An Inventory-Theory-Based Inexact Multistage Stochastic Programming Model for Water Resources Management

Abstract

An inventory-theory-based inexact multistage stochastic programming (IB-IMSP) method is developed for planning water resources systems under uncertainty. The IB-IMSP is based on inexact multistage stochastic programming and inventory theory. The IB-IMSP cannot only effectively handle system uncertainties represented as probability density functions and discrete intervals but also efficiently reflect dynamic features of system conditions under different flow levels within a multistage context. Moreover, it can provide reasonable transferring schemes (i.e., the amount and batch of transferring as well as the corresponding transferring period) associated with various flow scenarios for solving water shortage problems. The applicability of the proposed IB-IMSP is demonstrated by a case study of planning water resources management. The solutions obtained are helpful for decision makers in not only identifying different transferring schemes when the promised water is not met, but also making decisions of water allocation associated with different economic objectives.

An Inexact Inventory Theory-Based Water Resources Distribution Model for Yuecheng Reservoir, China

“…e demand is D units per unit time, and the relative costs include K (setup cost for ordering one batch ($)), C (unit cost for producing or purchasing each unit ($/unit)), and C1 (holding cost per unit per unit of time held in inventory ($/month)). e objective is to determine when and how much to replenish inventory in order to minimize the sum of the produce or purchase costs per unit time [40].…”

“…e setup cost for water diversion in this paper mainly considers the travelling expenses for diversion agreement per time, whose value is [260, 370] RMB by calculating the costs of tickets, meals, and accommodation. According to "Notice on the trial implementation of financial benchmark yield and annual operating standard rates" [43], the holding cost of Yuecheng Reservoir is [30,40] RMB/10 3 m 3 by calculating the ratio between the sum of three costs: maintenance fee (41.5 × 10 6 RMB), salary and welfare funds for managers (12.13 × 10 9 RMB), the reservoir management fee (1.82 × 10 6 RMB), and the annual runoff of the reservoir [44,45]. In addition, due to the lack of related information, the distribution of water supply of Yuecheng Reservoir for irrigation is difficult to obtain.…”

The treatment of optimizing container transportation dynamic programming and planning

“…The analysis of the famous works [2][3][4][5][6][7] shows that decision trees and the planning of scenarios based on their analysis are the main tools in the management of uncertainty and risk in math programming models. It should be noted that optimization models and, in particular, dynamic and stochastic programming models [8][9][10][11][12] are used for solving tasks of optimization of logistic network, reserves management and transportation routing. Some authors examine the theoretical aspects of logistics and optimizing transportation models [13][14][15].…”

Inexact Multistage Stochastic Chance Constrained Programming Model for Water Resources Management under Uncertainties

“…Suo et al [11] proposed an inventory-theory-based inexact multistage stochastic programming for water resources management through introducing an inventory theory into the framework of IMSP to provide reasonable transferring schemes associated with various flow scenarios. IMSP was also combined with other types of uncertainties, such as fuzziness [12][13][14], to solve the water resources management problems.…”