Distributionally Robust Optimization of Two‐Stage Lot‐Sizing Problems

This paper studies two‐stage lot‐sizing problems with uncertain demand, where lost sales, backlogging and no backlogging are all considered. To handle the ambiguity in the probability distribution of demand, distributionally robust models are established only based on mean‐covariance information about the distribution. Based on shortest path reformulations of lot‐sizing problems, we prove that robust solutions can be obtained by solving mixed 0‐1 conic quadratic programs (CQPs) with mean‐risk objective functions. An exact parametric optimization method is proposed by further reformulating the mixed 0‐1 CQPs as single‐parameter quadratic shortest path problems. Rather than enumerating all potential values of the parameter, which may be the super‐polynomial in the number of decision variables, we propose a branch‐and‐bound‐based interval search method to find the optimal parameter value. Polynomial time algorithms for parametric subproblems with both uncorrelated and partially correlated demand distributions are proposed. Computational results show that the proposed models greatly reduce the system cost variation at the cost of a relative smaller increase in expected system cost, and the proposed parametric optimization method is much more efficient than the CPLEX solver.     

Three‐Stage Decision‐Making Model under Restricted Conditions for Emergency Response to Ships Not under Control

A ship that is not under control (NUC) is a typical incident that poses serious problems when in confined waters close to shore. The emergency response to NUC ships is to select the best risk control options, which is a challenge in restricted conditions (e.g., time limitation, resource constraint, and information asymmetry), particularly in inland waterway transportation. To enable a quick and effective response, this article develops a three‐stage decision‐making framework for NUC ship handling. The core of this method is (1) to propose feasible options for each involved entity (e.g., maritime safety administration, NUC ship, and ships passing by) under resource constraint in the first stage, (2) to select the most feasible options by comparing the similarity of the new case and existing cases in the second stage, and (3) to make decisions considering the cooperation between the involved organizations by using a developed Bayesian network in the third stage. Consequently, this work provides a useful tool to achieve well‐organized management of NUC ships.     

Design of Flexible Multi‐Stage Processes

Faced with demand uncertainty across multiple product lines, many companies have recourse to flexible capacities which can process different products in order to better balance the trade‐off between capacity utilization and cost efficiency. Many studies demonstrated the potential benefit of using flexible capacity at the aggregate level by treating a whole plant or a whole process as a single stage. This paper extends these analyses by studying the benefits of flexible capacity while considering the multi‐stage structure of processes and consequently determining which stages should be flexible, which should be dedicated, and how much capacity to assign to each stage. We consider a two‐product firm which operates in a process‐to‐order environment and faces uncertain demand. Each stage of the process can be designed as dedicated or flexible. Dedicated resources are highly cost efficient but limited to the single product they are exclusively designed for, whereas flexible resources are versatile to handle several products but are more expensive. Using a general mathematical formulation our analysis shows that the optimal design may have some dedicated and some flexible stages along the process. Interestingly, this decision should be decoupled from the chronological order of the stages along the process.     

Multi‐Echelon Inventory Management under Short‐Term Take‐or‐Pay Contracts

We extend the Clark–Scarf serial multi‐echelon inventory model to include procuring production inputs under short‐term take‐or‐pay contracts at one or more stages. In each period, each such stage has the option to order/process at two different cost rates; the cheaper rate applies to units up to the contract quantity selected in the previous period. We prove that in each period and at each such stage, there are three base‐stock levels that characterize an optimal policy, two for the inventory policy and one for the contract quantity selection policy. The optimal cost function is additively separable in its state variables, leading to conquering the curse of dimensionality and the opportunity to manage the supply chain using independently acting managers. We develop conditions under which myopic policies are optimal and illustrate the results using numerical examples. We establish and use a generic one‐period result, which generalizes an important such result in the literature. Extensions to cover variants of take‐or‐pay contracts are included. Limitations are discussed.     

Non‐dominated Time‐Window Policies in City Distribution

Urban freight contributes significantly to pollution, noise disturbance, traffic congestion, and safety problems in city centers. In many cities, local governments have introduced policy measures, in particular time‐access restrictions, to alleviate these problems. However, setting time windows is very challenging due to the conflicting interests and objectives of the stakeholders involved. In this article, we examine whether it is possible to develop time‐window policies that enhance environmental sustainability and distribution efficiencies, while meeting the objectives of the municipalities. We develop a framework for balancing retailer (costs), municipality (satisfaction), and environmental (emissions) objectives, using data envelopment analysis, under different urban time‐window policies. The approach is illustrated by a case study of three Dutch retail organizations, with a large number of stores affected by such time windows. On the basis of an evaluation of 99 different time‐window policies, our results show that harmonizing time windows between neighboring cities leads to the best overall performance. The currently used time‐window policy appears to perform reasonably well, but can be improved on all dimensions . However, harmonizing time‐window policies may be difficult to realize in practice.     

Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed‐form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between GlueVaR, value‐at‐risk, and tail value‐at‐risk is explained. Tail subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in nonfinancial problems such as health, safety, environmental, or catastrophic risk management.     

Analysis of Two‐Level Support Systems with Time‐Dependent Overflow—A Banking Application

In this paper, we analyze the performance of call centers of financial service providers with two levels of support and a time‐dependent overflow mechanism. Waiting calls from the front‐office queue flow over to the back office if a waiting‐time limit is reached and at least one back‐office agent is available. The analysis of such a system with time‐dependent overflow is reduced to the analysis of a continuous‐time Markov chain with state‐dependent overflow probabilities. To approximate the system with time‐dependent overflow, some waiting‐based performance measures are modified. Numerical results demonstrate the reliability of this Markovian performance approximation for different parameter settings. A sensitivity analysis shows the impact of the waiting‐time limit and the dependence of the performance measures on the arrival rate.     

Branch‐and‐Price Methods for Prescribing Profitable Upgrades of High‐Technology Products with Stochastic Demands*

This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high‐technology products over its life cycle. The model integrates various organizations in the enterprise: product design, marketing, manufacturing, production planning, and supply chain management. Customer demand is assumed random and this uncertainty is addressed using scenario analysis. A branch‐and‐price (B&P) solution approach is devised to optimize the stochastic problem effectively. Sets of random instances are generated to evaluate the effectiveness of our solution approach in comparison with that of commercial software on the basis of run time. Computational results indicate that our approach outperforms commercial software on all of our test problems and is capable of solving practical problems in reasonable run time. We present several examples to demonstrate how managers can use our models to answer “what if” questions.     

ON‐THE‐JOB SEARCH AND MORAL HAZARD

We analyze the interaction between intertemporal incentive contracts and search frictions associated with on‐the‐job search. In our model, agency problems call for wage contracts with deferred compensation. At the same time workers do on‐the‐job search. Deferred compensation improves workers' incentives to exert effort but distorts their on‐the‐job search decisions. We show that deferred compensation is less attractive when the value to the worker–firm pair of on‐the‐job search is high. Moreover, the interplay between search frictions and wage contracts creates feedback effects. If firms in equilibrium use contracts with deferred compensation, fewer firms with vacancies enter the on‐the‐job search market, and this in turn reduces the distortions created by deferred compensation. These feedback effects between the incentive contracts used and the activity level in the search markets can lead to multiple equilibria: a low‐turnover equilibrium where firms use deferred compensation, and a high‐turnover equilibrium where they do not. Furthermore, the model predicts that firms are more likely to use deferred compensation when search frictions are high and when the gains from on‐the‐job search are small.     

Opt‐Out Options in New Product Co‐development Partnerships

We study three contractual arrangements—co‐development, licensing, and co‐development with opt‐out options—for the joint development of new products between a small and financially constrained innovator firm and a large technology company, as in the case of a biotech innovator and a major pharma company. We formulate our arguments in the context of a two‐stage model, characterized by technical risk and stochastically changing cost and revenue projections. The model captures the main disadvantages of traditional co‐development and licensing arrangements: in co‐development the small firm runs a risk of running out of capital as future costs rise, while licensing for milestone and royalty (M&R) payments, which eliminates the latter risk, introduces inefficiency, as profitable projects might be abandoned. Counter to intuition we show that the biotech's payoff in a licensing contract is not monotonically increasing in the M&R terms. We also show that an option clause in a co‐development contract that gives the small firm the right but not the obligation to opt out of co‐development and into a pre‐agreed licensing arrangement avoids the problems associated with fully committed co‐development or licensing: the probability that the small firm will run out of capital is greatly reduced or completely eliminated and profitable projects are never abandoned.     

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.     

Preferences for One‐Shot Resolution of Uncertainty and Allais‐Type Behavior

Experimental evidence suggests that individuals are more risk averse when they perceive risk that is gradually resolved over time. We address these findings by studying a decision maker who has recursive, nonexpected utility preferences over compound lotteries. The decision maker has preferences for one‐shot resolution of uncertainty if he always prefers any compound lottery to be resolved in a single stage. We establish an equivalence between dynamic preferences for one‐shot resolution of uncertainty and static preferences that are identified with commonly observed behavior in Allais‐type experiments. The implications of this equivalence on preferences over information systems are examined. We define the gradual resolution premium and demonstrate its magnifying effect when combined with the usual risk premium.     

Panel Size and Overbooking Decisions for Appointment‐Based Services under Patient No‐Shows

Many service systems that work with appointments, particularly those in healthcare, suffer from high no‐show rates. While there are many reasons why patients become no‐shows, empirical studies found that the probability of a patient being a no‐show typically increases with the patient's appointment delay, i.e., the time between the call for the appointment and the appointment date. This paper investigates how demand and capacity control decisions should be made while taking this relationship into account. We use stylized single server queueing models to model the appointments scheduled for a provider, and consider two different problems. In the first problem, the service capacity is fixed and the decision variable is the panel size; in the second problem, both the panel size and the service capacity (i.e., overbooking level) are decision variables. The objective in both cases is to maximize some net reward function, which reduces to system throughput for the first problem. We give partial or complete characterizations for the optimal decisions, and use these characterizations to provide insights into how optimal decisions depend on patient's no‐show behavior in regards to their appointment delay. These insights especially provide guidance to service providers who are already engaged in or considering interventions such as sending reminders in order to decrease no‐show probabilities. We find that in addition to the magnitudes of patient show‐up probabilities, patients' sensitivity to incremental delays is an important determinant of how demand and capacity decisions should be adjusted in response to anticipated changes in patients' no‐show behavior.     

General Probability‐Time Tradeoff and Intertemporal Risk‐Value Model

This article proposes an intertemporal risk‐value (IRV) model that integrates probability‐time tradeoff, time‐value tradeoff, and risk‐value tradeoff into one unified framework. We obtain a general probability‐time tradeoff, which yields a formal representation form to reflect the psychological distance of a decisionmaker in evaluating a temporal lottery. This intuition of probability‐time tradeoff is supported by robust empirical findings as well as by psychological theory. Through an explicit formalization of probability‐time tradeoff, an IRV model taking into account three fundamental dimensions, namely, value, probability, and time, is established. The object of evaluation in our framework is a complex lottery. We also give some insights into the structure of the IRV model using a wildcatter problem.     

Challenges in Development and Implementation of Health‐Risk‐Based Soil Quality Guidelines: Turkey's Experience

Management of contaminated sites is a critical environmental issue around the world due to the human health risk involved for many sites and scarcity of funding. Moreover, clean‐up costs of all contaminated sites to their background levels with existing engineering technologies may be financially infeasible and demand extended periods of operation time. Given these constraints, to achieve optimal utilization of available funds and prioritization of contaminated sites that need immediate attention, health‐risk‐based soil quality guidelines should be preferred over the traditional soil quality standards. For these reasons, traditional soil quality standards are being replaced by health‐risk‐based ones in many countries and in Turkey as well. The need for health‐risk‐based guidelines is clear, but developing these guidelines and implementation of them in contaminated site management is not a straightforward process. The goal of this study is to highlight the problems that are encountered at various stages of the development process of risk‐based soil quality guidelines for Turkey and how they are dealt with. Utilization of different definitions and methodologies at different countries, existence of inconsistent risk assessment tools, difficulties in accessing relevant documents and reports, and lack of specific data required for Turkey are among these problems. We believe that Turkey's experience may help other countries that are planning to develop health‐risk‐based guidelines achieve their goals in a more efficient manner.     

Practical Implications of Preference‐Based Conference Scheduling

Conference scheduling involves organizing presentations into sessions which are assigned to time periods and rooms. This includes assuring a feasible utilization of time periods and rooms, and avoiding individual schedule conflicts. The problem increases in complexity by considering the preferences of presenters: for time periods, for rooms, etc. A greater level of complexity comes from considering the preferences of conference attendees, which we define as preference‐based conference scheduling (PBCS). This article provides a structure on which PBCS problems are founded, including empirical demonstration of solution techniques. In addition, real‐world strategic planning issues of flexibility and preference detail are explored.     

‘Full‐time is a Given Here’: Part‐time Versus Full‐time Job Quality*

This study explores full‐time workers' understanding of and assumptions about part‐time work against six job quality components identified in recent literature. Forty interviews were conducted with employees in a public sector agency in Australia, a study context where part‐time work is ostensibly ‘good quality’ and is typically long term, voluntary, involving secure contracts (i.e. permanent rather than casual) and having predictable hours distributed evenly over the week and year. Despite strong collective bargaining arrangements as well as substantial legal and industrial obligations, the findings revealed some serious concerns for part‐time job quality. These concerns included reduced responsibilities and lesser access to high status roles and projects, a lack of access to promotion opportunities, increased work intensity and poor workplace support. The highly gendered, part‐time labour market also means that it is women who disproportionately experience this disadvantage. To foster equity, greater attention needs to focus on monitoring and enhancing job quality, regardless of hours worked.     

A Competitive Model of Customization with Lead‐Time Effects

In this article, we study the competitive interactions between a firm producing standard products and a firm producing custom products. Consumers with heterogeneous preferences choose between n standard products, which may not meet their preferences exactly but are available immediately, and a custom product, available only after a certain lead time l. Standard products incur a variety cost that increases with n and custom products incur a lead time cost that is decreasing in the lead time l. We consider a two‐stage game wherein at stage 1, the standard product firm chooses the variety and the custom firm chooses the lead time and then both firms set prices simultaneously. We characterize the subgame‐perfect Nash equilibrium of the game. We find that both firms can coexist in equilibrium, either sharing the market as local monopolists or in a price‐competitive mode. The standard product firm may offer significant or minimal variety depending on the equilibrium outcome. We provide several interesting insights on the variety, lead time, and prices of the products offered and on the impact of problem parameters on the equilibrium outcomes. For instance, we show that the profit margin and price of the custom product are likely to be higher than that of standard products in equilibrium under certain conditions. Also, custom firms are more likely to survive and succeed in product markets with larger potential market sizes. Another interesting insight is that increased consumer sensitivity to product fit may result in lower lead time for the custom product.     

Mitigating Inventory Overstocking: Optimal Order‐up‐to Level to Achieve a Target Fill Rate over a Finite Horizon

Service level agreements (SLAs) are widely adopted performance‐based contracts in operations management practice, and fill rate is the most common performance metric among all the measurements in SLAs. Traditional procedures characterizing the order‐up‐to level satisfying a specified fill rate implicitly assume an infinite performance review horizon. However, in practice, inventory managers are liable to maintain and report fill rates over a finite performance review horizon. This horizon discrepancy leads to deviation between the target fill rate and actual achieved fill rate. In this study, we first examine the behavior of the fill rate distribution over a finite horizon with positive lead time. We analytically prove that the expected fill rate assuming an infinite performance review horizon exceeds the expected fill rate assuming a finite performance review horizon, implying that there exists some inventory “waste” (i.e., overstocking) when the traditional procedure is used. Based on this observation and the complexity of the problem, we propose a simulation‐based algorithm to reduce excess inventory while maintaining the contractual target fill rate. When the lead time is significant relative to the length of the contract horizon, we show that the improvement in the inventory system can be over 5%. Further, we extend our basic setting to incorporate the penalty for failing to meet a target, and show how one can solve large‐scale problems via stochastic approximation. The primary managerial implication of our study is that ignoring the performance review horizon in an SLA will cause overstocking, especially when the lead time is large.     

Short‐Run Subsidies and Long‐Run Adoption of New Health Products: Evidence From a Field Experiment

Short‐run subsidies for health products are common in poor countries. How do they affect long‐run adoption? A common fear among development practitioners is that one‐off subsidies may negatively affect long‐run adoption through reference‐dependence: People might anchor around the subsidized price and be unwilling to pay more for the product later. But for experience goods, one‐off subsidies could also boost long‐run adoption through learning. This paper uses data from a two‐stage randomized pricing experiment in Kenya to estimate the relative importance of these effects for a new, improved antimalarial bed net. Reduced form estimates show that a one‐time subsidy has a positive impact on willingness to pay a year later inherit. To separately identify the learning and anchoring effects, we estimate a parsimonious experience‐good model. Estimation results show a large, positive learning effect but no anchoring. We black then discuss the types of products and the contexts inherit for which these results may apply.