Multi-period Setting Research Articles

Capacitated Mobile Facility Location Problem with Mobile Demand: Efficient Relief Aid Provision to En Route Refugees

As a humanity crisis, the tragedy of forced displacement entails relief aid distribution efforts among en route refugees to alleviate their migration hardships. This study aims to assist humanitarian organizations in cost-efficiently optimizing the logistics of capacitated mobile facilities utilized to deliver relief aid to transiting refugees in a multi-period setting. The problem is referred to as the Capacitated Mobile Facility Location Problem with Mobile Demands (CMFLP-MD). In CMFLP-MD, refugee groups follow specific paths, and meanwhile, they receive relief aid at least once every fixed number of consecutive periods, maintaining continuity of service. To this end, the overall costs associated with capacitated mobile facilities, including fixed, service provision, and relocation costs, are minimized. We formulate a mixed integer linear programming (MILP) model and propose two solution methods to solve this complex problem: an accelerated Benders decomposition approach as an exact solution method and a matheuristic algorithm that relies on an enhanced fix-and-optimize agenda. We evaluate our methodologies by designing realistic instances based on the Honduras migration crisis that commenced in 2018. Our numerical results reveal that the accelerated Benders decomposition excels MILP with a 46% run time improvement on average while acquiring solutions at least as good as the MILP across all instances. Moreover, our matheuristic acquires high-quality solutions with a 2.4% average gap compared to best-incumbents rapidly. An in-depth exploration of the solution properties underscores the robustness of our relief distribution plans under varying migration circumstances. Across several metrics, our sensitivity analyses also highlight the managerial advantages of implementing CMFLP-MD solutions.

Managing Hybrid Manufacturing/Remanufacturing Inventory Systems With Random Production Capacities

In this article, we consider hybrid manufacturing/remanufacturing inventory systems that produce a single product to satisfy demands over a finite planning horizon. In each period, the firm receives random demand and returns of end-of-life products. A serviceable product can be manufactured from ample raw materials or remanufactured from a returned product. The two operations possess random dedicated capacities. The firm’s objective is to minimize the expected total discounted cost over the planning horizon. We partially characterize the firm’s optimal inventory policy when the two capacities are positively dependent and completely characterize it when only one capacity is random. When there is ample manufacturing capacity, we connect the model with an auxiliary dual-sourcing inventory model and derive a more detailed structure of the optimal policy. Finally, our numerical study provides actionable insights into the effects of random capacities. Among others, we find that approximating a slightly/moderately variable remanufacturing capacity as its deterministic mean capacity or ignoring the correlation between two random capacities under a multi-period setting incurs a limited cost to the firm.

Intertemporal Price Competition in the Two-Sided Market: Reexamining the Seesaw Principle for Startup Platforms

Pricing represents a crucial element in the platform business model search, particularly for startups that face the “cold-start” problem in launching a two-sided marketplace. In a static setting, the literature recommends the “seesaw principle” (i.e., charging a relatively low price, even subsidizing, on the one side and a high price on the other) as the solution. However, little is known about whether the seesaw principle still works in a dynamic setting and how it is influenced by intertemporal factors such as retention capabilities and early period financial pressure. This paper develops a game-theoretic model to examine optimal pricing strategies in a multiperiod setting. We first show that, in the symmetric scenario, the adjustment to the seesaw principle (i.e., the difference between the single- and multiperiod price gaps) increases with the platforms’ retention rate. This insight holds true in the asymmetric case where a startup platform faces greater early period financial pressure than an established competitor. Interestingly, the startup platform should charge a higher price to the less profitable side to differentiate itself and avoid a price war. We also explore the robustness of these insights by considering an endogenous, price-sensitive retention rate.

A multi-marginal c-convex duality theorem for martingale optimal transport

A convex duality result for martingale optimal transport problems with two marginals was established in Beiglböck et al. (2013). In this paper we provide a generalization of this result to the multi-period setting.

Integrated inventory replenishment and online demand allocation decisions for an omnichannel retailer with ship-from-store strategy

Retailing has changed dramatically from single-channel brick-and-mortar stores to multi-channel and omnichannel retailers over the last few decades. Omnichannel retailers employ different strategies to integrate online and offline sales channels as well as order fulfillment processes. Among these strategies, the ship-from-store is the most popular and widely accepted among retailers. It enables retailers to use inventory from store locations to fulfill online demand. An omnichannel retailer with a distribution center and a retail store has to make important, interlinked decisions — (1) how much inventory to keep at the retail store, and (2) where to fulfill the online demand from and how much. In this work, we model the integrated inventory replenishment and online demand allocation decisions for an omnichannel retailer employing the ship-from-store strategy. We analyze this problem for both single-period and multi-period settings. We extend the analytical framework of the single-period problem by providing a finite-horizon Markov decision process (MDP) formulation for the multi-period problem. Our findings suggest that for a single-period setting, decentralized inventory replenishment and demand allocation system maximizes the profit of the omnichannel retailer for low values of the incentive for fulfilling the online demand through store inventory, while for sufficiently high values of the incentive, a pooled system provides the optimal profit. An increment in the discount factor has the same effect on the optimal decisions in a multi-period setting as that of salvage value in a single-period setting for a given value of the incentive for the ship-from-store strategy. We also provide several extensions (such as cross selling, endogenous and correlated demand streams) of our analytical framework for the multi-period problem.

Managing Home Health-Care Services With Dynamic Arrivals During a Public Health Emergency

We consider a public health emergency, during which a high number of patients and their varying health conditions necessitate prioritizing patients receiving home health care. Moreover, the dynamic emergence of patients needing urgent care during the day should be handled by rescheduling these patients. In this article, we present a reoptimization framework for this dynamic problem to periodically determine which patients will be visited in which order on each day to maximize the total priority of visited patients and to minimize the overtime for the health-care provider. This optimization framework also aims to minimize total routing time. A mixed-integer programming (MIP) model is formulated and solved at predetermined reoptimization times, to assure that urgent patients are visited within the current day, while visits of others may be postponed, if overtime is not desired or limited. The effectiveness of a schedule is evaluated with respect to several performance metrics, such as the number of patients whose visits are postponed to the next day, waiting time of urgent patients, and required overtime. The MIP-based approach is compared to two practical heuristics that achieve satisfactory performance under a nervous service system by excelling in different criteria. The MIP-based reoptimization approach is demonstrated for a case during the COVID-19 pandemic. We contribute to the home health-care literature by managing dynamic/urgent patient arrivals under a multiperiod setting with prioritized patients, where we optimize different rescheduling objectives via three alternative reoptimization approaches.

Locating hydrogen fuel stations: A comparative study for Istanbul

World’s energy sources are depleting while the need for alternative energy resources is increasing. Hydrogen energy is an essential alternative and its use in transportation sector through Hydrogen Fuel Cell Vehicles (HFCV) is increasing day by day. For HFCV to become widely used, however, it is necessary to establish a good infrastructure, i.e., hydrogen should be accessible. In this study, we investigate the problem of locating Hydrogen Refueling Stations (HRS) in İstanbul, the most crowded city of Turkey. The problem is addressed with multi-period set covering model and the different population densities in the city are integrated with a modification of this model. Due to the long computational time required by the multi-period set-covering model, two heuristics, namely the iterative model and the reduced model, are proposed. The results indicate that for a geographically distinct city like İstanbul, using Euclidean distance may yield very drastic conclusions, hence should be avoided. It is also shown that the HRS are densely located in areas with high population, and one should trade-off between the total distance to be travelled by the drivers and being served by one of the closest stations. In a multi-period setting where stations are opened incrementally, the findings from two different heuristics favor different stakeholders: the iterative model offers advantages from the perspective of decision-makers, while the multi-period model with an optimality gap is advantageous from the perspective of customers. We also introduce the partial coverage model, which serves as a combination of set covering and p-median models, to analyze the transition if the demand is fulfilled incrementally, not completely. It turns out that less number of stations are sufficient to meet high demand, but the number increases significantly if all demand should be satisfied.

Social contagion and the survival of diverse investment styles

We examine the contagion of investment ideas in a multiperiod setting in which investors are more likely to transmit their ideas to other investors after experiencing higher payoffs in one of two investment styles with different return distributions. We show that heterogeneous investment styles are able to coexist in the long run, implying a greater diversity than predicted by traditional theory. We characterize the survival and popularity of styles in relation to the distribution of security returns. In addition, we demonstrate that psychological effects such as conformist preference can lead to oscillations and bubbles in the choice of style. These results remain robust under a wide class of replication rules and endogenous returns. They offer empirically testable predictions, and provide new insights into the persistence of the wide range of investment strategies used by individual investors, hedge funds, and other professional portfolio managers.

A First “Stab” at Defining Temporal Flexibility-to-Cost Mapping

Despite the myriad of techniques for calculating flexibility envelopes in buildings and power grids, their analytical monetization has received practically zero attention. This obscure issue reaches even more unknown depths in the multi-period (MP) setting, where intertemporality hinders the design of a clear pricing framework. This letter builds on the author's previous work, which proposed a novel methodology for the one-to-one flexibility-to-cost mapping in grid-friendly smart sustainable buildings (GF-SSBs), and discusses alternatives for mapping MP flexibility envelope to costs in practice. Their comparison provides key insights into how different cost structures may affect end-user behavior and the grid's ability to procure flexibility. This letter hopes to kick-start the discussion around “fair” or intrinsic flexibility value, an issue that has largely been sidelined.

COVID-19: Agent-based simulation-optimization to vaccine center location vaccine allocation problem

This article presents an agent-based simulation-optimization modeling and algorithmic framework to determine the optimal vaccine center location and vaccine allocation strategies under budget constraints during an epidemic outbreak. Both simulation and optimization models incorporate population health dynamics, such as susceptible (S), vaccinated (V), infected (I) and recovered (R), while their integrated utilization focuses on the COVID-19 vaccine allocation challenges. We first formulate a dynamic location–allocation Mixed-Integer Programming (MIP) model, which determines the optimal vaccination center locations and vaccines allocated to vaccination centers, pharmacies, and health centers in a multi-period setting in each region over a geographical location. We then extend the agent-based epidemiological simulation model of COVID-19 (Covasim) by adding new vaccination compartments representing people who take the first vaccine shot and the first two shots. The Covasim involves complex disease transmission contact networks, including households, schools, and workplaces, and demographics, such as age-based disease transmission parameters. We combine the extended Covasim with the vaccination center location-allocation MIP model into one single simulation-optimization framework, which works iteratively forward and backward in time to determine the optimal vaccine allocation under varying disease dynamics. The agent-based simulation captures the inherent uncertainty in disease progression and forecasts the refined number of susceptible individuals and infections for the current time period to be used as an input into the optimization. We calibrate, validate, and test our simulation-optimization vaccine allocation model using the COVID-19 data and vaccine distribution case study in New Jersey. The resulting insights support ongoing mass vaccination efforts to mitigate the impact of the pandemic on public health, while the simulation-optimization algorithmic framework could be generalized for other epidemics.

The Impact of Product-Dependent Policyholder Risk Sensitivities in Life Insurance: Insights from Experiments and Model-Based Simulation Analyses

Abstract In contrast to previous work, this paper studies the product-dependent risk sensitivities of policyholders toward the reported safety levels of a life insurer in a long-term multi-period setting. With this aim, we first conduct two choice-based conjoint analyses using a German survey panel to investigate the effect of an insurer’s reported default probability on individuals’ willingness to pay for annuities and term life insurances. Our experimental results suggest that individuals (sharply) reduce their willingness to pay for probabilistic life insurance products, with (strong) product-specific differences. In light of these observations, the paper then revisits the impact of these differing risk sensitivities on a life insurer’s risk situation in a simulation study based on an asset-liability model with a specific focus on a life insurer offering annuities and term life insurances. The results reveal the potentially strong impact of such product-dependent risk sensitivities on risk-reducing portfolio compositions. One main driver is the deviation between risk sensitivities depending on the respective product (annuities vs. term life).

Revenue-sharing and volume flexibility in the supply chain

We model capacity choice and utilization of a manufacturer selling products through a retailer under a revenue sharing contract. We derive the optimal revenue sharing contract which internalizes the impact on capacity, utilization choice and the final downstream price of the product and provide a valuation of the retailer and supplier under uncertainty in a multiperiod setting. In extensions of this framework, we analyze constraints on minimum delivered quantities and also build a finite-time numerical method that considers an abandonment option for the supplier and hold-up problems for the retailer, as well as the supplier's option to expand capacity. Our model predicts higher revenue sharing ratios charged by retailers when suppliers operate in more volatile upstream markets, when the product is a necessity rather than a luxury good and when retailers can impose minimum delivered quantities. On the contrary, we find that suppliers will be able to obtain a higher revenue share when operating in industries with high fixed costs and for contracts of shorter horizon since hold-up problems for retailers increase and the retailer has to provide more incentives to suppliers not to abandon operations. The option to expand capacity benefits more significantly the supplier compared to the retailer. Finally, we consider the decisions of a vertically integrated firm showing the gains from vertical integration and demonstrating that the optimum vertically coordinated production can be achieved in the decentralized multiperiod setup through a combination of a fee per product and revenue sharing.

Manage Inventories with Learning on Demands and Buy-up Substitution Probability

Problem Definition: This paper considers a setting in which an airline company sells seats periodically, and each period consists of two selling phases, an early-bird discount phase and a regular-price phase. In each period, when the early-bird discount seat is stocked out, an early-bird customer who comes for the discounted seat either purchases the regular-price seat as a substitute (called buy-up substitution) or simply leaves. Methodology/Results: The optimal inventory level of the discounted seats reserved for the early-bird sale is a critical decision for the airline company to maximize its revenue. The airline company learns about the demands for both discounted and regular-price seats and the buy-up substitution probability from historical sales data, which, in turn, are affected by past inventory allocation decisions. In this paper, we investigate two information scenarios based on whether lost sales are observable, and we provide the corresponding Bayesian updating mechanism for learning about demand parameters and substitution probability. We then construct a dynamic programming model to derive the Bayesian optimal inventory level decisions in a multiperiod setting. The literature finds that the unobservability of lost sales drives the inventory manager to stock more (i.e., the Bayesian optimal inventory level should be kept higher than the myopic inventory level) to observe and learn more about demand distributions. Here, we show that when the buy-up substitution probability is known, one may stock less, because one can infer some information about the primary demand for the discounted seat from the customer substitution behavior. We also find that to learn about the unknown buy-up substitution probability drives the inventory manager to stock less so as to induce more substitution trials. Finally, we develop a SoftMax algorithm to solve our dynamic programming problem. We show that the obtained stock more (less) result can be utilized to speed up the convergence of the algorithm to the optimal solution. Managerial Implications: Our results shed light on the airline seat protection level decision with learning about demand parameters and buy-up substitution probability. Compared with myopic optimization, Bayesian inventory decisions that consider the exploration-exploitation tradeoff can avoid getting stuck in local optima and improve the revenue. We also identify new driving forces behind the stock more (less) result that complement the Bayesian inventory management literature. Funding: Z. Luo acknowledges the financial support by the Internal Start-up Fund of The Hong Kong Polytechnic University [Grant P0039035]. P. Guo acknowledges the financial support from the Research Grants Council of Hong Kong [Grant 15508518]. Y. Wang’s work was supported by the Research Grants Council of Hong Kong [Grant 15505318] and the National Natural Science Foundation of China [Grant 71971184]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.1169 .

The value of adaptive menu sizes in peer-to-peer platforms

We consider a peer-to-peer logistics system, where the agents and the platform communicate in both directions in a multi-period setting. The goal of the platform is to select a subset of the requests to offer to each agent that would result in a maximum valued matching for the platform. The platform utilizes the agent’s choice to learn about her preferences and improve the estimated decision mechanism of the agent. Through systematic experimentation, we first establish that at the earlier iterations and while the decision mechanism of the agent is not yet accurately estimated, a larger menu size could benefit the platform’s overall gain better. However, after the estimates become more accurate through the learning process, a smaller menu size can further increase the overall benefits.

Two-stage nested simulation of tail risk measurement: A likelihood ratio approach

Estimating tail risk measures is an important task in many financial and actuarial applications and often requires nested simulations, with the outer simulations representing real world scenarios, and the inner simulations typically used for risk neutral pricing or conditional risk measurement. The standard nested simulation method is highly flexible, able to incorporate complex asset models and exotic payoff structures, but it is also computationally highly burdensome, particularly in a multi-period setting, when inner simulation paths are required at each time step of each outer level scenario. In this study, we propose and analyze a two-stage simulation procedure that efficiently estimates the conditional tail expectation of cost of a dynamic hedging program for a Variable Annuity Guaranteed Minimum Withdrawal Benefit (GMWB), under a multi-period nested simulation. In each of the two stages, the method re-uses the same set of inner level simulation paths for each outer scenario at each time point, using a likelihood ratio method to re-weight the probabilities of each individual path for the different outer scenarios. Our numerical study shows that our two-stage, likelihood ratio weighted procedure can offer a very significant improvement in efficiency, of the order of 95% as measured by the RMSE, compared with a standard nested simulation with the same computational cost.

The two-echelon stochastic multi-period capacitated location-routing problem

Given the emergence of two-echelon distribution systems in several practical contexts, this paper tackles, at the strategic level, a distribution network design problem under uncertainty. This problem is defined as the two-echelon stochastic multi-period capacitated location-routing problem (2E-SM-CLRP). It considers a network partitioned into two capacitated distribution echelons: each echelon involves a specific location-assignment-transportation schema that must cope with the future demand. It aims to decide the number and location of warehousing/storage platforms (WPs) and distribution/fulfillment platforms (DPs), and on the capacity allocated from first echelon to second echelon platforms. In the second echelon, the goal is to construct vehicle routes that visit ship-to locations (SLs) from operating distribution platforms under a stochastic and time-varying demand and varying costs. This problem is modeled as a two-stage stochastic program with integer recourse, where the first-stage includes location and capacity decisions to be fixed at each period over the planning horizon, while routing decisions of the second echelon are determined in the recourse problem. We propose a logic-based Benders decomposition approach to solve this model. In the proposed approach, the location and capacity decisions are taken by solving the Benders master problem. After these first-stage decisions are fixed, the resulting sub-problem is a capacitated vehicle-routing problem with capacitated multiple depots (CVRP-CMD) that is solved by a branch-cut-and-price algorithm. Computational experiments show that instances of realistic size can be solved optimally within a reasonable time and provide relevant managerial insights on the impact of the stochastic and multi-period settings on the 2E-CLRP.

The Implications of Strategic Inventory for Short-Term vs. Long-Term Supply Contracts in Nonexclusive Reselling Environments

Problem definition: Although it is well known that a reseller’s ability to hold strategic inventory under a short-term supply contract can potentially benefit both the reseller and a supplier, existing research on strategic inventory focuses almost exclusively on exclusive reselling environments. However, in practice, multiple suppliers often sell to the same nonexclusive reseller, and it is not uncommon for suppliers to ask for future commitments to order quantities from resellers in return for their own commitment to wholesale prices. We investigate how the possibility of strategic inventory influences competing suppliers’ choices between short-term transactional and long-term commitment contracts to a nonexclusive reseller. Methodology/results: Using a game-theoretic model, we consider the interactions between two partially substitutable suppliers and a single, nonexclusive reseller over a two-period horizon in which demand is deterministic. We demonstrate that in nonexclusive reselling environments, where more than one supplier sells its product through the same reseller, the use of strategic inventory under short-term contracts intensifies the price competition between suppliers. We show how this effect can be mitigated when one or both suppliers offer a long-term contract. Moreover, we show that long-term contracts can arise as an equilibrium outcome, particularly when products are more substitutable or holding costs are large. Managerial implications: By considering the interactions between two partially substitutable suppliers and a nonexclusive reseller in a multiperiod setting, we contribute to the literature on strategic contracting and long versus short-term contracts. Our research provides managers with a new explanation, beyond the need to encourage idiosyncratic investments or eliminate the possibility of hold-up, for why long-term contracts may benefit suppliers in practice, who face competition while selling through a nonexclusive reseller.

Tele-medicine question response service: Analysis of benefits and costs

Medicare and other healthcare payers are increasing reimbursement for tele-monitoring with in-home devices, but have not expanded reimbursement to include tele-medicine question response services. We model the costs and benefits of providing these services in a multi-period setting for healthcare payers and providers compared to a central planner baseline model. We also consider how patients’ risk level and potentially shorter skilled nursing facility stays can increase the benefit of these services. While many payers worry that reimbursing for question response services will cause excessive payouts, we find that payers would benefit from providing a per-call subsidy to providers to incentivize optimal question response service staffing levels. We also find that payers could provide a per-patient subsidy for patients discharged early from skilled nursing facilities that would more than cover the costs of providing the question response service for all patients. These models are grounded in data and multiple discussions with regional home health providers that provide these question response services.

Multi-period green reverse logistics network design: An improved Benders-decomposition-based heuristic approach

There has been extensive academic research on the optimisation of reverse logistics (RL) and closed-loop supply chain (CLSC) network design. However, the existing literature is lacking in several features of practical relevance, and the simultaneous consideration of dynamic characteristics, including the multi-period setting, inventory factors, environmental footprints, and scalability of the application. This shortcoming is primarily due to the challenges associated with computation complexity, mathematical formulation, and the need for a faster solution method to solve such large-scale problems in real-time. In this research, we address these challenges and investigate the multi-facility green RL network design problem, integrating carbon footprint and vehicle selection, entailing allocation between the facilities in the multi-period setting to incorporate the dynamic characteristics. We formulate a mixed-integer linear programming (MILP) model to minimise the total cost, comprising the carbon emission cost due to transport and production at the facilities. We also investigate the effects of carbon emissions and the choice of the vehicle fleet on the network's structure. The novelty of our research lies in the development and application of an exact solution method, namely “Improved Benders Decomposition (IBD)” with several algorithmic enhancements, including a strengthened master problem, valid inequalities, a heuristic, and a multi-stage strategy to accelerate the convergence of the Benders decomposition method. By combining these elements, the proposed IBD solves the MILP model, provides a faster solution methodology with improved convergence of the bounds, and addresses the inherent intractability of the existing problem. We apply our proposed heuristic on a set of 12 problem configurations under distinct scenarios. We show that the proposed IBD heuristic outperforms existing traditional methods in terms of solution quality, computational time, and robustness.

Rent, sell, and remanufacture: The manufacturer's choice when remanufacturing can be outsourced

Manufacturers have increasingly started offering rental options for the products they sell. Renting products offers an opportunity: segmenting consumers. However, this also raises a challenge: what to do with the returned products? One solution is to remanufacture these products and then rent or resell them. Subsequently, should remanufacturing be outsourced to a third-party firm that can remanufacture at a lower cost? Here, we use a multi-period setting and examine the optimal decisions for different selling and renting constellations. Importantly, we allow the manufacturing costs of the sales and rental products to differ, as they seem to be critical in determining the manufacturer's renting and selling decisions and remanufacturing strategies. For example, under integrated (i.e. in-house) remanufacturing, when the new rental product's manufacturing cost is sufficiently high, no remanufacturing happens. Under both remanufacturing strategies—integrated and outsourced—the manufacturer does not rent new products in the second period if the manufacturing costs of the sales and rental products are identical. If the rental product's manufacturing cost is either sufficiently low or high, then integrated remanufacturing is more profitable; when this manufacturing cost is within a moderate range, the manufacturer outsources remanufacturing to an independent remanufacturer. Surprisingly, in some situations, the production quantity of the new sales product may even increase with its manufacturing cost. This is because the manufacturer may extract an even higher margin compared with the new rental product. Finally, we also consider several extensions such as uncertainty regarding the quality of the returned goods, simultaneous selling and renting of remanufactured goods, and longer horizons and the product's life cycle.