A model of supply-chain decisions for resource sharing with an application to ventilator allocation to combat COVID-19

We present a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory for a central agency are to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse condition. The model is applied to study the allocation of ventilator inventory in the COVID-19 pandemic by FEMA to different U.S. states. Findings suggest that if less than 60% of the ventilator inventory is available for non-COVID-19 patients, FEMA's stockpile of 20 000 ventilators (as of March 23, 2020) would be nearly adequate to meet the projected needs in slightly above average demand scenarios. However, when more than 75% of the available ventilator inventory must be reserved for non-COVID-19 patients, various degrees of shortfall are expected. In a severe case, where the demand is concentrated in the top-most quartile of the forecast confidence interval and states are not willing to share their stockpile of ventilators, the total shortfall over the planning horizon (until May 31, 2020) is about 232 000 ventilator days, with a peak shortfall of 17 200 ventilators on April 19, 2020. Results are also reported for a worst-case where the demand is at the upper limit of the 95% confidence interval. An important finding of this study is that a central agency (FEMA) can act as a coordinator for sharing critical resources that are in short supply over time to add efficiency in the system. Moreover, through properly managing risk-aversion of different entities (states) additional efficiency can be gained. An additional implication is that ramping up production early in the planning cycle allows to reduce shortfall significantly. An optimal timing of this production ramp-up consideration can be based on a cost-benefit analysis.     

Experimental and numerical study of the blast wave decrease using sandwich panel by granular materials core

Among the intrinsic properties of some materials, e.g., foams, porous materials, and granular materials, are their ability to mitigate shock waves. This paper investigated shock wave mitigation by a sandwich panel with a granular core. Numerical simulations and experimental tests were performed using Autodyn hydro-code software and a shock tube, respectively. The smoothed particle hydrodynamics (SPH) method was used to model granular materials. Sawdust and pumice, whose properties were determined by several compression tests, were used as granular materials in the sandwich panel core. These granular materials possess many mechanisms, including compacting (e.g., sawdust) and crushing (e.g., pumice) that mitigate shock/blast wave. The results indicated the ineffectiveness of using a core with low thickness, yet it was demonstrated to be effective with high thickness. Low-thickness pumice yielded better results for wave mitigation. The use of these materials with a core with appropriate core reduces up to 88% of the shock wave. The results of the experiments and numerical simulations were compared, suggesting a good agreement between the two. This indicates the accuracy of simulation and the ability of the SPH method to modeling granular material under shock loading. The effects of grain size and the coefficient of friction between grains have also been investigated using simulation, implying that increasing the grain size and coefficient of friction between grains both reduce overpressure.     

Bending and stress analysis of polymeric composite plates reinforced with functionally graded graphene platelets based on sinusoidal shear-deformation plate theory

The bending and stress analysis of a functionally graded polymer composite plate reinforced with gra-phene platelets are studied in this paper. The governing equations are derived by using principle of virtual work for a plate which is rested on Pasternak's foundation. Sinusoidal shear deformation theory is used to describe displacementfield. Four different distribution patterns are employed in our analysis. The analytical solution is presented for a functionally graded plate to investigate the influence of important parameters. The numerical results are presented to show the deflection and stress results of the problem for four employed patterns in terms of geometric parameters such as number of layers, weight fraction and two parameters of Pasternak's foundation.     

Oligopolistic contracting: Channel coordination under competition

We study contracts between a single retailer and multiple suppliers of two substitutable products, where suppliers have fixed capacities and present the retailer cost contracts for their supplies. After observing the contracts, the retailer decides how much capacity to purchase from each supplier, to maximize profits from the purchased capacity from the suppliers plus his possessed inventory (endowment). This is modeled as a noncooperative, nonzero‐sum game, where suppliers, or principals, move simultaneously as leaders and the retailer, the common agent, is the sole follower. We are interested in the form of the contracts in equilibrium, their effect on the total supply chain profit, and how the profit is split between the suppliers and the retailer. Under mild assumptions, we characterize the set of all equilibrium contracts and discuss all‐unit and marginal‐unit quantity discounts as special cases. We also show that the supply chain is coordinated in equilibrium with a unique profit split between the retailer and the suppliers. Each supplier's profit is equal to the marginal contribution of her capacity to supply chain profits in equilibrium. The retailer's profit is equal to the total revenue collected from the market minus the payments to the suppliers and the associated sales costs.