Financial Innovation and the Transactions Demand for Cash

We document cash management patterns for households that are at odds with the predictions of deterministic inventory models that abstract from precautionary motives. We extend the Baumol–Tobin cash inventory model to a dynamic environment that allows for the possibility of withdrawing cash at random times at a low cost. This modification introduces a precautionary motive for holding cash and naturally captures developments in withdrawal technology, such as the increasing diffusion of bank branches and ATM terminals. We characterize the solution of the model, which qualitatively reproduces several empirical patterns. We estimate the structural parameters using micro data and show that quantitatively the model captures important economic patterns. The estimates are used to quantify the expenditure and interest rate elasticity of money demand, the impact of financial innovation on money demand, the welfare cost of inflation, and the benefit of ATM ownership.     

A Note on the Effect of Sudden Obsolescence on the Optimal Lot Size

In most management situations, the decision to hold inventory involves some element of obsolescence risk The traditional approach to this problem, in both theory and practice, is to incorporate obsolescence costs in the inventory holding cost. This note explores this issue and demonstrates that the traditional approach is appropriate for items subject to sudden obsolescence; that is, for items with demand lifetimes that are exponentially distributed.     

A Model for Master Production Scheduling in Uncertain Environments

In uncertain environments, the master production schedule (MPS) is usually developed using a rolling schedule. When utilizing a rolling schedule, the MPS is replanned periodically and a portion of the MPS is frozen in each planning cycle. The cost performance of a rolling schedule depends on three decisions: the choice of the replanning interval (R), which determines how often the MPS should be replanned; the choice of the frozen interval (F), which determines how many periods the MPS should be frozen in each planning cycle; and the choice of the forecast window (T), which is the time interval over which the MPS is determined using newly updated forecast data. This paper uses an analytical approach to study the master production scheduling process in uncertain environments without capacity constraints, where the MPS is developed using a rolling schedule. It focuses on the choices of F, R, and T for the MPS. A conceptual framework that includes all important MPS time intervals is described. The effects of F, R, and T on system costs, which include the forecast error, MPS change, setup, and inventory holding costs, are also explored. Finally, a mathematical model for the MPS is presented. This model approximates the average system cost as a function of F, R, T, and several environmental factors. It can be used to estimate the associated system costs for any combination of F, R, and T.     

Dynamic Supply Risk Management with Signal‐Based Forecast,Multi‐Sourcing,and Discretionary Selling

We examine the critical role of advance supply signals—such as suppliers’ financial health and production viability—in dynamic supply risk management. The firm operates an inventory system with multiple demand classes and multiple suppliers. The sales are discretionary and the suppliers are susceptible to both systematic and operational risks. We develop a hierarchical Markov model that captures the essential features of advance supply signals, and integrate it with procurement and selling decisions. We characterize the optimal procurement and selling policy, and the strategic relationship between signal‐based forecast, multi‐sourcing, and discretionary selling. We show that higher demand heterogeneity may reduce the value of discretionary selling, and that the mean value‐based forecast may outperform the stationary distribution‐based forecast. This work advances our understanding on when and how to use advance supply signals in dynamic risk management. Future supply risk erodes profitability but enhances the marginal value of current inventory. A signal of future supply shortage raises both base stock and demand rationing levels, thereby boosting the current production and tightening the current sales. Signal‐based dynamic forecast effectively guides the firm's procurement and selling decisions. Its value critically depends on supply volatility and scarcity. Ignoring advance supply signals can result in misleading recommendations and severe losses. Signal‐based dynamic supply forecast should be used when: (a) supply uncertainty is substantial, (b) supply‐demand ratio is moderate, (c) forecast precision is high, and (d) supplier heterogeneity is high.     

基于供应链金融的随机需求条件下的订货策略

本文将供应链金融中的融资问题融入到允许延迟支付的报童模型中,同时考虑了订货商的销售情况对偿还能力的影响,融资利息、销售收入利息以及支付信用期等现金管理要素,建立起订货商在连续随机需求条件下的库存管理模型,通过对模型的求解与灵敏度分析,对供应链金融模式下订货商的订货策略进行了深入探讨,得出了一系列有益的结论。所建立的模型同时为中小销售型企业提供一种新的资金获取以及确定订货策略的方法。     

The Effects of Sharing Upstream Information on Product Rollover

The process of introducing new and phasing out old products is called product rollover. This paper considers a periodic‐review inventory system consisting of a manufacturer and a retailer, where the manufacturer introduces new and improved products over an infinite planning horizon using the solo‐roll strategy. We consider two scenarios: (1) the manufacturer does not share the upstream information about new‐product introduction with the retailer and (2) the manufacturer shares the information. For each scenario, we first derive the decentralized ordering policy and the system‐optimal ordering policy with given cost parameters. We then devise an optimal supply chain contract that coordinates the inventory system. We demonstrate that when the inventory system is coordinated, information sharing improves the performance of both supply chain entities. However, this may not be true if the inventory system is not coordinated. We also show that under the optimal contract, the manufacturer has no incentive to mislead the retailer about new‐product information in the information‐sharing model. When demand variability increases, information sharing adds more benefits to the coordinated supply chain. Our research provides insights about coordinating product, financial, and information flows in supply chains with product rollover.     

Viability of Auction‐Based Revenue Management in Sequential Markets

The Internet is providing an opportunity to revenue management practitioners to exploit the potential of auctions as a new price distribution channel. We develop a stochastic model for a high‐level abstraction of a revenue management system (RMS) that allows us to understand the potential of incorporating auctions in revenue management in the presence of forecast errors associated with key parameters. Our abstraction is for an environment where two market segments book in sequence and revenue management approaches consider auctions in none, one, or both segments. Key insights from our robust results are (i) limited auctions are best employed closest to the final sale date, (ii) counterbalancing forecast errors associated with overall traffic intensity and the proportion of customer arrivals in a segment is more important if an auction is adopted in that segment, and (iii) it is critically important not to err on the side of overestimating market willingness to pay.     

Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs

We develop a new, unified approach to treating continuous‐time stochastic inventory problems with both the average and discounted cost criteria. The approach involves the development of an adjusted discounted cycle cost formula, which has an appealing intuitive interpretation. We show for the first time that an (s, S) policy is optimal in the case of demand having a compound Poisson component as well as a constant rate component. Our demand structure simultaneously generalizes the classical EOQ model and the inventory models with Poisson demand, and we indicate the reasons why this task has been a difficult one. We do not require the surplus cost function to be convex or quasi‐convex as has been assumed in the literature. Finally, we show that the optimal s is unique, but we do not know if optimal S is unique.     

Interorganizational Collaborative Forecasting and Replenishment Systems and Supply Chain Implications

Collaborative Forecasting and Replenishment (CFAR) is a new interorganizational system that enables retailers and manufacturers to forecast demand and schedule production jointly. The capabilities of CFAR exceed those of the traditional EDI because CFAR allows exchange of complex decision support models and manufacturer/retailer strategies. The proponents of CFAR claim that the fastest way for retailers and manufacturers to slash inventory costs and product shortages is by coordinating their decisions. The impact of CFAR on the supply chain using a model consisting of a manufacturer selling its product through two independent identical retailers is analyzed. The model assumes that the manufacturer doesn't face capacity constraints, the demand is stationary, and retailer prices are constant over time; the shortages are backordered at the manufacturer and retailers to isolate the effects of information sharing in CFAR. The most significant findings relate to the increase in the cost incurred by the nonparticipant in CFAR, the increase in the manufacturer's cost of serving the nonparticipant if the participant can obtain delivery guarantees in return for demand information sharing, and the incentives of the players to move towards universal retailer participation in CFAR. The findings are explained using the risk structure faced by the players in the supply chain. The managerial implications of the impact of CFAR on the supply chain structure are also discussed.     

Inventory Positioning/Partitioning for Backorders Optimization for a Class of Multi-Echelon Inventory Problems*

Inventory management has undergone significant philosophical changes in recent decades such as the advent of the zero inventory concept. However, as attractive as the concept of minimal inventories may be, it is often unrealistic in application. Attention to basic features of inventory control systems such as order quantities, base stock levels, and reorder points remain crucial to ensure customer service at minimal cost. A nonlinear optimization model for determining base stock levels in a multi-echelon inventory network is presented. Lagrangian relaxation results in (1) newsboy-style relations that provide the optimal solutions, and (2) instantaneous shadow prices for the budget constraint. Sensitivity analysis of this model will facilitate making decisions concerning the desired investment in inventory for the entire system. This model may be solved on standard nonlinear programming software and is generalizable to problems in both production and distribution settings.     

Shareholders' Wealth‐Maximizing Operating Decisions and Risk Management Practices in a Mixed Contracts Economy

This paper establishes a critically important positive role for operations management practices and financial hedging. We show that operations management decisions and financial hedging are intertwined, and we advance a framework that can identify their combined effects on investors' wealth. We show that: (a) firms (publicly traded corporations) will optimally hold adequate riskless working capital (e.g., cash) to minimize the cost of obtaining non‐financial inputs, and the magnitude of this cash holding depends on operating details, and (b) operations management and financial hedging can lower firms' cash requirements, and boost productivity, defined as the wealth created in the firm per dollar of invested capital. Productivity‐enhancing practices—by “freeing up” some of the firm's cash—can maximize the investors' wealth. We show that these results obtain because firms' contracts with many of the providers of non‐financial inputs are not traded, and because investors can invest not just in public corporations but also in businesses “outside the markets” (e.g., proprietorships, partnerships, and private equity).     

A ONE-PERIOD STOCHASTIC INVENTORY PROBLEM WITH A LUMP-SUM PENALTY COST

This paper presents an inventory problem related to the one-period stochastic inventory (or “newsboy”) problem. In this problem, the firm has to decide how much product to order to meet a random one-period demand. The version of the problem presented is novel in two respects. First, demand is explicitly permitted to be negative, and second, the penalty (or shortage) cost is assumed to be independent of the magnitude of the shortage. This situation is shown to change the form of the cost function and to complicate the determination of optimal policies. The form of the optimal policy is developed, and two example problems are presented in some detail.     

MODELS FOR OPTIMAL LEAD TIME REDUCTION

Most inventory and production planning models in the academic literature treat lead times either as constants or random variables with known distributions outside of management control. However, a number of recent articles in the popular press have argued that reducing lead times is a dominant issue in manufacturing strategy. The benefits of reducing customer lead times that are frequently cited include increased customer demand, improved quality, reduced unit cost, lower carrying cost, shorter forecast horizon, less safety stock inventory, and better market position. Although the costs of reducing lead times in the long term may be relatively insignificant compared with the benefits, in the short term these costs can have a significant impact on the profitability of a firm. This article develops a conceptual framework within which the costs and benefits of lead time reduction can be compared. Mathematical models for optimal lead time reduction are developed within this framework. The solutions to these models provide methods for calculating optimal lead times, which can be applied in practice. Sensitivity analysis of the optimal solutions provides insight into the structure of these solutions.     

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.     

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.     

Managing finished-goods inventory under capacitated delayed differentiation

Delayed differentiation or postponement is widely advocated to mitigate conflicts between product diversity and inventory cost savings. Manufacturers practicing postponement often suffer from severely constrained finishing capacities and noticeable finishing lead times. Therefore, inventories are still needed for finished products. Using the concept of inventory shortfall, this paper studies base-stock inventory models with and without demand forecasting and provides a computationally efficient method to set optimal inventory targets for finished products under capacitated postponement. Computations show inventory-saving benefit quickly vanishes after the capacity reaches a certain level. The value of forecasted advance-demand information (ADI) to postponement is justified, but can easily be overstated. Finishing capacities usually force manufacturers to build ahead according to demand forecast. When capacity limitation becomes severe, intuitions often guide producers to build to forecast even more than finishing lead times ahead. Results of this research indicate that these intuitions may be invalid and build to forecast more than finishing lead times ahead may not be a good practice. Further studies reveal that under capacitated postponement the forecasted advance-demand information is useful only when the variance of demand forecast errors is less than that of demands, and show that the optimal forecast lead time can be obtained in the same way as if the capacity is unlimited.     

Multiple In‐Cycle Transshipments with Positive Delivery Times

We study a centralized inventory sharing system of two retailers that are replenished periodically. Between two replenishments, a unit can be transshipped to a stocked‐out retailer from the other. It arrives a transshipment time later, during which the stocked‐out retailer incurs backorder cost. Without transshipment, backorder cost is incurred until the next replenishment. Since the transshipment time is shorter than the time between two replenishments, transshipments can reduce the backorder cost at the stocked‐out retailer and the holding costs at the other retailer. The system is directed by a centralized inventory manager, who minimizes the long‐run average cost consisting of replenishment, holding, backorder, and transshipment costs. The transshipment policy is characterized by hold‐back inventory levels, which are nonincreasing in the remaining time until the next replenishment. The transshipment policy differs from those in the literature because we allow for multiple transshipments between replenishments, positive transshipment times, and backorder costs. We also discuss the challenges associated with positive replenishment time and develop upper and lower bounds of average cost in this case. Bounds are numerically shown to have an average gap of 1.1%. A heuristic solution is based on the upper bound and differs from the optimal cost by at most this gap.     

具有多元马氏需求的多产品多阶段库存优化模型

本文研究一类新的多产品库存控制策略,即具有多元马氏需求特征的多产品多阶段的订货点订货量(Q, R, SS)策略,该策略考虑市场需求在不同产品之间具有多元马氏转移特征,并考虑缺货因素设置安全库存。论文首先建立了多产品多阶段的多元马氏需求预测模型,并通过该模型确定了各种产品需求之间的关系。同时,在该模型的理论基础上,提出了多产品多阶段的总期望成本模型及其最优(Q, R, SS)策略,进而结合算例给出模型的最优策略的数值解。     

基于EVT-POT-SV-MT模型的极值风险度量

针对金融资产收益的异常变化,采用SV-MT模型对风险资产的预期收益做风险补偿并捕捉收益序列的厚尾性、波动的异方差性等特征,将收益序列转化为标准残差序列,通过SV-MT模型与极值理论相结合拟合标准残差的尾部分布,建立了一种新的金融风险度量模型——基于EVT-POT-SV-MT的动态VaR模型.通过该模型对上证综指做实证分析,结果表明该模型能够合理有效地度量上证综指收益的风险.