Risk Pooling Effect Research Articles

Digital transformation and port operations: Optimal investment under incomplete information

Port digital transformation requires substantial investments. However, the benefits after transformation are difficult to accurately predict due to incomplete information available to ports. Balancing digital investments with benefits poses a key challenge for ports. We propose a game model based on revenue sharing between the port and the technology company to determine the digital level in equilibrium under incomplete information. Our study reveals that the incomplete information influences digital level of ports. When information is incomplete and ambiguous, the digital level of ports may be lower. However, significant ambiguous does not necessarily decrease the digital level due to risk pooling and agent cost effects. Additionally, revenue sharing reduces the incentive for technology company to withhold private information, and specific sharing ratios are identified. The study also finds that under incomplete information, digital level of port initially increases and then decreases with increasing optimism or the ratio of port's retained revenue. By considering these factors, our study provides guidance for ports in optimal investment strategies for digital transformation.

The effects of government subsidy on manufacturers' technology sharing behavior with risk consideration

AbstractThis study focuses on how consumer subsidy (COS) and manufacturer subsidy (MAS) influence a focal risk‐averse manufacturer's technology sharing, who balances between risk pooling effect and competition effect along with new entry for decision. When consumers' uncertain valuations are highly positively (or negatively) correlated for the manufacturers' products, the higher COS and the higher MAS can (or cannot) enhance the manufacturer's technology sharing because the risk pooling effect is strong (or weak), but the competition effect is weak (or strong). Only when the risk pooling effect dominates the competition effect, COS is more conducive than MAS to promoting technology sharing.

Using common redundancy components for suppliers in a supply chain network design problem considering energy costs and environmental effects

Improving the reliability of factories and suppliers through appropriate allocation of redundancy components is crucial in responding to customer demand. However, if individual factories independently buy and allocate redundancy components, huge investments will be required. To optimize the reliability level and costs of the supply chain network, the present study allocates these components to suppliers based on customer demand. While allocating redundancy components to factories improves the chain's reliability, it increases energy consumption and greenhouse gas emissions. Therefore, a balance between cost, reliability, and pollution needs to be established. The study considers a three-level supply chain, including the supplier (factories), distributor, and retailer, with stochastic and normally distributed demand assumed for each retailer. To address demand fluctuations, the risk pooling effect is implemented. As the problem belongs to the class of NP-hard problems, the study develops three multi-objective meta-heuristic algorithms, namely Non-dominated Sorting Genetic Algorithm II (NSGAII), Archived Multi-Objective Simulated Annealing (AMOSA), and Multi-Objective Artificial Bee Colony (MOABC) to solve it. The performance of these algorithms is evaluated using the results of the complete enumeration method. The comparison results based on six multi-objective performance metrics show that the MOABC algorithm has better performance in finding high-quality solutions in less time, while the NSGAII algorithm provides more diverse Pareto optimal solutions.

Multi-location newsvendor problem with random yield: Centralization versus decentralization

We study a multi-location newsvendor problem with an additive or multiplicative random yield assumption. We derive the expected cost and variance of cost under both centralized and decentralized systems. Given the additive random yield, we show that centralization is better than decentralization if demand is deterministic, or demand is uncertain and service level is 0.5. This result is driven by the risk pooling effect, where risk refers to supply risk. Given the multiplicative random yield, we show that decentralization is better than centralization if demand is deterministic. This result is driven by the risk diversification effect, where risk refers to supply risk. Through numerical experiments, we find that in general there is no risk pooling effect nor risk diversification effect if demand is uncertain. Specifically, under additive random yield the cost variance of centralized system can be either higher or lower than the decentralized system. Under multiplicative random yield, centralization is better than decentralization in terms of the expected cost, while decentralization is better than centralization in terms of the cost variance. Both the analytical and numerical results suggest that, when considering supply uncertainty, the comparison between centralization and decentralization highly depends on demand uncertainty.

Variability scaling and capacity planning in Covid-19 pandemic

Capacity planning is a very important global challenge in the face of Covid-19 pandemic. In order to hedge against the fluctuations in the random demand and to take advantage of risk pooling effect, one needs to have a good understanding of the variabilities in the demand of resources. However, Covid-19 predictive models that are widely used in capacity planning typically often predict the mean values of the demands (often through the predictions of the mean values of the confirmed cases and deaths) in both the temporal and spatial dimensions. They seldom provide trustworthy prediction or estimation of demand variabilities, and therefore, are insufficient for proper capacity planning. Motivated by the literature on variability scaling in the areas of physics and biology, we discovered that in the Covid-19 pandemic, both the confirmed cases and deaths exhibit a common variability scaling law between the average of the demand μ and its standard deviation σ, that is, σ∝μβ, where the scaling parameter β is typically in the range of 0.65 to 1, and the scaling law exists in both the temporal and spatial dimensions. Based on the mechanism of contagious diseases, we further build a stylized network model to explain the variability scaling phenomena. We finally provide simple models that may be used for capacity planning in both temporal and spatial dimensions, with only the predicted mean demand values from typical Covid-19 predictive models and the standard deviations of the demands derived from the variability scaling law.

Exploring risk pooling in hospitals to reduce demand and lead time uncertainty

Nearly every eighth German hospital faces an elevated risk of bankruptcy. An inappropriate use of inventory management practices is among the causes. Hospitals suffer from demand and lead time uncertainty, and the current COVID-19 pandemic worsened the plight. The popular business logistics concept of risk pooling has been shown to reduce these uncertainties in industry and trade, but has been neglected as a variability reduction method in healthcare operations research and practice. Based on a survey with 223 German hospitals, this study explores how ten risk pooling methods can be adapted and applied in the healthcare context to reduce economic losses while maintaining a given service level. The results suggest that in general risk pooling may improve the economic situation of hospitals and, in particular, inventory pooling, transshipments, and product substitution for medications and consumer goods are the most effective methods in the healthcare context, while form postponement may be unsuitable for hospitals due to the required efforts, delay in treatments, and liability issues. The application of risk pooling in healthcare requires willingness to exchange information and to cooperate, adequate IT infrastructure, compatibility, adherence to healthcare laws and regulations, and securing the immediate treatment of emergencies. Compared to manufacturing and trading companies, hospitals seem to currently neglect the variability reducing effect of risk pooling.

Designing a resilient and reliable biomass-to-biofuel supply chain under risk pooling and congestion effects and fleet management

The utilization of renewable biomass as feedstock for biofuel production has been gaining prestige to mitigate carbon emissions. This paper aims to render an optimization model for designing a resilient and reliable biomass-to-biofuel supply chain network in which multi-modal terminals, biorefineries, and their connection link could be faced with disruption. For this purpose, risk-averse optimization, transitional probabilities, and spatial statistics models are employed. What is more, to overcome the repercussions of uncertain demand and the availability of raw materials, risk pooling and M/M/1 queuing system are considered. Finally, since the proposed model is an NP-hard problem, two meta-heuristic algorithms called improved ray optimization and colliding bodies optimization are employed to solve the proposed model. Computational results reveal that by increasing 20% of the conversion rate of biomass to biofuel, which leads to increase biomass supply, biofuel production increases by 20.88%, and the SC cost declines by 9.32% due to the better capacity distribution of bio-refineries. Also, the proposed model increases by 20.87% in the total SC costs under random disruptions than the risk-neutral model, although the failure costs of SC decline by 80.45%.

Did the American Recovery and Reinvestment Act help counties most affected by the Great Recession

One of the statements of purpose of the American Recovery and Reinvestment Act (ARRA) was “to assist those most impacted by the recession.” To consider this facet, the grants-in-aid portion of the ARRA is assessed from the perspective of fiscal federalism. We estimate a trend-stationary autoregressive model of county-level wage income dynamics where each county is subject to a common shock (with county-specific factor loading) and an idiosyncratic shock. We then ask if counties that experienced larger negative wage income shocks during the Great Contraction subsequently received more transfers per capita in the form of grants-in-aid. The fact that the negative business cycle shocks pre-date the passage of the ARRA and subsequent disbursements allows identification of the risk-pooling channel of the grants before fiscal multiplier effects confound these two channels. We find statistically significant and economically large risk-pooling effects.

Multi-commodity inventory-location problem with two different review inventory control policies and modular stochastic capacity constraints

In this article, we introduce two novel multi-commodity inventory-location models considering continuous and periodic review inventory control policies and modular stochastic capacity constraints. The models address a logistic problem in which a single plant supplies a set of commodities to warehouses where they serve a set of customers or retailers. The problem consists of determining which warehouses should be opened, which commodities are assigned, and which customers should be served by the located warehouses; as well as their reorder points and order sizes in order to minimize costs of the system while satisfying service level requirements. This problem can be formulated as a mixed-integer nonlinear programming model, which is non-convex in terms of modular stochastic capacity constraints and the objective function. A Lagrangian relaxation and the subgradient method solution approach is proposed. We consider the relaxation of three sets of constraints, including customer assignment, warehouse demand, and variance constraints. Thus, we develop a Lagrangian heuristic to determine a feasible integer solution at each iteration of the subgradient method. An experimental study shows that the proposed algorithm provides good quality gaps and near-optimal solutions in a short time. It also evinces significant impacts of the selected inventory control policy into total costs and network design, including risk pooling effects, when it is compared with different review period values and continuous review.

Role of resource flexibility and responsive pricing in mitigating the uncertainties in production systems

Two effective strategies that mitigate a firm’s demand risk are resource flexibility investment and responsive pricing. In addition to demand uncertainties firms also face capacity uncertainties and capacity disruptions and the effectiveness of these strategies under these risks are less clear. We investigate the value of resource flexibility and responsive pricing under different risk settings for a firm that produces two substitutable products each with its own dedicated resource that can be optionally reconfigured to produce the other product. Reconfiguration or cross-production incurs efficiency loss which can be mitigated by choosing the degree of flexibility of these resources, at a cost, in the planning stage along with capacity levels. In the production stage, after capacities and market potentials are realized, the firm allocates resources and sets prices.We find that under only demand uncertainties the value of flexibility is very low and only a moderate degree of flexibility is sufficient under high demand risk. Responsive pricing is the dominant strategy as the firm avoids investment in costly flexibility. When facing both demand and capacity uncertainties the firm invests in higher levels of flexibility but the value of flexibility is lower than the value of responsive pricing. However, under demand and capacity disruptions flexibility arises as the dominant strategy due to the resource risk pooling effect and the value of flexibility eclipses the value of pricing as the firm invests in full flexibility. For a firm with responsive pricing investment in flexibility is economically justified under high capacity uncertainties and capacity disruptions.

Did the American Recovery and Reinvestment Act Help Counties Most Affected by the Great Recession?

One of the statements of purpose of the American Recovery and Reinvestment Act (ARRA) was “to assist those most impacted by the recession.” To consider this facet, the grants-in-aid portion of the ARRA is assessed from the perspective of fiscal federalism. We estimate a trend-stationary autoregressive model of county-level wage income dynamics where each county is subject to a common shock (with county-specific factor loading) and an idiosyncratic shock. We then ask if counties that experienced larger negative wage income shocks during the Great Contraction subsequently received more transfers per capita in the form of grants-in-aid. The fact that the negative business cycle shocks pre-date the passage of the ARRA and subsequent disbursements allows identification of the risk-pooling channel of the grants before fiscal multiplier effects confound these two channels. We find statistically significant and economically large risk-pooling effects.

Overcommitment in Cloud Services: Bin Packing with Chance Constraints

This paper considers a traditional problem of resource allocation: scheduling jobs on machines. One such recent application is cloud computing; jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, that is, selling resources beyond capacity. Setting the right overcommitment level can yield a significant cost reduction for the cloud provider while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint to a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement, and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services and suggest a cost reduction of 1.5% to 17%, depending on the provider’s risk tolerance. The online appendices are available at https://doi.org/10.1287/mnsc.2018.3091 . This paper was accepted by Yinyu Ye, optimization.

Impact of Auto-regressive (AR) Process in Bullwhip Analysis in a Multi-location Supply Chain Network

The present study is an attempt to quantify the Bullwhip Effect (BWE) -the phenomenon in which information on demand is distorted in moving up a supply chain. Assuming that the retailer employs an order-up-to level policy with auto-regressive process (AR), the paper investigates the influence of forecasting methods on bullwhip effect. Determining the order-up-to levels and the orders for the retailers’ demands in an isolated manner neglects the correlation of the demands and the relevant risk pooling effects associated with the network structure of the supply chains are disregarded. It is illustrated that the bullwhip effects are significantly reduced with consideration of potential correlation between the retailers’ demand.

Risk pooling through physical probabilistic selling

This paper investigates the impacts of a new type of probabilistic selling (PS) where the retailer orders specific products and package some as a discounted physical probabilistic product (PPP) rather than merely a virtual choice. We call this PS strategy as physical probabilistic selling (PPS). The price gap between the specific products and the probabilistic product results in demand reshape, i.e., some customers who originally buy specific products will switch to buying the probabilistic product, which decreases aggregate demand uncertainty. However, the price discount decreases the profit margin. Considering this trade-off, we develop a three-product newsvendor model to address the question of how to set the price for the PPP and make inventory allocation decisions. We prove that there are two effects under PPS, namely the risk pooling effect due to demand reshape and the risk diversification effect due to inventory flexibility. With demand uncertainty, PPS can improve the retailer's profit at lower inventory levels with proper demand reshape induced by the optimal price discount. PPS is more profitable with smaller product differentiation, higher customer price sensitivity, higher demand uncertainty, and lower package cost. With supply uncertainty, we demonstrate through numerical studies that PPS is a viable strategy to combat asymmetrical supply risk that yields higher profits and service levels.

Capturing the Risk-Pooling Effect through Inventory Planning and Demand Switching

This paper demonstrates how firms can deal with demand uncertainty through inventory planning and demand switching, which take advantage of the risk-pooling effect and contribute to supply-chain sustainability. Considering two types of products and two outsourcing strategies (competitive bidding, and consignment stock under the (Q, R) inventory policy with variable lead times), the study helps determine the appropriate outsourcing strategy when a firm practices demand switching. Under certain conditions, the study further identifies the proper demand-switching direction and optimum switching-rate to achieve the minimum total purchase and inventory costs in association with outsourcing. Prior research generally implies that demand switching increases costs or profit benefits. This implication, however, does not hold true in the present context. The study presents numerical examples to illustrate the derived models. The findings enrich the extant literature by incorporating demand switching into the outsourcing practices, which is beneficial to both practitioners and scholars.

Designing a bio-fuel network considering links reliability and risk-pooling effect in bio-refineries

Bio-fuel is one of the most important alternatives to fossil fuels due to energy shortages. The bio-fuel is derived from biomass that is obtained from agricultural products such as plant debris. In addition, the supply chain is affected by risks which are due to several reasons such as economic, natural phenomena, political and etc. The occurrence of such events can cause disruption in supply chain which can significantly increase the total supply chain costs and also prevent serve to customers. Reliability is involved the capability of a network to achieve an anticipated process such as ``communication". Analysis of network reliability has acknowledged significant consideration and is consequently broadly studied to forecast and avoid any network failure. In order to distribute bio-fuel to the customers, designing a reliable and sustainable bio-fuel supply chain is very importance. Thus a growth in bio-fuel production demonstrates the requirement for establishing an effective and reliable network of chain that not only accomplishes sound under regular circumstances nevertheless restricted risk under various unanticipated disruption situations. This paper presents mathematical model to design an efficient bio-fuel supply chain network at pre-disaster stage that considering failure in the connecting links between the facilities. In which the probability of failure of the links is forecasted by a spatial statistic approach and also due to the fact that disasters can cause disruptions in bio-refineries, leads to use the risk-pooling effect in order to reduce total costs. In order to solve the proposed mathematical model, two meta-heuristic algorithms containing genetic algorithm (GA) and bat algorithm (BA) are utilized. The results show that by increasing the reliability and improvement of connecting links between facilities and considering the risk-pooling effect on disrupted bio-refineries, the total costs of supply chain can be considerably reduced.

The fundamental theorem of mutual insurance

The essence of mutual insurance is the notion that re-distributing risk in a pool of risks is more beneficial than taking the risk alone. Interpreting ‘more beneficial’ as an increase in utility and considering sequences of exchangeable risks, we are able to formalize this notion from the policyholder’s perspective and demonstrate its validity for various alternative preference functionals (e.g., expected utility, Choquet expected utility, and distortion risk measures). To obtain this result, we exploit that for a sequence of exchangeable risks the corresponding sequence of arithmetical averages is a reversed martingale.We conclude that pooling risks is fundamental for understanding the mechanisms of insurance because it favourably affects the utility of policyholders, and we refer to this phenomenon as the ‘utility-improving effect of risk pooling’. Moreover, we demonstrate that the utility of the policyholder is (strictly) increasing with the size of the risk pool.

Overcommitment in Cloud Services Bin packing with Chance Constraints

This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy , i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the provider's risk tolerance.

Efficient formulations for dynamic warehouse location under discrete transportation costs

A Mixed-integer Linear Programming model is proposed to determine the optimal number, location and capacity of the warehouses required to support a long-term forecast with seasonal demand. Discrete transportation costs, dynamic warehouse contracting, and the handling of safety stock are the three main distinctive features of the problem. Four alternatives for addressing discrete transportation costs are compared. The most efficient formulation is obtained using integer variables to account for the number of units used of each transportation mode. Contracting policies constraints are derived to ensure use of warehouses for continuous periods. Similar constraints are included for the case when a warehouse is closed. Safety stock with risk-pooling effect is considered using a piecewise-linear representation. To solve large-scale problems, tightening constraints, and simplified formulations are proposed. These formulations are based on single-sourcing assumptions and yield near-optimal results with large reduction in the solution time.

On multivariate countermonotonic copulas and their actuarial application

Extreme positive dependence, also known as comonotonicity or the Frechet upper bound, has been an important concept in insurance since it describes the most dangerous financial behaviors. However, there is no generally agreed upon definition for extreme negative dependence because the corresponding Frechet lower bound does not exist. To resolve this, a set of copulas under the name of d-Countermonotonicity (d-CTM) has been proposed to define extreme negative dependence rather than a single copula. The set of d-CTM copulas can be quite useful in various optimization problems. In this paper, we investigate various properties of d-CTM with more emphasis on the practical issues of actual optimization problems. As an application to insurance, we explore the effect of risk pooling under extreme dependence by adopting the so-called measure of uncertainty.