可替代产品库存模型的研究

市场上,很多产品之间可相互替代,商家为了获得的更多的利润,经常会用一种产品替代另一种产品.不仅如此.某种产品缺货时,也可以重新进货以满足顾客的需求.我们从销售商的角度,讨论这两个因素对库存策略的影响,建立了这类问题有两个产品的单周期的利润最大化模型,证明了目标函数是凹的和子模的,从而问题的解是存在的,给出了最优订货量(原始库存)的必要条件,讨论了各参数对库存的影响.通过比较,证明了商家采取替代策略和允许再订货可以提高利润并且可减少库存总量.     

可替代产品库存模型的研究

市场上，很多产品之间可相互替代，某种产品缺货时，可用另一种产品替代，也可以重新进货以满足顾客的需求。我们的目的是：从销售商的角度，讨论这两个因素对库存策略的影响。我们建立了这类问题有两个产品的单调期的利润最大化模型。证明了问题的解的存在性，给出了目标函数是凹函数和子模函数的充分条件，讨论了求解的方法和各参数对库存的影响。通过对几种特殊情况的讨论和比较，证明了替代和再订货可以提高利润并且可减少库存总量。     

可替代产品库存模型的研究

以零售商的角度,讨论了在允许进货的情况下可替代产品的库存问题,建立了这类问题利润最大化的库存模型,讨论了各参数对利润和库存的影响.然后证明了问题的解是存在的,利润函数是子模的,并给出了最优解的一阶必要性条件,同时探讨了目标函数的凹性问题.通过理论分析和数值试验证明了在一定条件下替代和重新进货都能提高利润,并能降低总的库存水平.     

分销仓储配送中心定货决策模拟系统研究

本对于分销仓储本着中心在客户需求量和再订货提前期都是随机性的情况，利用Arena模拟软件，通过对再订货点模型进行了模拟，求出可使系统成本较少的订购批量及再订货点存货水平的组合，从而确定最佳订货策略，解决现实中这种“双随机性”的复杂订货决策问题。     

The impact of product substitution on retail merchandising

We analyze the impact of product substitution on two key aspects of retail merchandising: order quantities and expected profits. To perform this analysis, we extend the basic news-vendor model to include the possibility that a product with surplus inventory can be used as a substitute for out of stock products. This extension requires a definition and an approximation for the resulting effective demand under substitution. A service rate heuristic is developed to solve the extended problem. The performance of this heuristic is evaluated using an upper bound generated by solving the associated Lagrangian dual problem. Our analysis suggests that this heuristic provides a tractable and accurate method to determine order quantities and expected profits under substitution. We apply this heuristic to examine how the level of demand uncertainty and correlation, and the degree of substitution between products affect order quantities and expected profits under substitutable demand. In addition, we use the heuristic to better understand the mechanism by which substitution improves expected profits.     

Sourcing from suppliers with random yield for price-dependent demand

We study a multi-period inventory planning problem. In each period, the firm under consideration can source from two possibly unreliable suppliers for a price-dependent demand. Our analysis suggests that the optimal procurement policy is neither a simple reorder-point policy nor a complex one without any structure, as previous studies suggest. Instead, we prove the existence of a reorder point for each supplier. No order is placed to that supplier for any inventory level above the reorder point and a positive order is issued to that supplier for almost every inventory level below the reorder point. We characterize conditions under which the optimal policy reveals monotone response to changes in the inventory level. Furthermore, two special cases of our model are examined in detail to demonstrate how our analysis generalizes a number of well-known results in the literature.     

Reducing lost-sales rate on the stochastic inventory model with defective goods for the mixtures of distributions

In this paper, we assume that the demands of different customers are not identical in the lead time. Thus, we investigate a continuous review inventory model involving controllable lead time and a random number of defective goods in buyer’s arriving order lot with partial lost sales for the mixtures of distributions of the lead time demand to accommodate more practical features of the real inventory systems. Moreover, we analyze the effects of increasing investment to reduce the lost sales rate when the order quantity, reorder point, lost sales rate and lead time are treated as decision variables. In our studies, we first assume that the lead time demand follows the mixture of normal distributions, and then relax the assumption about the form of the mixture of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. By analyzing the total expected cost function, we develop an algorithm to obtain the optimal ordering policy and the optimal investment strategy for each case. Finally, we provide numerical examples to illustrate the results.     

Two-resource stochastic capacity planning employing a Bayesian methodology

We examine a stochastic capacity-planning problem with two resources that can satisfy demand for two services. One of the resources can only satisfy demand for a specific service, whereas the other resource can provide both services. We formulate the problem of choosing the capacity levels of each resource to maximize expected profits. In addition, we provide analytic, easy-to-interpret optimal solutions, as well as perform a comparative statics analysis. As applying the optimal solutions effectively requires good estimates of the unknown demand parameters, we also examine Bayesian estimates of the demand parameters derived via a class of conjugate priors. We compare the optimal expected profits when demands for the two services follow independent distributions with informative and non-informative priors, and demonstrate that using good informative priors on demand can significantly improve performance.     

On a dual model with a dividend threshold

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual of the compound Poisson model under a threshold dividend strategy. We derive a set of two integro-differential equations satisfied by the expected total discounted dividends until ruin and show how the equations can be solved by using only one of the two integro-differential equations. The cases where profits follow an exponential or a mixture of exponential distributions are then solved and the discussion for the case of a general profit distribution follows by the use of Laplace transforms. We illustrate how the optimal threshold level that maximizes the expected total discounted dividends until ruin can be obtained, and finally we generalize the results to the case where the surplus process is a more general skip-free downwards Lévy process.     

Reorder quantities for (<Emphasis Type="Italic">Q,R</Emphasis>) inventory models

The reorder level R and the reorder quantity Q are the parameters to be decided in a continuous review inventory policy. Their optimal values can be approached through iterative methods, but these are tedious and inconvenient for control routines. A frequent practice is to set Q as the economic reorder quantity and compute R accordingly. Yet this practice may introduce a substantial cost penalty. The paper re-arranges conventional theoretical expressions in order to facilitate the use of numerical approximations to help find a quasi-optimal solution. This approach is then applied to Gamma distributed demands showing that computations are straightforward.     

产能限制下单向替代产品供应链生产、订货与定价研究

考虑一个产能受限的制造商和一个零售商组成的二级供应链上供需双方信息不完全对称的情景,研究具有单向替代的两种产品生产、订货及响应性定价的供应链决策问题,把问题建立成一个三阶段博弈模型。理论分析得出不同条件下制造商的最优产量及零售商的最优订货和定价决策。通过算例验证了供应链上的最优决策及其条件,灵敏度分析表明制造商产能、潜在市场需求及其方差、替代品的价格敏感系数在一定范围内增大有利于供应链系统及各成员利润增加,被替代产品的价格敏感系数增大可能会导致供应链及制造商利润下降。     

Optimal inventory replenishment policy for a queueing system with finite waiting room capacity

We treat an inventory control problem in a facility that provides a single type of service for customers. Items used in service are supplied by an outside supplier. To incorporate lost sales due to service delay into the inventory control, we model a queueing system with finite waiting room and non-instantaneous replenishment process and examine the impact of finite buffer on replenishment policies. Employing a Markov decision process theory, we characterize the optimal replenishment policy as a monotonic threshold function of reorder point under the discounted cost criterion. We present a simple procedure that jointly finds optimal buffer size and order quantity.     

考虑乘客取消订单的网约车平台定价策略

针对乘运市场供需不匹配的情况,考虑乘客在网约车平台预约订单后的取消行为,以平台利润最大化为目标,首先建立乘客选择模型计算乘客取消订单概率,再分别构建市场供过于求和供不应求状态下的利润模型,求解平台最优定价。研究表明:制定适当的违约规则可以有效减少乘客取消订单的概率,提高平台利润;最优定价随着服务质量的提高而增加,在打车非高峰期,平台可以通过提高服务质量来增加平台利润;非高峰期平台最优定价随着出租车费用的增加而减少,而高峰期定价策略受出租车费用影响较小。     

An EOQ Model with Substitutions Between Products

In this paper, we present an economic order quantity (EOQ) model when two products are required, and one can be substituted for the other, if necessary, at a given unit cost. We consider three cases: (i) when there is no substitution between the products, (ii) when there is full substitution between the products, and (iii) when there is partial substitution between the products. In a deterministic setting with proportional substitution costs, we would expect to find full substitution or no substitution being optimal, depending on the cost parameters. However, we observe that full substitution is never optimal; only partial substitution or no substitution may be optimal. This result can best be explained due to the non-linearity of the decision variables in the total cost expression. Finally, we present an algorithm to compute the optimal order quantities.     

Inventory models with variable lead time and present value

The figures for inventory make up a huge proportion of a company's working capital. Because of this, we formulated the optimal replenishment policy considering the time value of money to represent opportunity cost. In this article, we provide a mixed inventory model, in which the distribution of lead time demand is normal, to consider the time value. First, the study tries to find the optimal reorder point and order quantity at all lengths of lead time with components crashed to their minimum duration. Secondly, we develop a method to insure the uniqueness of the reorder point to locate the optimal solution. Finally, some numerical examples are given to illustrate our findings.     

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 inventory management for a retail chain with diverse store demands

Item demands at individual retail stores in a chain often differ significantly, due to local economic conditions, cultural and demographic differences and variations in store format. Accounting for these variations appropriately in inventory management can significantly improve retailers’ profits. For example, it is shown that having greater differences across the mean store demands leads to a higher expected profit, for a given inventory and total mean demand. If more than one inventory shipment per season is possible, the analysis becomes dynamic by including updated demand forecasts for each store and re-optimizing store inventory policies in midseason. In this paper, we formulate a dynamic stochastic optimization model that determines the total order size and the optimal inventory allocation across nonidentical stores in each period. A generalized Bayesian inference model is used for demands that are partially correlated across the stores and time periods. We also derive a normal approximation for the excess inventory from the previous period, which allows the dynamic programming formulation to be easily solved. We analyze the tradeoffs between obtaining information and profitability, e.g., stocking more stores in period 1 provides more demand information for period 2, but does not necessarily lead to higher total profit. Numerical analyses compare the expected profits of alternative supply chain strategies, as well as the sensitivity to different distributions of demand across the stores. This leads to novel strategic insights that arise from adopting inventory policies that vary by store type.     

模糊随机需求的连续盘点存储策略研究

考虑到需求的模糊随机性,建立模糊随机需求情况下连续盘点存储策略的模糊随机成本模型。利用模糊随机变量的期望值理论,推导出了其成本期望值模型的解析表达式,进而给出了最优再订货点所属区间的判别条件以及最优再订货点和经济订货量的计算式;基于此,设计了一模糊随机需求的连续盘点最优存储策略算法。最后结合数值算例,分析了模糊随机需求概率分布及缺货成本对最优存储策略的影响。     

A Recursive Algorithm for Order Cycle-time that Minimizes Logistics Cost

A firm's logistics cost, including shipping and inventory-carrying, is a substantial percentage of its sales. Nevertheless, typical inventory-control methods ignore or insufficiently represent the shipping cost. This paper describes a recursive algorithm that determines the reorder cycle-time that minimizes total logistics cost. It allows for a realistic accounting of shipping cost, which is modelled here as a function of shipping distance and weight. The algorithm uses a relaxation procedure to identify a suitable initial approximation to the optimal order cycle-time and then, through a series of recursive steps, moves to the optimal result. We demonstrate the algorithm with a single item, with a group of items that share a common order cycle, and with multi-items when item demands are random variables. Experience with this algorithm indicates that it converges to the optimal result in a very few steps.     

Bundling retail products: Models and analysis

We consider the impact of bundling products on retail merchandising. We consider two broad classes of retail products: basic and fashion. For these product classes, we develop models to calculate the optimal bundle prices, order quantities, and profits under bundling. We use this analysis to establish conditions and insights under which bundling is profitable. Our analysis confirms that bundling profitability depends on individual product demands, bundling costs, and the nature of the relationship between the demands of the products to be bundled. We also provide detailed numerical examples.