Greenhouse gas emission reduction is strongly advocated within the European Union (EU). Biomass has emerged as a renewable energy source and as manufacturing raw material with ecological credentials to mitigate carbon imbalance. The EU has defined the bioeconomy encompassing these material sources as a basis for technological and economic development. Biocenology, describing the study of natural communities, however, additionally demands inclusion of a circular economy, in which it needs to be assumed that endless renewable products are kept in continuous circulation of use and reuse. Thus, there arises the question whether the bioeconomy route alone, promoted by the EU, is sustainable. Using research literature, based on the Delphi method, and EU documents, we discuss the importance of sustainable management of bioresources. Short term solutions may remain necessary to ensure economic stability but, without embracing the circular economy, only limited mitigation of greenhouse gas emissions can be expected.
The increasing prevalence of rich sources of data and the availability of electronic medical record databases and electronic registries opens tremendous opportunities for enhancing medical research. For example, controlled trials are ubiquitously used to investigate the effect of a medical treatment, perhaps dependent on a set of patient covariates, and traditional approaches have relied primarily on randomized patient sampling and allocation to treatment and control group. However, when covariate data for a large cohort group of patients have already been collected and are available in a database, one can potentially design a treatment/control sample and allocation that provides far better estimates of the covariate-dependent effects of the treatment. In this paper, we develop a new approach that uses optimal design of experiments (DOE) concepts to accomplish this objective. The approach selects the patients for the treatment and control samples upfront, based on their covariate values, in a manner that optimizes the information content in the data. For the optimal sample selection, we develop simple guidelines and an optimization algorithm that provides solutions that are substantially better than random sampling. Moreover, our approach causes no sampling bias in the estimated effects, for the same reason that DOE principles do not bias estimated effects. We test our method with a simulation study based on a testbed data set containing information on the effect of statins on low-density lipoprotein (LDL) cholesterol.
This article presents certain new approaches to the reliability modeling of systems subject to shared loads. It is assumed that components in the system degrade continuously through an additive impact under load. The reliability assessment of such systems is often complicated by the fact that both the arriving load and the failure of components influence the degradation of the surviving components in a complex manner. The proposed approaches seek to ease this problem, by first deriving the time to prior failures and the arrival of random loads and then determining the number of failed components. Two separate models capable of analyzing system reliability as well as arriving at system maintenance and design decisions are proposed. The first considers a constant load and the other a cumulative load. A numerical example is presented to illustrate the effectiveness of the proposed models.
In many different applications of group decision-making, individual ranking agents or judges are able to rank only a small subset of all available candidates. However, as we argue in this article, the aggregation of these incomplete ordinal rankings into a group consensus has not been adequately addressed. We propose an axiomatic method to aggregate a set of incomplete rankings into a consensus ranking; the method is a generalization of an existing approach to aggregate complete rankings. More specifically, we introduce a set of natural axioms that must be satisfied by a distance between two incomplete rankings; prove the uniqueness and existence of a distance satisfying such axioms; formulate the aggregation of incomplete rankings as an optimization problem; propose and test a specific algorithm to solve a variation of this problem where the consensus ranking does not contain ties; and show that the consensus ranking obtained by our axiomatic approach is more intuitive than the consensus ranking obtained by other approaches.
In this work, we examine a staff scheduling problem in a governmental food safety center that is responsible for the surveillance of imported food at an international airport. In addition to the fact that the staff have different levels of efficiency and have different preference for work shifts, the Operations Manager of the food safety center would like to balance the dissimilarities of workers in order to provide unbiased work schedules for staff members. We adopt a two-phase approach, where the first phase is to schedule the work shifts of food safety inspectors (including rest days and shift types) with schedule fairness and staff preference taken into account and the second phase is to best-fit them to tasks in terms of skill-matches and create diversity of team formations. We also provide polyhedral results and devise valid inequalities for the two formulations. For the first-phase problem, we relax some constraints of the fairness criteria to reduce the problem size to reduce computational effort. We derive an upper bound for the objective value of the relaxation and provide computational results to show that the solutions devised from our proposed methodology are of good quality. For the second-phase problem, we develop a shift-by-shift assignment heuristic to obtain an upper bound for the maximum number of times any pair of workers is assigned to the same shift at the same location. We propose an enumeration algorithm, that solves the problems for fixed values of this number until an optimality condition holds or the problem is infeasible. Computational results show that our proposed approach can produce solutions of good quality in a much shorter period of time, compared with a standalone commercial solver.
Analysts predict impending shortages in the health care workforce, yet wages for health care workers already account for over half of U.S. health expenditures. It is thus increasingly important to adequately plan to meet health workforce demand at reasonable cost. Using infinite linear programming methodology, we propose an infinite-horizon model for health workforce planning in a large health system for a single worker class; e.g., nurses. We give a series of common-sense conditions that any system of this kind should satisfy and use them to prove the optimality of a natural lookahead policy. We then use real-world data to examine how such policies perform in more complex systems; in particular, our experiments show that a natural extension of the lookahead policy performs well when incorporating stochastic demand growth.
The accurate determination of control limits is crucial in statistical process control. The usual approach consists in computing the limits so that the in-control run-length distribution has some desired properties; for example, a prescribed mean. However, as a consequence of the increasing complexity of process data, the run-length of many control charts discussed in the recent literature can be studied only through simulation. Furthermore, in some scenarios, such as profile and autocorrelated data monitoring, the limits cannot be tabulated in advance, and when different charts are combined, the control limits depend on a multidimensional vector of parameters. In this article, we propose the use of stochastic approximation methods for control chart calibration and discuss enhancements for their implementation (e.g., the initialization of the algorithm, an adaptive choice of the gain, a suitable stopping rule for the iterative process, and the advantages of using multicore workstations). Examples are used to show that simulated stochastic approximation provides a reliable and fully automatic approach for computing the control limits in complex applications. An R package implementing the algorithm is available in the supplemental materials.
We consider three types of purchase contracts a manufacturer could offer in order to maximize its profit when supplying a retailer that uses responsive pricing to sell in an uncertain market: buy-now before the selling season starts, reserve stock for possible future purchase, and wait-and-see the market before making purchases. The existing literature has shown that adding a recourse purchase-i.e.,the wait-and-see alternative-is always beneficial for the retailer who faces an uncertain demand. We find that this is not necessarily the case for the manufacturer who supplies the retailer, as its optimal contract mix depends on the market uncertainty as well as its production characteristics. The manufacturer should offer only the buy-now alternative if its recourse production is much more costly than advance production. As the recourse production cost decreases, the manufacturer should add a second contract to the portfolio: initially the reserve contract and then the wait-and-see contract. However, when the recourse production is cheaper than advance production, the manufacturer should drop the buy-now contract from the mix. As such, it is only in a small region, which shrinks with decreasing uncertainty in demand, that the manufacturer finds it optimal to offer all three purchasing alternatives.
This research improves upon the monopsonist vaccine formulary design problem in the literature by incorporating several modeling enhancements and applying different methodologies to efficiently obtain solutions and derive insights. Our multi-objective formulation seeks to minimize the overall price to immunize a cohort of children, maximize the net profit shared among pediatric vaccine manufacturers, and minimize the average number of injections per child among the prescribed formularies. Accounting for Centers for Disease Control and Prevention (CDC) guidelines, we restrict vaccines utilized against a given disease within a given formulary to those produced by a single manufacturer. We also account for a circumstance in which one manufacturer's vaccine has a greater relative efficacy. For the resulting nonconvex mixed-integer nonlinear program, we bound the second and third objectives using optimal formulary designs for current public sector prices and utilize the E -constraint method to solve an instance representative of contemporary immunization schedule requirements. Augmenting our formulation with symmetry reduction constraints to reduce the required computational effort, we identify a set of non-inferior solutions. Of practical interest to the CDC, our model enables the design of a pricing and purchasing policy, creating a sustainable and stable capital investment environment for the provision of pediatric vaccines.
The geometric quality of a wafer is an important quality characteristic in the semiconductor industry. However, it is difficult to monitor this characteristic during the manufacturing process due to the challenges created by the complexity of the data structure. In this article, we propose an Additive Gaussian Process (AGP) model to approximate a standard geometric profile of a wafer while quantifying the deviations from the standard when a manufacturing process is in an in-control state. Based on the AGP model, two statistical tests are developed to determine whether or not a newly produced wafer is conforming. We have conducted extensive numerical simulations and real case studies, the results of which indicate that our proposed method is effective and has potentially wide application.
Single-crystal silicon ingots are produced from a complex crystal growth process. Such a process is sensitive to subtle process condition changes, which may easily become failed and lead to the growth of a polycrystalline ingot instead of the desired monocrystalline ingot. Therefore, it is important to model this polycrystalline defect in the crystal growth process and identify key process variables and their features. However, to model the crystal growth process poses great challenges due to complicated engineering mechanisms and a large amount of functional process variables. In this article, we focus on modeling the relationship between a binary quality indicator for polycrystalline defect and functional process variables. We propose a logistic regression model with hierarchical nonnegative garrote-based variable selection method that can accurately estimate the model, identify key process variables, and capture important features. Simulations and a case study are conducted to illustrate the merits of the proposed method in prediction and variable selection.
ABSTRACT We consider a production planning problem in which a producer procures an input component for production by offering a price to suppliers. The available supply quantity for the production input depends on the price the producer offers, and this supply level constrains production output. The producer seeks to meet a set of demands over a finite horizon at a minimum cost, including component procurement costs. We model the problem as a discrete-time production and component supply–pricing planning problem with nonstationary costs, demands, and component supply levels. This leads to a two-level lot-sizing problem with an objective function that is neither concave nor convex. Although the most general version of the problem is -hard, we provide polynomial-time algorithms for two special cases of the model under particular assumptions on the cost structure. We then apply the resulting algorithms heuristically to the more general problem version and provide computational results that demonstrate the high performance quality of the resulting heuristic solution methods.
This article presents a new interpretation and formulation of the Reliability-Redundancy Allocation Problem (RRAP) and demonstrates that solutions to this new problem provide distinct advantages compared with traditional approaches. Using redundant components is a common method to increase the reliability of a system. In order to add the redundant components to a system or a subsystem, there are two traditional types of strategies called active and standby redundancy. Recently a new redundancy strategy, called the mixed strategy, has been introduced. It has been proved that in the Redundancy Allocation Problem (RAP), this new strategy has a better performance compared with active and standby strategies alone. In this article, the recently introduced mixed strategy is implemented in the RRAP, which is more complicated than the RAP, and the results of using the mixed strategy are compared with the active and standby strategies. To analyze the performance of the new approach, some benchmark problems on the RRAP are selected and the mixed strategy is used to optimize the system reliability in these situations. Finally, the reliability of benchmark problems with the mixed strategy is compared with the best results of the systems when active or standby strategies are considered. The final results show that the mixed strategy results in an improvement in the reliability of all the benchmark problems and the new strategy outperforms the active and standby strategies in RRAP.
Due to the sustainable nature and stimulus plans from government, renewable energy (such as wind and solar) has been increasingly used in power systems. However, the intermittency of renewable energy creates challenges for power system operators to keep the systems reliable and cost-effective. In addition, information about renewable energy is usually incomplete. Instead of knowing the true probability distribution of the renewable energy course, only a set of historical data samples can be collected from the true (while ambiguous) distribution. In this article, we study two risk-averse stochastic unit commitment models with incomplete information: the first model being a chance-constrained unit commitment model and the second one a two-stage stochastic unit commitment model with recourse. Based on historical data on renewable energy, we construct a confidence set for the probability distribution of the renewable energy and propose data-driven stochastic unit commitment models to hedge against the incomplete nature of the information. Our models also ensure that, with a high probability, a large portion of renewable energy is utilized. Furthermore, we develop solution approaches to solve the models based on deriving strong valid inequalities and Benders' decomposition algorithms. We show that the risk-averse behavior of both models decreases as more data samples are collected and eventually vanishes as the sample size goes to infinity. Finally, our case studies verify the effectiveness of our proposed models and solution approaches.
In this article, we extend the modified Box-Meyer method and propose an approach to identify both active location and dispersion factors in a screening experiment. Since several candidate models can be simultaneously considered under the framework of Bayesian model averaging, the proposed method can overcome the problem of missing the identification of some active factors caused by either the alias structure or mis-specification of the location model. For illustration, three practical experiments and one synthetic data set are analyzed.
In this article, we introduce an age-based replacement policy in which the preventive replacements are restricted to specific calendar times. Under the new policy, the assets are renewed at failure or if their ages are greater than or equal to a replacement age at given calendar times, whichever occurs first. This policy is logistically applicable in industries such as utilities where there are large and geographically diverse populations of deteriorating assets with different installation times. Since preventive replacements are performed at fixed times, the renewal cycles are dependent random variables. Therefore, the classic renewal reward theorem cannot be directly applied. Using the theory of Markov chains with general state space and a suitably defined ergodic measure, we analyze the problem to find the optimal replacement age, minimizing the long-run expected cost per time unit. We further find the limiting distributions of the backward and forward recurrence times for this policy and show how our ergodic measure can be used to analyze more complicated policies. Finally, using a real data set of utility wood poles' maintenance records, we numerically illustrate some of our results including the importance of defining an appropriate ergodic measure in reducing the computational expense.
In this article we develop a procedure for estimating service levels (fill rates) and for optimizing stock and threshold levels in a two-demand-class model managed based on a lot-for-lot replenishment policy and a static threshold allocation policy. We assume that the priority demand classes exhibit mutually independent, stationary, Poisson demand processes and non-zero order lead times that are independent and identically distributed. A key feature of the optimization routine is that it requires computation of the stationary distribution only once. There are two approaches extant in the literature for estimating the stationary distribution of the stock level process: a so-called single-cycle approach and an embedded Markov chain approach. Both approaches rely on constant lead times. We propose a third approach based on a Continuous-Time Markov Chain (CTMC) approach, solving it exactly for the case of exponentially distributed lead times. We prove that if the independence assumption of the embedded Markov chain approach is true, then the CTMC approach is exact for general lead time distributions as well. We evaluate all three approaches for a spectrum of lead time distributions and conclude that, although the independence assumption does not hold, both the CTMC and embedded Markov chain approaches perform well, dominating the single cycle approach. The advantages of the CTMC approach are that it is several orders of magnitude less computationally complex than the embedded Markov chain approach and it can be extended in a straightforward fashion to three demand classes.
In recent years, many resource allocation models have been developed to protect critical infrastructure by maximizing system resiliency or minimizing its vulnerability to disasters or disruptions. However, these are often computationally intensive and require simplifying assumptions and approximations. In this study, we develop a robust and representative, yet tractable, model for optimizing maintenance planning of generic network-structured systems (transportation, water, power, communication). The proposed modeling framework examines models that consider both linear and nonlinear objective functions and enhances their structure through suitable manipulations. Moreover, the designed models inherently capture the network topography and the stochastic nature of disruptions and can be applied to network-structured systems where performance is assessed based on network flow efficiency and mobility. The developed models are applied to the Istanbul highway system in order to assess their relative computational effectiveness and robustness using several test cases that consider single- and multiple-treatment types, and the problems are solved on the NEOS server using different available software. The results demonstrate that our models are capable of obtaining optimal solutions within a very short time. Furthermore, the linear model is shown to yield a good approximation to the nonlinear model (it determined solutions within 0.3% of optimality, on average). Managerial insights are provided in regard to the optimal policies obtained, which generally appear to favor selecting fewer links and applying a higher quality treatment to them.
Closed-form likelihood expansion is an important method for econometric assessment of continuous-time models driven by stochastic differential equations based on discretely sampled data. However, practical applications for sophisticated models usually involve significant computational efforts in calculating high-order expansion terms in order to obtain the desirable level of accuracy. We provide new and efficient algorithms for symbolically implementing the closed-form expansion of the transition density. First, combinatorial analysis leads to an alternative expression of the closed-form formula for assembling expansion terms from that currently available in the literature. Second, as the most challenging task and central building block for constructing the expansions, a novel analytical formula for calculating the conditional expectation of iterated Stratonovich integrals is proposed and a new algorithm for converting the conditional expectation of the multiplication of iterated Stratonovich integrals to a linear combination of conditional expectation of iterated Stratonovich integrals is developed. In addition to a procedure for creating expansions for a nonaffine exponential Ornstein-Uhlenbeck stochastic volatility model, we illustrate the computational performance of our method.
We study the problem of capacity planning for long-term care services, which is important not only for the elderly and disabled who cannot adequately care for themselves but also for long-term care providers and health policymakers. Patients with long-term care needs usually have to transfer between different settings such as nursing homes and home- and community-based services. We model patient flows among these settings using an open migration network and formulate the planning of the capacity needed to provide long-term care with a newsvendor-type model. We explore the structural properties of the model and identify the most influential factors, such as the penalty cost for capacity shortage and transition rates between different care settings, in making capacity decisions. With the model developed, capacity decisions for long-term care service networks can be made more systematically with full consideration of different patient flow patterns and budget constraints. The research will be especially useful to long-term care policymakers in a state or nationwide given the worsening shortage of care providers and the escalating long-term care needs resulting from population aging.
