Commitment,Flexibility, and Optimal Screening of Time Inconsistency

This paper develops a theory of optimal provision of commitment devices to people who value both commitment and flexibility and whose preferences differ in the degree of time inconsistency. If time inconsistency is observable, both a planner and a monopolist provide devices that help each person commit to the efficient level of flexibility. However, the combination of unobservable time inconsistency and preference for flexibility causes an adverse‐selection problem. To solve this problem, the monopolist and (possibly) the planner curtail flexibility in the device for a more inconsistent person at both ends of the efficient choice range; moreover, they may have to add unused options to the device for a less inconsistent person and also distort his actual choices. This theory has normative and positive implications for private and public provision of commitment devices.     

Lower Cost Arrivals for Airlines: Optimal Policies for Managing Runway Operations under Optimized Profile Descent

Optimized profile descent (OPD) is an operating procedure being used by airlines to improve fuel and environmental efficiency during arrival operations at airports. In this study, we develop a stochastic dynamic programming framework to manage the sequencing and separation of flights during OPD operations. We find that simple calculation based measures can be used as optimal decision rules, and that the expected annual savings can be around $29 million if such implementations are adapted by major airports in the United States. Of these savings, $24 million are direct savings for airlines due to reduced fuel usage, corresponding to a potential savings of 10%–15% in fuel consumption over current practice. We also find that most of these savings will be due to the optimal spacing of OPD flights, as opposed to the optimal sequencing policies which contribute only 14% to the total savings. Hence, optimal spacing of OPD flights is much more important than optimal sequencing of these flights. We also conclude that there is not much difference between the environmental costs of fuel‐optimal and sustainably‐optimal spacing policies. Hence, an airline‐centric approach in improving OPD operations is likely to be not in conflict with objectives that might be prioritized by other stakeholders.     

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.     

Dynamic Preference for Flexibility

We consider a decision maker who faces dynamic decision situations that involve intertemporal trade‐offs, as in consumption–savings problems, and who experiences taste shocks that are transient contingent on the state of the world. We axiomatize a recursive representation of choice over state contingent infinite horizon consumption problems, where uncertainty about consumption utilities depends on the observable state and the state follows a subjective Markov process. The parameters of the representation are the subjective process that governs the evolution of beliefs over consumption utilities and the discount factor; they are uniquely identified from behavior. We characterize a natural notion of greater preference for flexibility in terms of a dilation of beliefs. An important special case of our representation is a recursive version of the Anscombe–Aumann model with parameters that include a subjective Markov process over states and state‐dependent utilities, all of which are uniquely identified.     

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)     

Quantitative Comparison of Approximate Solution Sets for Bi‐criteria Optimization Problems*

We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near‐pareto‐optimal solutions to bi‐criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives.     

Sequential and Simultaneous Decision Making for Optimizing Health Care Resource Flexibilities

Health care administrators commonly employ two types of resource flexibilities (demand upgrades and staffing flexibility) to efficiently coordinate two critical internal resources, nursing staff and beds, and an external resource (contract nurses) to satisfy stochastic patient demand. Under demand upgrades, when beds are unavailable for patients in a less acute unit, patients are upgraded to a more acute unit if space is available in that unit. Under staffing flexibility, nurses cross‐trained to work in more than one unit are used in addition to dedicated and contract nurses. Resource decisions (beds and staffing) can be made at a single point in time (simultaneous decision making) or at different points in time (sequential decision making). In this article, we address the following questions: for each flexibility configuration, under sequential and simultaneous decision making, what is the optimal resource level required to meet stochastic demand at minimum cost? Is one type of flexibility (e.g., demand upgrades) better than the other type of flexibility (e.g., staffing flexibility)? We use two‐stage stochastic programming to find optimal resource levels for two nonhomogeneous hospital units that face stochastic demand following a continuous, general distribution. We conduct a full‐factorial numerical experiment and find that the benefit of using staffing flexibility on average is greater than the benefit of using demand upgrades. However, the two types of flexibilities have a positive interaction effect and they complement each other. The type of flexibility and decision timing has an independent effect on system performance (capacity and staffing costs). The benefits of cross‐training can be largely realized even if beds and staffing levels have been determined prior to the establishment of a cross‐training initiative.     

Temptation and Taxation

We study optimal taxation when consumers have temptation and self‐control problems. Embedding the class of preferences developed by Gul and Pesendorfer into a standard macroeconomic setting, we first prove, in a two‐period model, that the optimal policy is to subsidize savings when consumers are tempted by “excessive” impatience. The savings subsidy improves welfare because it makes succumbing to temptation less attractive. We then study an economy with a long but finite horizon which nests, as a special case, the Phelps–Pollak–Laibson multiple‐selves model (thereby providing guidance on how to evaluate welfare in this model). We prove that when period utility is logarithmic, the optimal savings subsidies increase over time for any finite horizon. Moreover, as the horizon grows large, the optimal policy prescribes a constant subsidy, in contrast to the well known Chamley–Judd result.     

Flexibility Structure and Capacity Design with Human Resource Considerations

Most service systems consist of multidepartmental structures with multiskill agents that can deal with several types of service requests. The design of flexibility in terms of agents' skill sets and assignments of requests is a critical issue for such systems. The objective of this study was to identify preferred flexibility structures when demand is random and capacity is finite. We compare structures recommended by the flexibility literature to structures we observe in practice within call centers. To enable a comparison of flexibility structures under optimal capacity, the capacity optimization problem for this setting is formulated as a two‐stage stochastic optimization problem. A simulation‐based optimization procedure for this problem using sample‐path gradient estimation is proposed and tested, and used in the subsequent comparison of the flexibility structures being studied. The analysis illustrates under what conditions on demand, cost, and human resource considerations, the structures found in practice are preferred.     

Envelope Theorems for Arbitrary Choice Sets

The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function. We also provide conditions for the value function to be, variously, absolutely continuous, left‐ and right‐differentiable, or fully differentiable. These results are applied to mechanism design, convex programming, continuous optimization problems, saddle‐point problems, problems with parameterized constraints, and optimal stopping problems.     

Allocation of Returned Products among Different Recovery Options through an Opportunity Cost–Based Dynamic Approach*

In a make‐to‐order product recovery environment, we consider the allocation decision for returned products decision under stochastic demand of a firm with three options: refurbishing to resell, parts harvesting, and recycling. We formulate the problem as a multiperiod Markov decision process (MDP) and present a linear programming (LP) approximation that provides an upper bound on the optimal objective function value of the MDP model. We then present two solution approaches to the MDP using the LP solution: a static approach that uses the LP solution directly and a dynamic approach that adopts a revenue management perspective and employs bid‐price controls technique where the LP is resolved after each demand arrival. We calculate the bid prices based on the shadow price interpretation of the dual variables for the inventory constraints and accept a demand if the marginal value is higher than the bid price. Since the need for solving the LP at each demand arrival requires a very efficient solution procedure, we present a transportation problem formulation of the LP via variable redefinitions and develop a one‐pass optimal solution procedure for it. We carry out an extensive numerical analysis to compare the two approaches and find that the dynamic approach provides better performance in all of the tested scenarios. Furthermore, the solutions obtained are within 2% of the upper bound on the optimal objective function value of the MDP model.     

Temptation and Self‐Control

We study a two‐period model where ex ante inferior choice may tempt the decision‐maker in the second period. Individuals have preferences over sets of alternatives that represent second period choices. Our axioms yield a representation that identifies the individual's commitment ranking, temptation ranking, and cost of self‐control. An agent has a preference for commitment if she strictly prefers a subset of alternatives to the set itself. An agent has self‐control if she resists temptation and chooses an option with higher ex ante utility. We introduce comparative measures of preference for commitment and self‐control and relate them to our representations.     

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.     

Lifecycle Pricing for Installed Base Management with Constrained Capacity and Remanufacturing

Installed base management is the policy in which the manufacturer leases the product to consumers, and bundles repair and maintenance services along with the product. In this article, we investigate for the optimal leasing price and leasing duration decisions by a monopolist when the production and servicing capacity are constrained. The effect of diffusion of consumers in the installed base is considered, with the ownership of the product resting with the monopolist during the product lifecycle. The monopolist operating the installed base jointly optimizes the profits from leasing the product/service bundle along with maintenance revenues and remanufacturing savings. We formulate the manufacturer's problem as an optimal control problem and show that the optimal pricing strategy of the firm should be a skimming strategy. We also find that the effect of remanufacturing savings on the pricing decision and the length of the leasing duration changes significantly depending on the duration of the product's lifecycle. If the product lifecycle is long and remanufacturing savings are low, the firm should offer a shorter leasing duration, whereas if the remanufacturing savings are high, the firm should optimally offer a higher leasing duration. In contrast, if the time duration of the product lifecycle is low and remanufacturing savings are low, the firm prefers to offer a shorter leasing duration, whereas if the remanufacturing savings are high, the firm should optimally have a longer leasing duration. The article also shows that if the production capacity is small, the manufacturer increases the leasing duration. If the production capacity is very small, the manufacturer sets the leasing duration to be equal to the product lifecycle and does not use remanufacturing.     

Inventory Management for Customers with Alternative Lead Times

It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.     

UNEMPLOYED BUT OPTIMISTIC: OPTIMAL INSURANCE DESIGN WITH BIASED BELIEFS

This paper analyzes how biased beliefs about employment prospects affect the optimal design of unemployment insurance. Empirically, I find that the unemployed greatly overestimate how quickly they will find work. As a consequence, they would search too little for work, save too little for unemployment and deplete their savings too rapidly when unemployed. I analyze the use of the “sufficient‐statistics” formula to characterize the optimal unemployment policy when beliefs are biased and revisit the desirability of providing liquidity to the unemployed. I also find that the optimal unemployment policy may involve increasing benefits during the unemployment spell.     

Coordinating Service‐Sensitive Demand and Capacity by Adaptive Decision Making: An Application of Case‐Based Decision Theory*

The subject of this article is the simultaneous choice of product price and manufacturing capacity if demand is stochastic and service‐level sensitive. In this setting, capacity as well as price have an impact on demand because several aspects of service level depend on capacity. For example, delivery time will be reduced if capacity is increased given a constant demand rate. We illustrate the relationship between service level, capacity, and demand reaction by a stylized application problem from the after‐sales services industry. The reaction of customers to variations in service level and price is represented by a kinked price‐demand‐rate function. We first derive the optimal price‐capacity combination for the resulting decision problem under full information. Subsequently, we focus on a decision maker (DM) who lacks complete knowledge of the demand function. Hence the DM is unable to anticipate the service level and consequently cannot identify the optimal solution. However, the DM will acquire additional information during the sales process and use it in subsequent revisions of the price‐capacity decision. Thus, this decision making is adaptive and based on experience. In contrast to the literature, which assumes certain repetitive procedures somewhat ad hoc, we develop an adaptive decision process based on case‐based decision theory (CBDT) for the price‐capacity problem. Finally, we show that a CBDT DM in our setting eventually finds the optimal solution, if the DM sets the price based on absorption costs and adequately adjusts the capacity with respect to the observed demand.     

Flexibility or Cost Saving? Sourcing Decisions with Two Suppliers

This article studies a decentralized supply chain in which there are two suppliers and a single buyer. One supplier offers the quantity flexibility (QF) contract to the buyer, while the other offers the cheaper price. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity with additional buffer inventory. On the other hand, the price‐only contract places full inventory burden on the buyer, but with a cheaper price. We study this problem from the buyer's perspective and solve for the buyer's optimal procurement and forecasting decisions. We identify areas where flexibility and cheaper price have an advantage, one over the other. Our results indicate that the buyer significantly benefits from having multiple sources of supply. We also find that, from the system's standpoint, a multisupplier system may outperform a single‐supplier supply chain under certain conditions. Interestingly, we observe that providing too much flexibility may benefit the low‐price supplier rather than benefiting the QF supplier. We discuss the managerial implications and provide directions for future research opportunities.     

SUPPLY CONTRACTS WITH PERIODIC,STATIONARY COMMITMENT

The purpose of this paper is to model and analyze supply contracts with periodical commitment, in which the order quantities are fixed and stationary, with limited flexibility to change the order quantity at a cost to the buyer. A solution methodology is provided for the general, stochastic problem, and consideration is given to specific demand distributions. The deterministic model is also investigated, formulating the problem as a mixed‐integer linear program and as a network flow problem. Computational analyses are conducted, and the extension of the basic problem to the multiple‐product, multiple‐constraint problem is discussed.     

AMBIVALENT INVESTMENT AND THE HOLD‐UP PROBLEM

In this paper we add to the foundations of incomplete contracting literature. We study the hold‐up problem with ambivalent investment, where investment benefits the investing party if ex post the right decision is undertaken but harms the investing party if the wrong decision is made. In this context, we show that the power of contracts to provide investment incentives depends on three factors: the commitment value of contracts, the amount of quasirents that the investing party can expect in the case of out‐of‐contract renegotiation, and the degree of ambivalence of investment. First, contracts provide first‐best investment incentives when parties can commit to a contract regardless of the type of investment. Second, with sufficiently ambivalent investment, if parties cannot commit not to renegotiate a contract and if the investing party's bargaining power is intermediate, contracts cannot improve investment incentives above those provided by no contract. In contrast, a simple buyer or seller option contract is optimal when the investing party's bargaining power is extreme. (JEL: D23, K12, L22)