Dual Bounds for Periodical Stochastic Programs

A construction of the dual of a periodical formulation of infinite-horizon linear stochastic programs with a discount factor is discussed. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound, especially when the discount factor is close to one.

Simulation Model to Reduce the Traffic Jams with a Stochastic Program

Traffic congestion needs a simulation model to reduce its effects on traffics jams and pollution. The traffic cessation caused by the large number of vehicles exceeding the capacity of the road users. This study applied a stochastic program to the traffic congestion; it causes most of the working hours to be spent on roads that indirectly place a negative impact on economic growth. It also causes serious air pollution that will worsen the overall environmental condition. Data obtained show the factors causing traffic congestion in the city of Medan and with approach the stochastic program model used to solve this problem. Data indicated that there are four factors causing traffic congestion in Medan, which are non-growth of road, economic growth, population growth, and increase of motor vehicle.Population factor; the existence of good population growth caused by natural and migration growth. It concludes that the traffic jams are due to the socio-economic factors; namely the development of community business activities. Also socio-cultural factors; the existence of changes in the pattern of life and public order due to outside influences, communication, and information systems.

Distributionally Robust Optimization with Confidence Bands for Probability Density Functions

Distributionally robust optimization (DRO) has been introduced for solving stochastic programs in which the distribution of the random variables is unknown and must be estimated by samples from that distribution. A key element of DRO is the construction of the ambiguity set, which is a set of distributions that contains the true distribution with a high probability. Assuming that the true distribution has a probability density function, we propose a class of ambiguity sets based on confidence bands of the true density function. As examples, we consider the shape-restricted confidence bands and the confidence bands constructed with a kernel density estimation technique. The former allows us to incorporate the prior knowledge of the shape of the underlying density function (e.g., unimodality and monotonicity), and the latter enables us to handle multidimensional cases. Furthermore, we establish the convergence of the optimal value of DRO to that of the underlying stochastic program as the sample size increases. The DRO with our ambiguity set involves functional decision variables and infinitely many constraints. To address this challenge, we apply duality theory to reformulate the DRO to a finite-dimensional stochastic program, which is amenable to a stochastic subgradient scheme as a solution method.

The Optimal Harvest Decisions for Natural and Artificial Maturation Mangoes under Uncertain Demand, Yields and Prices

This study focuses on the decisions of picking, inventory, ripening, delivering, and selling mangoes in a harvesting season. Demand, supply, and prices are uncertain, and their probability density functions are fitted based on actual trading data collected from the largest spot market in Taiwan. A stochastic programming model is formulated to minimize the expected cost under the considerations of labor, storage space, shelf life, and transportation restrictions. We implement the sample-average approximation to obtain a high-quality solution of the stochastic program. The analysis compares deterministic and stochastic solutions to assess the uncertain effect on the harvest decisions. Finally, the optimal harvest schedule of each mango variety is suggested based on the stochastic program solution.

Two-stage stochastic programming approach for limited medical reserves allocation under uncertainties

At the early stage of public health emergencies, when the conventional medical reserves prepared are insufficient, and productivity could temporarily not meet the surge in demand, donations can be used to cover excess demand for medical supplies to a large extent. This paper explicitly considers the allocation problem of limited medical reserves during a public health emergency, incorporating uncertainty in demand and donated supplies and the priorities of health care centers. The problem is formulated as a two-stage stochastic program that regards the donated supplies as an efficient recourse action, aiming to minimize the total losses. The optimal allocation strategy of limited medical reserves and donations is obtained by solving the model using Gurobi solver. Finally, the effectiveness of the proposed approach is verified by a series of computational results, which show that the solutions of our method not only benefit the emergency demand fulfill rate but reduce the total losses as well.

The Optimal Harvest Decisions for Natural and Artificial Maturation Mangoes Under Uncertain Demand, Yields, and Prices

This study focuses on the decisions of picking, inventory, ripening, delivering, and selling mangoes in a harvesting season. Demand, supply, and prices are uncertain, and their probability density functions are fitted based on actual trading data collected from the largest spot market in Taiwan. A stochastic programming model is formulated to minimize the expected cost under the considerations of labor, storage space, shelf life, and transportation restrictions. We implement the sample-average approximation to obtain a high-quality solution of the stochastic program. The analysis compares deterministic and stochastic solutions to assess the uncertain effect on the harvest decisions. Finally, the optimal harvest schedule of each mango type is suggested based on the stochastic program solution.