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Due to stochastic demand during the pandemics and uncertain environment, the vendor and the retailer share their risks and benefits by applying revenue sharing and markdown policy in order to reduce the risks and achieve a win-win contract. Three supply chain coordination policies, decentralized policy, centralized vendor-retailer policy and centralized vendor-retailer revenue sharing policy are developed. An example with uniform probability demand is used to illustrate the model. The result shows that the revenue sharing contract is more attractive for the retailer, and the centralized policy is more attractive for the vendor. Therefore, price markdowns are used to share benefits. The sensitivity analysis shows that the number of markdowns is not sensitive to the variances in the uniform demand distribution. A win-win contract based on a revenue sharing and price markdown is developed. A case example shows that the mechanism of price markdowns and revenue sharing contract affect the optimal supply chain profit in view of the pandemics and uncertain environment.

Optimization problems occur in system designs with simulation applications. The decision variables are controllable system parameters of interest and the objective function is a system performance measure that can be estimated via simulation experiments. Using the estimates of objective function values to find the optimal point is called the stochastic optimization problem. The literature of such problems focuses on stochastic approximation. Despite its convergence proof, stochastic approximation may converge slowly if the algorithm parameter values are not well chosen. For practical uses, good algorithms should provide real-time solutions besides guaranteeing convergence. We propose the FDRA algorithm assuming that the objective function is differentiable. FDRA uses the RA-Broyden's algorithm to find the zero of the gradient function, where gradients are estimated by the finite-difference method. In our empirical results, FDRA converges quickly and is robust to its algorithm parameters.

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