Multi-period Model Research Articles

Optimization of vertical farms energy efficiency via multiperiodic graph-theoretical approach

A systematic method is proposed for enhancing the energy efficiency of vertical farms when integrated into urban infrastructure. The method relies on the optimization of a multiperiod model that determines the system's best operation plan considering variations in its parameters throughout the day. These parameters include factors such as resources availability from the urban infrastructure and fluctuations in electricity prices. The model is formulated and solved via the tools of the P-graph framework, which permits the automatic formulation of the rigorous superstructure and the efficient optimization of the integrated system's operation. The method is illustrated via a case study comprising three scenarios. The most efficient case demonstrates up to 40% electricity cost saving potential for a particular operation day, and up to 31% for the entire year. The method presented constitutes an optimization tool that can use real data on electricity prices and forecasts of weather conditions to reduce operating costs and enhance the energy efficiency and sustainability of vertical farming systems.

Portfolio optimization: A multi-period model with dynamic risk preference and minimum lots of transaction

Sufficient description of stock returns is essential to generate an efficient model of portfolio optimization. Security returns are considered to be random variables where there exist sufficient data of historical returns. Nonetheless, uncertain variables may be applied to increase the effectiveness of security returns. The following research entails an optimization objective problem focusing on minimum lots of transaction in uncertain environments of dynamic trading. Also, the changing risk preference of the investor over the horizon of investment has been factored in the model. An average- Value at Risk (VaR) framework has been used to maximize wealth creation using genetic algorithms.

Dual sourcing models with stock-out dependent substitution

Companies use different criteria such as lead time, cost and quality to evaluate suppliers; often using multiple suppliers with the aim of reducing stockout risk. But in many industries there may be significant differences between the quality levels of different suppliers. Thus quality-sensitive companies may prefer an item from a primary supplier, but be forced to accept substitute products of lesser quality in case of a stock-out. Motivated by an example in the aviation industry, we introduce a Dual Sourcing problem With Stock-out dependent substitution (DSWS) which includes quality differences. Due to nonconvexity of the multi-period model, analytical characterization of the optimal policy appears intractable. To overcome this problem, we prove a relation between the optimal cost of DSWS and costs of three other problems - dual sourcing without substitution and single sourcing problems with and without backlogging. This leads us to propose the use of the dual index policy (and a variant) as heuristics for DSWS, and to develop an algorithm for parameter optimization of our heuristics. Extensive numerical experiments show that the dual index policy outperforms all other candidate solutions from the literature by at least 8%. Our experiments show that the utilization of the back-up supplier leads to substantial cost savings and service rate increase, especially in case of high differences between holding cost rates of different quality items.

Dynamic analysis of pandemic cross-regional transmission considering quarantine strategies in the context of limited medical resources

This work aims to quantitatively analyze the effect of quarantine strategies on controlling the spread of the pandemic in multiple regions under limited medical resources. First, a multi-regional discrete-time susceptible-infected-quarantined -recovered (SIQR) pandemic model considering intra-regional and inter-regional quarantine strategies is proposed. The basic reproduction number of the model is derived and shown to be a non-increasing function of the quarantine control parameters. Due to the limited medical resources, a multi-period model of resource allocation coupled with quarantine control is developed. Numerical results demonstrate that quarantine strategies reduce the speed and size of pandemic spreading. In the context of limited medical resources, intra-regional control is less effective at reducing infected individuals than inter-regional control, and most of the resources are allocated to high-risk regions.

Multi-period design and optimization of classified municipal solid waste supply chain integrating seasonal fluctuations in waste generation

Municipal solid waste (MSW) management should be consistent with the principles of supply chain management, and the integration of relevant theories in supply chain has been proven to be feasible while contributing positively to the management model of MSW. Waste management operators have developed a multiperiod model that optimizes and designs the MSW supply chain by incorporating seasonal variations in classified MSW supply to obtain the optimal supply chain network for each type of MSW in each season. The optimal supply chain network includes the collection, transportation and treatment of MSW. The results of the case study indicated that seasonal fluctuations in MSW fraction generation during different seasons affected the total amount and generation of the four different MSW waste fraction. Consequently, the optimal supply chain network was altered. The model demonstrated the seasonal impact on the MSW supply chain and determine the optimal supply chain network that integrates seasonal fluctuations in MSW fraction generation. The quarterly cost of the model was the largest in summer at 9.72 × 109 CNY and the smallest in winter at 5.80 × 109 CNY.

Optimizing Renewable Injection in Integrated Natural Gas Pipeline Networks Using a Multi-Period Programming Approach

In this paper, we propose an optimization model that considers two pathways for injecting renewable content into natural gas pipeline networks. The pathways include (1) power-to-hydrogen or PtH, where off-peak electricity is converted to hydrogen via electrolysis, and (2) power-to-methane, or PtM, where carbon dioxide from different source locations is converted into renewable methane (also known as synthetic natural gas, SNG). The above pathways result in green hydrogen and methane, which can be injected into an existing natural gas pipeline network. Based on these pathways, a multi-period network optimization model that integrates the design and operation of hydrogen from PtH and renewable methane is proposed. The multi-period model is a mixed-integer non-linear programming (MINLP) model that determines (1) the optimal concentration of hydrogen and carbon dioxide in the natural gas pipelines, (2) the optimal location of PtH and carbon dioxide units, while minimizing the overall system cost. We show, using a case study in Ontario, the optimal network structure for injecting renewable hydrogen and methane within an integrated natural gas network system provides a $12M cost reduction. The optimal concentration of hydrogen ranges from 0.2 vol % to a maximum limit of 15.1 vol % across the network, while reaching a 2.5 vol % at the distribution point. This is well below the maximum limit of 5 vol % specification. Furthermore, the optimizer realized a CO2 concentration ranging from 0.2 vol % to 0.7 vol %. This is well below the target of 1% specified in the model. The study is essential to understanding the practical implication of hydrogen penetration in natural gas systems in terms of constraints on hydrogen concentration and network system costs.

Flexible heat integration system in first-/second-generation ethanol production via screening pinch-based method and multiperiod model

In sugarcane biorefineries, energy integration plays a fundamental role regarding by-product destination and final sales profitability. In biorefineries, the by-product of the sugar/ethanol production process – sugarcane bagasse – can be burned in boilers to produce steam to supply the thermal demands of the plant. Normally, the quantity of bagasse from the plant exceeds the quantity necessary for supplying the energy requirements of the plant. This surplus can be used for either (i) additional electricity production and selling to the grid or (ii) second-generation (2G) ethanol production. To maximize profit, the plant should be flexible to produce either electricity or 2G ethanol according to the current market prices of these products. In this work, an approach is presented for designing a flexible heat exchanger network (HEN) based on a multiperiod synthesis. It involves assessing probabilities of occurrence for different bagasse use scenarios. These values are obtained from a pinch-based approach for screening optimal heat integration in a range of ethanol/electricity prices. A multiperiod HEN synthesis problem is then solved with variable flow rates. Results show that maximum bagasse diverted to 2G ethanol production is increased from 66% to 77% with the new HEN compared to the original design considered.

A quantitative analysis of inaccuracy inventory reducing in multi-period mode: Comparison between RFID and inventory counting

Inventory management decisions are one of the essential factors influencing the profitability of each supply chain member. However, in the real world and due to errors, the physical inventory and the inventory on the information system are frequently not matched, impacting the decision-making regarding inventory control. As a result, managers are constantly looking for ways to eliminate or reduce inventory errors. This study examines a retailer’s inventory control problem with transaction errors over time. For this purpose, a single-item multi-period model that adheres to a periodic review policy will be used. Therefore, the impact of two solutions, inventory counting and using RFID technology, on eliminating or reducing errors is assessed. In the section on inventory counting, unlike most papers that consider a counting cycle for inventory, it will be determined at the end of which period the inventory counting should be performed by acquiring the profit functions and their parameters. Also, when using RFID technology, it may occasionally fail to track the products, so the profit function is acquired with this error rate in mind. Moreover, it is determined when the inventory on the information system should be reset to eliminate errors accumulated over time. Furthermore, because these solutions each have costs, the discrete-event simulation approach calculates their profitability. Also, the profit changing of these solutions will be analyzed about various parameters.

Optimal Relative Performance Criteria in Mean-Field Contribution Games

We consider mean-field contribution games, where players in a team choose some effort levels at each time period and the aggregate reward for the team depends on the aggregate cumulative performance of all the players. Each player aims to maximize the expected reward of her own share subject to her cost of effort. To reduce the free-rider issue, we propose some relative performance criteria (RPC), based on which the reward is redistributed to each player. We are interested in those RPCs that implement the optimal solution for the corresponding centralized problem, and we call such RPC an optimal one. That is, the expected payoff of each player under the equilibrium associated with an optimal RPC is as large as the value induced by the corresponding problem where players completely cooperate. We first analyze a one-period model with homogeneous players and obtain natural RPCs of different forms. Then, we generalize these results to a multiperiod model in discrete time. Next, we investigate a two-layer mean-field game. The top layer is an interteam game (team-wise competition), in which the reward of a team is impacted by the relative achievement of the team with respect to other teams; the bottom layer is an intrateam contribution game where an RPC is implemented for reward redistribution among team members. We establish the existence of equilibria for the two-layer game and characterize the intrateam optimal RPC. Finally, we extend the (one-layer) results of optimal RPCs to the continuous-time setup as well as to the case with heterogenous players.

Optimizing design and performance assessment of a sustainability hydrogen supply chain network: A multi-period model for China

The potential future use of hydrogen as transportation fuel should be assessed from supply chain point. However, the main challenge to motivate hydrogen supply chain (HSC) network is the insufficiency of the present hydrogen infrastructure. This paper presents a mixed integer linear programming (MILP) optimization model for a rational HSC design, given that primary energy source availability, production technologies, transportation modes and storage types. A sustainable principle based on Markov chain is innovatively introduced in the design of HSC network. The strategic decisions for sustainability infrastructure plans can be hierarchically analyzed in time-associated steps (2025–2030–2035). Meanwhile the spatiotemporal-resolved design is further used for an explicit consideration of specific city (Dalian in China), not heavily focused on national/country scale. Furthermore, optimizations are evaluated with total daily costs, carbon tax and CO2 emissions reduction constraints. The results show that the route of WE(S2)→WE(S2)→WE(S3) is the strategic decisions for Dalian hydrogen infrastructure plan from economic-environmental sustainable viewpoint, with the whole HSC costs of 18.44 $ kg−1 H2 in 2025, 10.56 $ kg−1 H2 in 2030 and 5.98 $ kg−1 H2 in 2035. Finally, the proposed design can provide policy-makers with the selection of sustainability pathways for dynamic hydrogen development planning.

A Multi-Period Model for Optimal Changi Airport Check-In Counter Operations

Growth in air passenger flow has caused severe congestion at the airport check-in counter, posing a significant problem for airport management. Particularly during the check-in process, the necessary authorities must coordinate sufficient facilities with adequate staffing levels. The airport check-in counter problem (ACCAP) is a field concerned with establishing the optimal number of check-in counters to balance operating expenses and passenger wait times in order to reduce airport congestion. Expanding the number of counters and staff to a minimum operating cost is able to prevent the congestion problem from escalating without incurring further operating expenses. This paper focused on proposing optimal scheduling of airport check-in counters operations, including staffing. A dynamic model with multi-period principles is adapted to address the aforementioned problem by balancing the trade-off between service performance and operational cost. As a case study, data from Singapore Changi International Airport was utilized. The findings are also discussed in terms of the flow of passengers throughout the airport check-in procedure and operations. As a result, the number of activated counters is minimized throughout all shifts by applying the dynamic model at the average service time. At the same time, there are fewer passengers in the queue.

Acuity-Based Allocation of ICU-Downstream Beds with Flexible Staffing

Intensive care units (ICUs) are crucial resources within hospitals, caring for the most critically ill patients. We propose a novel modeling framework that improves the outflow of ICU patients by anticipating unit interactions and resource sharing within the system. Across an arbitrary bipartite network of units, we consider two types of downstream staffing (baseline and flexible) and a two-stage decision process. In the first stage, we determine the level of flexible bed staffing using existing physical beds at downstream units in anticipation of incoming transfers from the ICUs. In the second stage, we determine the allocation of ICU patients to downstream beds. The goal of the model is to reduce inefficiencies and transfer delays causing ICU bed block due to lack of space in downstream units. We formulate a dynamic multiperiod model and analyze the dual of its (relaxed) stationary counterpart. Decomposing the relaxed stationary model into an ICU and downstream subproblems, we calculate the relative values of downstream beds and derive a practical acuity-based policy for the daily operational decisions. Using a large-scale simulation calibrated with historic hospital data, we demonstrate that our acuity-based policy reduces the number of long-run diverted ICU arrivals, particularly in high-demand scenarios, thus improving ICU throughput, when compared with a deterministic, a generalized randomized-most-idle, and static policies. History: Accepted by J. Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. Funding: This work was partially supported by National Science Foundation [Grants CMMI-1635301/1635410/1635642]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1267 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0133 ) at ( http://dx.doi.org/10.5281/zenodo.7194693 ).

Recycled content claims under demand benefit and supply uncertainty: Multi-period model and application to glasswool insulation

Manufacturers often declare recycled content claims that are specific (e.g., to each production period) or average (e.g., across many production periods). Such claims are manifested through the choice of certification and generate demand for the manufacturer’s recycled content product. However, since the amount of usable recycled input available from local sources is often limited and uncertain, and external (non-local) sources are expensive, a manufacturer needs to balance the demand-side benefits of a recycled content claim with the associated sourcing and inventory costs. In this paper, we develop a multi-period model over a planning horizon, where a manufacturer makes a product’s source mix decision (recycled input vs. virgin content) and recycled input carryover decision each period in the presence of a stochastic supply and external sourcing cost. We solve for the manufacturer’s optimal recycled content claim decision over a planning horizon and calculate the manufacturer’s profit, recycled input, and virgin raw material usage at the optimal claim. Our key contributions are as follows. We show that (i) a shorter (longer) planning horizon may sometimes increase (decrease) the recycled content claim, (ii) demand stimulation for recycled products may sometimes decrease the optimal recycled content claim, and (iii) supply stabilization (i.e., lowering variability in the municipal stream) may decrease the recycled content claim. We provide numerical results for parameters driven by European data from the fiberglass insulation industry and use our analysis to quantify the impact of several European policies relevant to the glasswool insulation industry on a manufacturer’s incentive to incorporate recycled content.

Indifference pricing of credit default swaps in a multi-period model

Credit default swaps (CDS) are the most common type of credit derivatives used for hedging and speculative purposes in credit markets. We consider a representative risk-averse investor who has initial endowment in credit instrument and invests in traditional financial instruments. Using the utility indifference pricing approach, we construct a pricing framework for single-name CDS contracts with periodic payments in a multi-period model. Moreover, we analyze CDS buyers with different trading motives, and examine the effect of risk aversion on the indifference upfront prices and credit spreads of CDS for investors with hedging or speculative motives. In particular, our results show that speculation in the CDS market provides a potential explanation for the formation of the negative CDS-bond bases during and after the global financial crisis.

A new model to design the suppliers portfolio in newsvendor problem based on product reliability

<p style='text-indent:20px;'>Suppliers' selection problem has always been daunting challenges in the Newsvendor problem. Furthermore, since the failures in the supplier's products cause irreparable damage to the retailer, it is necessary to consider the reliability of products in ordering suppliers' products. This paper develops the Newsvendor model by considering the impactful criteria in supplier selection and product reliability so that the total cost of the chain is minimized in a multi-product and multi-period model with multiple suppliers. While multiple criteria decision making (MCDM) accounts for multiple criteria and their tradeoffs, its application in Newsvendor model is not considered. This paper applies the Bayesian best worst method (BWM), as one of the MCDM methods, for ranking criteria and the fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) for prioritizing the suppliers. Then, the obtained weights are plugged into the model as the inputs of the designed model. A case study with real data in the electronic supply chain is considered. To validate the results obtained by the proposed method, genetic algorithm (GA) and particle swarm optimization (PSO) are leveraged to solve the proposed model. Finally, the efficiency of the designed model is verified through a case study.</p>

The Generalized Risk-Adjusted Cost-Effectiveness (GRACE) Model for Measuring the Value of Gains in Health: An Exact Formulation

AbstractThe generalized risk-adjusted cost-effectiveness (GRACE) analysis method modifies standard cost-effectiveness analysis (CEA), the primary method currently used worldwide to value health improvements arising from healthcare interventions. Generalizing standard CEA, GRACE allows for decreasing or even increasing returns to health. Previous presentations of GRACE have relied extensively on Taylor Series expansion methods to specify key model parameters, including those that properly adjust for illness severity and preexisting disability, consequences of uncertain treatment outcomes, and the marginal rate of substitution between life expectancy and health-related quality of life. Standard CEA cannot account for these sources of value or cost in its valuation of medical treatments. However, calculations of GRACE measures based on Taylor Series are approximations, which may be poorly behaved in some contexts. This paper provides a new approach for implementing GRACE, using exact utility functions instead of Taylor Series approximations. While any proper utility function will suffice, we illustrate with three well-known functions: constant relative risk aversion (CRRA) utility; hyperbolic absolute risk aversion (HARA) utility, of which CRRA is a special case; and expo-power (EP) utility, of which constant absolute risk aversion (CARA) is a special case. The analysis then extends from two-period to multiperiod models. We discuss methods to estimate parameters of HARA and EP functions using two different types of data, one from discrete choice experiments and the other from “happiness economics” methods. We conclude with some reflections on how this analysis might affect benefit-cost analysis studies of healthcare interventions.

An inverse multi-period FDH model with undesirable outputs

In some examinations, the changes in performance measures and the efficiency of entities should be addressed over a span of time despite the undesirable outputs and unsatisfactory convexity property. In this study, the performance of processes is analyzed over several periods of time by presenting a multi-period model based on the free disposal hull (FDH) approach, incorporating undesirable outputs. Using the product of availability, performance (efficiency) and quality, the overall equipment effectiveness (OEE) is calculated which shows the level of productivity. After estimating the performance and OEE, an inverse multi-period FDH model is introduced to measure the input changes for the changes made to outputs in different time periods. The proposed approaches are used in the automotive industry to analyze the performance and changes in input measures over multiple periods of time. The results show that the proposed technique is reasonable for assessing the multi-period efficiency, the period and overall OEE of the systems, and the input changes related to several periods while the convexity assumption is violated.

A Multi-Period Model of an Emissions Trading System

A Multi-Period Model of an Emissions Trading System

Fast Solving Method for Two-Stage Multi-Period Robust Optimization of Active and Reactive Power Coordination in Active Distribution Networks

This paper considers constraints on the cycle number of energy storage systems (ESSs), travel distances of switchable capacitors reactors (SCRs), on load tap changers (OLTCs) and step voltage regulators (SVRs). The characteristics and operational constraints of these equipments are properly formulated with binaries and big-M method, obtaining desirable linear descriptions. The branch flow equations of distribution systems for active and reactive power coordination are constructed. Considering physical constraints, a multi-period mixed-integer deterministic second-order conic programming (SOCP) to minimize network losses is formulated. Then, considering uncertainties of loads and active power of renewable distributed generators (DGs), a two-stage robust model is developed. A directly iteratively solving method between the first and second stage models is proposed. In contrast to the traditional column-and-constraint generation (CCG) method, increases to variables and constraints are not needed to solve the first stage model. To solve the second stage multi-period model, only the model of each single period needs to be solved first. Then their objective function values are accumulated, and the worst scenarios of each period are concatenated. As a result, the solving complexity is greatly reduced. The capabilities of the proposed method are validated by three simulation cases. It is found that the computational rate using the proposed method is significantly enhanced with much less computer storage. Specifically, the simulation results of 4, 33 and 69-bus systems indicate that the computing rate of the proposed method is about 28 times higher than CCG method when 8 iterations are performed. Meanwhile, the precision of optimization results is also improved.

A sustainable network design of a hybrid biomass supply chain by considering the water–energy–carbon nexus

AbstractNowadays, with population growth, rising global energy demand, increasing water consumption, carbon emissions, and excessive use of fossil fuels, the world faces a major challenge. Biomass is one of the most attractive sources of energy production, with positive effects on the economy, environment, and society, which can decrease the world's reliance on fossil fuels and deal with this universal challenge. Consequently, the biomass supply chain network design has received more attention in recent decades. Since energy and water are two significant sources for society's sustainable development and carbon emissions are essential for environmental health, the study of the water–energy–carbon (WEC) nexus is essential. In this study, a multiobjective multiperiod model for designing a sustainable supply chain network based on hybrid second‐generation (i.e., Jatropha, agricultural waste, and animal waste) and third‐generation (i.e., microalgae) biomasses is presented. The proposed multiobjective model consists of five objective functions that maximize the total energy produced and the number of jobs created and minimize the total water consumed, carbon emitted, and total costs. Case study results demonstrate the performance of the model utilizing the MINMAX goal programming approach. Based on the results, energy production from Jatropha is more appropriate in comparison with energy production from microalgae, agriculture waste, and animal waste. The findings also show that the proposed model in this research considering the WEC nexus performs significantly better than the classical model without considering the WEC nexus.