Note on “The Backroom Effect in Retail Operations”

Eroglu et al. (2013) study a retailer with limited shelf capacity and a backroom. They study a continuous review (r, q) ordering policy with a known order quantity, q. Assuming that backorders can be satisfied from the backroom inventory (if available), they find the expression for the optimal reorder level, r. Our work builds on Eroglu et al. (2013). We correct an erroneous derivation of the expected overflow term, as well as derive an exact expression for the expected cost function, and hence optimal reorder level, instead of the approximate one used by Eroglu et al. (2013).     

随机需求下单向替代的两产品订货与定价联合决策研究

考虑了存在单向替代的两产品订货和定价联合决策问题。通过构建订货与定价联合决策模型,研究了单周期两产品的最优订货量和价格的存在条件,进一步将研究拓展到多周期的情况,建立了多周期的订货和定价联合决策模型,并进行了模型结构分析。同时,分析了信息对订货与定价联合决策的影响程度。     

Myopic Analysis for Multi‐Echelon Inventory Systems with Batch Ordering and Nonstationary/Time‐Correlated Demands

We provide an exact myopic analysis for an N‐stage serial inventory system with batch ordering, linear ordering costs, and nonstationary demands under a finite planning horizon. We characterize the optimality conditions of the myopic nested batching newsvendor (NBN) policy and the myopic independent batching newsvendor (IBN) policy, which is a single‐stage approximation. We show that echelon reorder levels under the NBN policy are upper bounds of the counterparts under both the optimal policy and the IBN policy. In particular, we find that the IBN policy has bounded deviations from the optimal policy. We further extend our results to systems with martingale model of forecast evolution (MMFE) and advance demand information. Moreover, we provide a recursive computing procedure and optimality conditions for both heuristics which dramatically reduces computational complexity. We also find that the NBN problem under the MMFE faced by one stage has one more dimension for the forecast demand than the one faced by its downstream stage and that the NBN policy is optimal for systems with advance demand information and stationary problem data. Numerical studies demonstrate that the IBN policy outperforms on average the NBN policy over all tested instances when their optimality conditions are violated.     

随机需求下考虑零售商风险偏好的生鲜农产品最优订货策略

针对生鲜农产品销售期内存在的期初期末销售量大而期中销售量小的现象,将零售商单销售期划分为三阶段;考虑顾客到达服从强度随机的非齐次Poisson过程,单位顾客购买量受产品价格和新鲜度影响;引入风险偏爱系数表征零售商的风险偏爱程度,着重分析产品新鲜度衰变系数和零售商风险偏爱系数对订货决策的影响,给出不同风险偏爱系数零售商的最优订货策略.结论表明,考虑零售商风险偏好和新鲜度衰变速率影响的订货策略,更能体现生鲜农产品的特性.最后用数值算例描述了有关结论.     

Replenishment Policies for Multi‐Product Stochastic Inventory Systems with Correlated Demand and Joint‐Replenishment Costs

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi‐product stochastic inventory systems. The distinguishing feature of the multi‐product inventory system that we analyze is the existence of correlated demand and joint‐replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real‐world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s, c, d, S)‐policies, and also develop an algorithm to compute good policies in this class, for large multi‐product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.     

Managing a Remanufacturing System with Random Yield: Properties,Observations, and Heuristics

We study a remanufacturing system that involves the ordering of a serviceable product and the remanufacturing of multiple types of returned products (cores) into the serviceable product. In addition to random demand for the serviceable product and random returned quantities of different types of cores in each time period, the remanufacturing yield of each type of core is also uncertain. By analyzing a multi‐period stochastic dynamic program, we derive several properties of the optimal ordering/remanufacturing policy. In addition to some insights, these properties can be used to reduce the search effort of the optimal policy. We also demonstrate that some existing results derived from related models no longer hold in remanufacturing systems with random yield. Recognizing the optimal ordering/remanufacturing policy is highly complex, we examine three simple heuristics that can be efficiently solved and implemented in practice. Among these three heuristics, our numerical analysis suggests that the heuristic that captures most of the yield uncertainty and future system evolvement as well as some of the properties of the optimal ordering/remanufacturing policy outperforms the other two heuristics.     

随机需求条件下产品退货政策协调与优化

本文研究了随机需求条件下基于退货的单周期单一产品逆向供应链模型.首先,研究了集中决策条件下集成厂商的利润函数,并讨论了实现利润最大化的最优性条件及其最优订货量;其次,在分散决策条件下,分别研究了制造商和销售商的利润函数,并讨论了销售商的最优性条件及其最优订货量;最后,在集中决策和分散决策模型的基础上,重点研究了供应链的协调与优化,得出了实现供应链协调的基本条件和两者之间的利润分配机制.通过制定批发价格和退货价格来实现两者之间的增加利润的任意分配.     

Promoting Seismic Retrofit Implementation Through “Nudge”: Using Warranty as a Driver

This article proposes a new type of warranty policy that applies the “nudge” concept developed by Thaler and Sunstein to encourage homeowners in Japan to implement seismic retrofitting. Homeowner adaptation to natural disasters through loss reduction measures is known to be inadequate. To encourage proactive risk management, the “nudge” approach capitalizes on how choice architecture can influence human decision‐making tendencies. For example, people tend to place more value on a warranty for consumer goods than on actuarial value. This article proposes a “warranty for seismic retrofitting” as a “nudge” policy that gives homeowners the incentive to adopt loss reduction measures. Under such a contract, the government guarantees all repair costs in the event of earthquake damage to the house if the homeowner implements seismic retrofitting. To estimate the degree to which a warranty will increase the perceived value of seismic retrofitting, we use field survey data from 1,200 homeowners. Our results show that a warranty increases the perceived value of seismic retrofitting by an average of 33%, and an approximate cost‐benefit analysis indicates that such a warranty can be more economically efficient than an ex ante subsidy. Furthermore, we address the failure of the standard expected utility model to explain homeowners’ decisions based on warranty evaluation, and explore the significant influence of ambiguity aversion on the efficacy of seismic retrofitting and nonanalytical factors such as feelings or trust.     

Cash‐Flow Based Dynamic Inventory Management

Small‐to‐medium‐sized enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this study, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm's capital at the end of a finite planning horizon. The firm's state at the beginning of each period is characterized by the inventory level and the capital level measured in units of the product, whose sum represents the “net worth” of the firm. Our study shows that the optimal ordering policy is characterized by a pair of threshold parameters as follows. (i) If the net worth is less than the lower threshold, then the firm employs a base stock order up to the lower threshold. (ii) If the net worth is between the two thresholds, then the firm orders exactly as many units as it can afford, without borrowing. (iii) If the net worth is above the upper threshold, then the firm employs a base stock order up to the upper threshold. Further, upper and lower bounds for the threshold values are developed using two simple‐to‐compute myopic ordering policies which yield lower bounds for the value function. We also derive an upper bound for the value function by considering a sell‐back policy. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with extensive numerical studies.     

Experimental Results Indicating Lattice‐Dependent Policies May Be Optimal for General Assemble‐To‐Order Systems

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.     

Optimal Expediting Policies for a Serial Inventory System with Stochastic Lead Time

In recent supply chains, often operating multiple delivery modes such as standard freight shipping and air is an effective way of addressing both delivery lead time uncertainties and service rates. We propose a model on how to optimally operate multiple delivery modes. We consider a serial supply chain and an expediting option from intermediate installations to the downstream of the chain. The goods move stochastically among the installations and the system faces a stochastic demand. We identify systems that yield simple optimal policies, in which both regular ordering and expediting follow a variant of the base stock policy. Expediting allows the system to be leaner due to the reduced regular order amount. In addition, we provide managerial insights linking expediting, base stock levels, and expediting costs based on analytical and numerical results.     

Optimal Inventory Control with Retail Pre‐Packs

A pre‐pack is a collection of items used in retail distribution. By grouping multiple units of one or more stock keeping units (SKU), distribution and handling costs can be reduced; however, ordering flexibility at the retail outlet is limited. This paper studies an inventory system at a retail level where both pre‐packs and individual items (at additional handling cost) can be ordered. For a single‐SKU, single‐period problem, we show that the optimal policy is to order into a “band” with as few individual units as possible. For the multi‐period problem with modular demand, the band policy is still optimal, and the steady‐state distribution of the target inventory position possesses a semi‐uniform structure, which greatly facilitates the computation of optimal policies and approximations under general demand. For the multi‐SKU case, the optimal policy has a generalized band structure. Our numerical results show that pre‐pack use is beneficial when facing stable and complementary demands, and substantial handling savings at the distribution center. The cost premium of using simple policies, such as strict base‐stock and batch‐ordering (pre‐packs only), can be substantial for medium parameter ranges.     

Comment on “The Law of Large Demand for Information”

Say that one information structure is eventually Blackwell sufficient for another if, for every large enough n, an n‐sample from the first is Blackwell sufficient (Blackwell (1951, 1954)) for an n‐sample from the second. This note shows that eventual Blackwell sufficiency lies strictly between (one‐shot) Blackwell sufficiency and the ordering of information structures formulated by Moscarini and Smith (2002), and thus offers a new criterion for comparing experiments. A characterization of eventual Blackwell sufficiency in terms of the one‐shot experiments remains an open question.     

Distribution lot-sizing models for arborescent supply chains with discrete-period variable demand

This study formulates a novel mixed-integer programming lot-sizing model for arborescent supply chains with discrete-period variable demand and then develops an efficient two-phase heuristic method, in which a combined multi-period demand ordering policy, rather than the lot-for-lot ordering policy usually assumed in previous papers, is adopted. Two important properties are introduced and used to obtain a better initial feasible solution. The good performance of the proposed heuristic method is verified through a comparison with the optimal solution method. It is also shown that the performance of the proposed combined multi-period demand ordering method is superior to that of the lot-for-lot ordering method. Sensitivity analysis is conducted to explore the impacts of changing the values of relevant parameters on the total supply chain cost, the total number of orders and the total number of opened members. Finally, a well-known logistics company in Taiwan is chosen to demonstrate the excellent performance and the aptness of the proposed ordering method.     

Comments on “Convergence Properties of the Likelihood of Computed Dynamic Models”

We show by counterexample that Proposition 2 in Fernández‐Villaverde, Rubio‐Ramírez, and Santos (Econometrica (2006), 74, 93–119) is false. We also show that even if their Proposition 2 were corrected, it would be irrelevant for parameter estimates. As a more constructive contribution, we consider the effects of approximation error on parameter estimation, and conclude that second order approximation errors in the policy function have at most second order effects on parameter estimates.     

MRP Planned Orders in a Multiple‐Supplier Environment with Differing Lead Times

This study examines a deterministic material requirements planning (MRP) problem where lead times at subsequent ordering moments differ. Adequate replenishment methods that can cope with lead time differences are lacking because of the order crossover phenomenon, that is, replenishment orders are not received in the sequence they are ordered. This study specifies how to handle order crossovers and recalculate planned order releases after an update of gross requirements. The optimal (s, S) policy is based on dynamic programing. The state space is kept to a minimum due to three fundamental insights. The performance of the optimal solution approach is compared with two heuristics based on relaxations and a benchmark approach in which order crossovers are ignored. A numerical analysis reveals that average cost savings up to 25% are possible if the optimal policy is used instead of the benchmark approach. The contribution of this study is threefold: (1) it generalizes theory on MRP ordering, allowing for lead time differences and order crossovers; (2) it develops new fundamental insights and an optimal solution procedure, leading to substantial cost saving; and (3) it provides good‐performing heuristics for a general and realistic replenishment problem that can replace the current replenishment methods within MRP.     

Optimal Policy for a Stochastic Scheduling Problem with Applications to Surgical Scheduling

We consider the stochastic, single‐machine earliness/tardiness problem (SET), with the sequence of processing of the jobs and their due‐dates as decisions and the objective of minimizing the sum of the expected earliness and tardiness costs over all the jobs. In a recent paper, Baker ( 2014 ) shows the optimality of the Shortest‐Variance‐First (SVF) rule under the following two assumptions: (a) The processing duration of each job follows a normal distribution. (b) The earliness and tardiness cost parameters are the same for all the jobs. In this study, we consider problem SET under assumption (b). We generalize Baker's result by establishing the optimality of the SVF rule for more general distributions of the processing durations and a more general objective function. Specifically, we show that the SVF rule is optimal under the assumption of dilation ordering of the processing durations. Since convex ordering implies dilation ordering (under finite means), the SVF sequence is also optimal under convex ordering of the processing durations. We also study the effect of variability of the processing durations of the jobs on the optimal cost. An application of problem SET in surgical scheduling is discussed.     

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。     

Inventory Rationing in a Make‐to‐Stock System with Batch Production and Lost Sales

We address an inventory rationing problem in a lost sales make‐to‐stock (MTS) production system with batch ordering and multiple demand classes. Each production order contains a single batch of a fixed lot size and the processing time of each batch is random. Assuming that there is at most one order outstanding at any point in time, we first address the case with the general production time distribution. We show that the optimal order policy is characterized by a reorder point and the optimal rationing policy is characterized by time‐dependent rationing levels. We then approximate the production time distribution with a phase‐type distribution and show that the optimal policy can be characterized by a reorder point and state‐dependent rationing levels. Using the Erlang production time distribution, we generalize the model to a tandem MTS system in which there may be multiple outstanding orders. We introduce a state‐transformation approach to perform the structural analysis and show that both the reorder point and rationing levels are state dependent. We show the monotonicity of the optimal reorder point and rationing levels for the outstanding orders, and generate new theoretical and managerial insights from the research findings.     

Optimal Ordering Policies for Stochastic Inventory Problems with Observed Information Delays

Information delays exist in an inventory system when it takes time to collect, process, validate, and transmit inventory/demand data. A general framework is developed in this paper to describe information flows in an inventory system with information delays. We characterize the sufficient statistics for making optimal decisions. When the ordering cost is linear, the optimality of a state‐dependent base‐stock policy is established even when information flows are allowed to cross over time. Additional insights into the problem are obtained via a comparison between our models and the models with stochastic order lead times. We also show that inventory can substitute for information and vice versa.