information delays exist when the most recent inventory information available to the inventory manager (IM) is dated; namely, the IM observes only the inventory level of an earlier period. We introduce information delays into the standard multiperiod stochastic inventory problem with backorders. We consider two types of information delays: (i) a constant delay and (ii) a random delay. We define an appropriate reference inventory position, which is a sufficient statistics for finding the optimal order quantity. We show that the optimal ordering policy is of base-stock type with respect to the reference inventory position and is of (s, S) type if there is also a fixed cost of ordering.All authors were supported in part by NSF Grant DMS-0509278.     

一类过程需求存贮系统的策略研究及其费用弹性分析

本文首先讨论了需求到达为复合泊松随机过程的库存管理问题,给出了在单位时间内期望总成本费用最小的条件下的确定性的最优订货策略(Q,T).然后分析了在订购量和订购周期为随机变量,其联合分布已知的条件下,基于随机局部弹性理论,分析了总费用关于订购量和订购周期的局部弹性的联合分布,为订购策略的制定提供了合理的依据.     

Optimal policy for brownian inventory models with general convex inventory cost

We study an inventory system in which products are ordered from outside to meet demands, and the cumulative demand is governed by a Brownian motion. Excessive demand is backlogged. We suppose that the shortage and holding costs associated with the inventory are given by a general convex function. The product ordering from outside incurs a linear ordering cost and a setup fee. There is a constant leadtime when placing an order. The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.     

Dynamic inventory and pricing policy in a capacitated stochastic inventory system with fixed ordering cost

We study a dynamic inventory and pricing optimization problem in a periodic review inventory system with setup cost and finite ordering capacity in each period. We show that the optimal inventory control is characterized by an (s,s^′,p) policy in four regions of the starting inventory level.     

Cost-effective inventory control in a value-added manufacturing system

This paper considers the cost-effective inventory control of work-in-process (WIP) and finished products in a two-stage distributed manufacturing system. The first stage produces a common WIP, and the second stage consists of several production sites that produce differentiated products with different capacity and service level requirements. The unit inventory holding cost is higher at the second stage. This paper first uses a network of inventory-queue model to evaluate the inventory cost and service level achievable for given inventory control policy, and then derives a very simple algorithm to find the optimal inventory control policy that minimizes the overall inventory holding cost and satisfies the given service level requirements. Some managerial insights are obtained through numerical examples.     

Marketing-production decisions under independent and integrated channel structure

The topic of channel structure has recently attracted much attention among researchers in the marketing and economics area. However, in a majority of the existing literature the cost considerations are extremely simplified with the major focus being pricing policy. What happens when cost incurring decisions are strongly connected with pricing policies? This is the theme we wish to explore in the present paper. The non-trivial costs considered are production, inventory, and retailer effort rate, i.e. we seek to explore the marketing-production channel. We have used the methodology of differential games. The open-loop Stackelberg solution concept has been used to solve the manufacturer and retailer's problem. The Pareto solution concept has been used to solve the problem of the vertically integrated firm. The production, pricing, and effort rate policies thus derived have been compared to obtain insights into the impact of channel structure on these policies. Also, to examine the relation between channel structure and the retailing operation requiring effort, we derive the Stackelberg and Pareto solutions with and without effort rate as a decision variable. We show that once the production rate becomes positive, it does not become zero again. This implies production smoothing. However, none of the gains of production smoothing are passed on to the retailer. The optimal production rate and the inventory policy are a linear combination of the nominal demand rate, the peak demand factor, the salvage value, and the initial inventory. Also, as opposed to some of the existing literature, the optimal policies need not necessarily be concave in nature. In the scenario where the relating operation does not require effort, the pricing policies of the manufacturer and the retailer, and the production policy of the manufacturer have a synergistic effect. However, in the scenario where the retailing operation does benefit from effort, the retailer's pricing policy need not necessarily be synergistic with other policies. With regard to channel structures, it seems that production smoothing will be done more efficiently in the integrated setup. Also, we show that the price paid by the consumer need not necessarily be lower in the integrated setup. But despite higher prices, the channel profits are higher in the integrated setup. This implies a conflict between the interests of the consumers and the firm. Also, this contradicts the results of some of the earlier papers that have used simple static models.     

Optimal integrated production and inventory control of an assemble-to-order system with multiple non-unitary demand classes

We study a pure assemble-to-order system subject to multiple demand classes where customer orders arrive according to a compound Poisson process. The finished product is assembled from m different components that are produced on m distinct production facilities in a make-to-stock fashion. We show that the optimal production policy of each component is a state-dependent base-stock policy and the optimal inventory allocation policy is a multi-level state-dependent rationing policy. Using numerical experimentation, we first study the system behavior as a function of order size variability and order size. We show that the optimal average cost rate is more sensitive to order size variability than to order size. We also compare the optimal policy to the first-come first-serve policy and show that there is great benefit to inventory rationing. We also propose two simple heuristics and show that these can effectively mimic the optimal policy which is generally much more difficult to determine and, especially, to implement.