EXCHANGE RATE POLICY AND ENDOGENOUS PRICE FLEXIBILITY

Most theoretical analysis of flexible versus fixed exchange rates takes the degree of nominal rigidity to be independent of the exchange rate regime choice itself; however, informal policy discussion often suggests that a credible exchange rate peg may increase internal price flexi‐bility. This paper explores the relationship between exchange rate policy and price flexibility, in a model where price flexibility itself is an endogenous choice of profit‐maximizing firms. A fixed exchange rate can affect the optimal degree of price flexibility by altering the volatility of nominal demand facing price‐setting firms. We find that a unilateral peg, such as a currency board, adopted by a single country, will increase internal price flexibility, perhaps by a large amount. On the other hand, when an exchange rate peg is supported by bilateral participation of all monetary authorities such as in a monetary union, price flexibility may actually be less than under freely floating exchange rates. Quantitatively, we find that the endogenous increase in price flexibility following a unilateral peg might be large enough that output volatility is no greater than it would be under a floating exchange rate regime. (JEL: F0, F4)     

Capacity Planning with Financial and Operational Hedging in Low‐Cost Countries

The authors of this article outline a capacity planning problem in which a risk‐averse firm reserves capacities with potential suppliers that are located in multiple low‐cost countries. While demand is uncertain, the firm also faces multi‐country foreign currency exposures. This study develops a mean‐variance model that maximizes the firm's optimal utility and derives optimal utility and optimal decisions in capacity and financial hedging size. The authors show that when demand and exchange rate risks are perfectly correlated, a risk‐averse firm, by using financial hedging, will achieve the same optimal utility as a risk‐neutral firm. In this study as well, a special case is examined regarding two suppliers in China and Vietnam. The results show that if a single supplier is contracted, financial hedging most benefits the highly risk‐averse firm when the demand and exchange rate are highly negatively related. When only one hedge is used, financial hedging dominates operational hedging only when the firm is very risk averse and the correlation between the two exchange rates have become positive. With both theoretical and numerical results, this study concludes that the two hedges are strategic tools and interact each other to maximize the optimal utility.     

SPECULATIVE ATTACKS AND THE INFORMATION ROLE OF THE INTEREST RATE

This paper models currency attacks as carried out by speculators who condition their actions on private signals about the state and on the market‐clearing interest rate. Besides affecting speculators' payoffs, this interest rate also provides an endogenous public signal. For a plausible type of investment strategies, the dual role of the interest rate allows the model to explain abrupt and intense speculative attacks solely via economic fundamentals, without resorting to sunspot variables. This result underlies a novel policy implication: An official intervention in the foreign exchange market may reinforce a currency peg by influencing the precision of public information. (JEL: D82, D84, F31)     

A Newsvendor Who Chooses Informational Effort

We study a newsvendor who can acquire the services of a forecaster, or, more generally, an information gatherer (IG) to improve his information about demand. When the IG's effort increases, does the average ex ante order quantity rise or fall? Do average ex post sales rise or fall? Improvements in information technology and in the services offered by forecasters provide motivation for the study of these questions. Much depends on our model of the IG and his efforts. We study an IG who sends a signal to a classic single‐period newsvendor. The signal defines the newsvendor's posterior probability distribution on the possible demands and the newsvendor uses that posterior to calculate the optimal order. Each of the possible posteriors is a scale/location transform of the same base distribution. When the IG works harder, the average scale parameter drops. Higher IG effort is always useful to the newsvendor. We show that there is a critical value of order cost. For costs on one side of this value more IG effort leads to a higher average ex ante order and for costs on the other side to a lower average order. But for all costs, more IG effort leads to higher average ex post sales. We obtain analogous results for a “regret‐averse” newsvendor who suffers a penalty that is a nonlinear function of the discrepancy between quantity ordered and true demand.     

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.     

Dynamic Global Games of Regime Change: Learning,Multiplicity, and the Timing of Attacks

Global games of regime change—coordination games of incomplete information in which a status quo is abandoned once a sufficiently large fraction of agents attack it—have been used to study crises phenomena such as currency attacks, bank runs, debt crises, and political change. We extend the static benchmark examined in the literature by allowing agents to take actions in many periods and to learn about the underlying fundamentals over time. We first provide a simple recursive algorithm for the characterization of monotone equilibria. We then show how the interaction of the knowledge that the regime survived past attacks with the arrival of information over time, or with changes in fundamentals, leads to interesting equilibrium properties. First, multiplicity may obtain under the same conditions on exogenous information that guarantee uniqueness in the static benchmark. Second, fundamentals may predict the eventual fate of the regime but not the timing or the number of attacks. Finally, equilibrium dynamics can alternate between phases of tranquility—where no attack is possible—and phases of distress—where a large attack can occur—even without changes in fundamentals.     

Reducing Packaging Waste and Cost via Consumer Price Discounts

Low‐waste packaging may imply an inconvenience to consumers and cause firms to offer a compensating price discount. For example, Starbucks’ “Take the Mug Pledge” campaign provides a 10‐cent discount for customers who purchase coffee without a standard cup (i.e., customers provide their own cup). Understanding how such a discount drives demand and profit is the focus of this article. We consider a monopolist that can offer a reduced‐packaging option for its product at a variable cost savings. That option implies a transactional “inconvenience” cost for consumers. While that transactional cost is generally positive, our model also permits some consumers to associate convenience with reduced packaging. We derive the optimal price and discount that maximize profits. We show the optimal discount is bounded by the magnitude of the variable cost savings associated with the packaging reduction. We explore when the optimal discount is negative (a price premium), which requires a specific proportion of consumers to associate convenience with reduced packaging. We also derive conditions under which the firm should price to eliminate demand for the standard product, rather than segment the market, to leverage the variable cost savings of reduced packaging. When the variable cost savings are low (e.g., as is true for Starbucks), we show the profit curve for the segmenting policy is relatively flat for a discount up to several multiples of the cost differential. Finally, we demonstrate the potential for the reduced packaging option, with optimal discounting, to simultaneously increase profit and consumer surplus while reducing waste.     

Defender–Attacker Decision Tree Analysis to Combat Terrorism

We propose a methodology, called defender–attacker decision tree analysis, to evaluate defensive actions against terrorist attacks in a dynamic and hostile environment. Like most game‐theoretic formulations of this problem, we assume that the defenders act rationally by maximizing their expected utility or minimizing their expected costs. However, we do not assume that attackers maximize their expected utilities. Instead, we encode the defender's limited knowledge about the attacker's motivations and capabilities as a conditional probability distribution over the attacker's decisions. We apply this methodology to the problem of defending against possible terrorist attacks on commercial airplanes, using one of three weapons: infrared‐guided MANPADS (man‐portable air defense systems), laser‐guided MANPADS, or visually targeted RPGs (rocket propelled grenades). We also evaluate three countermeasures against these weapons: DIRCMs (directional infrared countermeasures), perimeter control around the airport, and hardening airplanes. The model includes deterrence effects, the effectiveness of the countermeasures, and the substitution of weapons and targets once a specific countermeasure is selected. It also includes a second stage of defensive decisions after an attack occurs. Key findings are: (1) due to the high cost of the countermeasures, not implementing countermeasures is the preferred defensive alternative for a large range of parameters; (2) if the probability of an attack and the associated consequences are large, a combination of DIRCMs and ground perimeter control are preferred over any single countermeasure.     

Managing Logistics in Regional Banknote Supply Chain Under Security Concerns

We study the logistics problem faced by Regional Branches (RBs) of a central bank in managing the currency supply under security concerns. While making banknote supply decisions to Sub‐Branches (SBs), the management of RB must achieve two goals simultaneously: (i) guarantee that each SB has sufficient inventories of all denominations of banknotes to satisfy the demands from all commercial banks within its service area, and (ii) control the annual spending on this banknote supply operation. Due to security concerns, the following methods are implemented in the process of transporting banknotes: (i) the capacity of a cash truck is limited by the total face value (instead of the physical space) of banknotes, and (ii) empty decoy trucks are deployed along with the trucks filled with banknotes. After deriving a polynomial‐time strategy to guarantee an optimal solution for the special Bin‐Packing Problem faced in this study, we provide an exact formulation for the RB's supply planning problem. We also propose several polynomial‐time algorithms for deriving either optimal or near‐optimal solutions for the problem under different settings. Using the weekly demand data obtained from the central bank, we verify the performance of our algorithms, and analyze the impacts of changes in these features and in the fleet capacity on the total cost incurred by an RB under various scenarios.     

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.     

How Collection Cost Structure Drives a Manufacturer's Reverse Channel Choice

This note discusses the impact of collection cost structure on the optimal reverse channel choice of manufacturers who remanufacture their own products. Using collection cost functions that capture collection rate and collection volume dependency, we show that the optimal reverse channel choice (retailer‐ vs. manufacturer‐managed collection) is driven by how the cost structure moderates the manufacturer's ability to shape the retailer's sales and collection quantity decisions.     

Heuristics for Base‐Stock Levels in Multi‐Echelon Distribution Networks

We study inventory optimization for locally controlled, continuous‐review distribution systems with stochastic customer demands. Each node follows a base‐stock policy and a first‐come, first‐served allocation policy. We develop two heuristics, the recursive optimization (RO) heuristic and the decomposition‐aggregation (DA) heuristic, to approximate the optimal base‐stock levels of all the locations in the system. The RO heuristic applies a bottom‐up approach that sequentially solves single‐variable, convex problems for each location. The DA heuristic decomposes the distribution system into multiple serial systems, solves for the base‐stock levels of these systems using the newsvendor heuristic of Shang and Song (2003), and then aggregates the serial systems back into the distribution system using a procedure we call “backorder matching.” A key advantage of the DA heuristic is that it does not require any evaluation of the cost function (a computationally costly operation that requires numerical convolution). We show that, for both RO and DA, changing some of the parameters, such as leadtime, unit backordering cost, and demand rate, of a location has an impact only on its own local base‐stock level and its upstream locations’ local base‐stock levels. An extensive numerical study shows that both heuristics perform well, with the RO heuristic providing more accurate results and the DA heuristic consuming less computation time. We show that both RO and DA are asymptotically optimal along multiple dimensions for two‐echelon distribution systems. Finally, we show that, with minor changes, both RO and DA are applicable to the balanced allocation policy.     

Terrorism Risks and Cost‐Benefit Analysis of Aviation Security

We evaluate, for the U.S. case, the costs and benefits of three security measures designed to reduce the likelihood of a direct replication of the 9/11 terrorist attacks. To do so, we assess risk reduction, losses, and security costs in the context of the full set of security layers. The three measures evaluated are installed physical secondary barriers (IPSB) to restrict access to the hardened cockpit door during door transitions, the Federal Air Marshal Service (FAMS), and the Federal Flight Deck Officer (FFDO) Program. In the process, we examine an alternate policy measure: doubling the budget of the FFDO program to $44 million per year, installing IPSBs in all U.S. aircraft at a cost of $13.5 million per year, and reducing funding for FAMS by 75% to $300 million per year. A break‐even cost‐benefit analysis then finds the minimum probability of an otherwise successful attack required for the benefit of each security measures to equal its cost. We find that the IPSB is costeffective if the annual attack probability of an otherwise successful attack exceeds 0.5% or one attack every 200 years. The FFDO program is costeffective if the annual attack probability exceeds 2%. On the other hand, more than two otherwise successful attacks per year are required for FAMS to be costeffective. A policy that includes IPSBs, an increased budget for FFDOs, and a reduced budget for FAMS may be a viable policy alternative, potentially saving hundreds of millions of dollars per year with consequences for security that are, at most, negligible.     

A Note on Air‐Cargo Capacity Contracts

Carriers (airlines) use medium‐term contracts to allot bulk cargo capacity to forwarders who deliver consolidated loads for each flight in the contractual period (season). Carriers also sell capacity to direct‐ship customers on each flight. We study capacity contracts between a carrier and a forwarder when certain parameters such as the forwarder's demand, operating cost to the carrier, margin, and reservation profit are its private information. We propose contracts in which the forwarder pays a lump sum in exchange for a guaranteed capacity allotment and receives a refund for each unit of unused capacity according to a pre‐announced refund rate. We obtain an upper bound on the informational rent paid by the carrier for a menu of arbitrary allotments and identify conditions under which it can eliminate the informational rent and induce the forwarder to choose the overall optimal capacity allotment (i.e., one that maximizes the combined profits of the carrier and the forwarder).     

A Continuous‐Review Inventory Model with Disruptions at Both Supplier and Retailer

We consider a continuous‐review inventory problem for a retailer who faces random disruptions both internally and externally (from its supplier). We formulate the expected inventory cost at this retailer and analyze the properties of the cost function. In particular, we show that the cost function is quasi‐convex and therefore can be efficiently optimized to numerically find the optimal order size from the retailer to the supplier. Computational experiments provide additional insight into the problem. In addition, we introduce an effective approximation of the cost function. Our approximation can be solved in closed form, which is useful when the model is embedded into more complicated supply chain design or management models.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

Security of Separated Data in Cloud Systems with Competing Attack Detection and Data Theft Processes

Empowered by virtualization technology, service requests from cloud users can be honored through creating and running virtual machines. Virtual machines established for different users may be allocated to the same physical server, making the cloud vulnerable to co‐residence attacks where a malicious attacker can steal a user's data through co‐residing their virtual machines on the same server. For protecting data against the theft, the data partition technique is applied to divide the user's data into multiple blocks with each being handled by a separate virtual machine. Moreover, early warning agents (EWAs) are deployed to possibly detect and prevent co‐residence attacks at a nascent stage. This article models and analyzes the attack success probability (complement of data security) in cloud systems subject to competing attack detection process (by EWAs) and data theft process (by co‐residence attackers). Based on the suggested probabilistic model, the optimal data partition and protection policy is determined with the objective of minimizing the user's cost subject to providing a desired level of data security. Examples are presented to illustrate effects of different model parameters (attack rate, number of cloud servers, number of data blocks, attack detection time, and data theft time distribution parameters) on the attack success probability and optimization solutions.     

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.     

Price Incentives and Coordination in a Two‐Product Decentralized Supply Chain

We investigate pricing incentives for competing retailers who distribute two variants of a manufacturer's product in a decentralized supply chain. Under a two‐dimensional Hotelling model, we derive decentralized retailers' prices for the products, and distortions in pricing when compared to centrally optimal prices. We show that price distortions decrease as consumers' travel cost between retailers increases, due to less intense competition. However, price distortions do not change monotonically in consumers' switching cost between products within stores. To fix decentralized retailers' price distortions, we construct a two‐part pricing contract that coordinates the supply chain. We show that the coordinating contract is Pareto‐improving and analyze increase in the supply chain profit under coordination.     

Comment on “Commitment vs. Flexibility”

This comment corrects two results in the 2006 Econometrica paper by Amador, Werning, and Angeletos (AWA), that features a model in which individuals face a trade‐off between flexibility and commitment. First, in contrast to Proposition 1 in AWA, we show that money‐burning can be part of the ex ante optimal contract when there are two states. Second, in contrast to Proposition 2 in AWA, we show that money‐burning can be imposed at the top (in the highest liquidity shock state), even when there is a continuum of states. We provide corrected versions of the above results.