High dimension dynamic programming model for water resources expansion projects

Abstract

An optimization model for High Dimension Dynamic Programming (HDDP) was developed to determine the optimal size of water resources projects within a planning period. The model uses Objective Space Dynamic Programming (OSDP) technique to determine the size of the projects and a Mixed Integer Programming (MIP) formulation to overcome the 'inner' and 'outer' problems of OSDP and to check for the global optimality of the solution. The model is applied to determine the optimal capacity of proposed desalination plants needed to satisfy a number of demand points from different cities, during a planning period of 20 years in Egypt. The model's speed towards the optimal solution depends on the objective space bounds and search method for these bounds. The integration of OSDP and MIP is shown to be an efficient approach for solving optimization problems. Results show that the model is well suited for solving large-scale water resources expansion problems.

Application of multiobjective optimization to scheduling capacity expansion of urban water resource systems

“…Although the construction of large infrastructure at the start of the planning period exploits the economies of scale, the time discounting of costs and the uncertain dynamics of growth may nonetheless favor smaller projects staged over the planning period. To analyze this trade‐off, a number of studies have considered scheduling expansion [ Braga et al ., ; Chang et al ., ; Gillig et al ., ; Grossman and Marks , ; Kim and Yeh , ; Knudsen and Rosbjerg , ; Lund , ; Mahmoud , ; Voivontas et al ., ; Watkins and McKinney , ].…”

Least Economic Cost Regional Water Supply Planning – Optimising Infrastructure Investments and Demand Management for South East England’s 17.6 Million People

“…Capacity expansion models can be deterministic (as in this paper), assuming one version of the future or stochastic, explicitly considering future uncertainty of supply and/or demand. Different optimisation algorithms have been used including mathematical programming (Labadie et al 1986;Kim and Hopkins 1995;Barros et al 2008;Hsu et al 2008), dynamic programming (Bellman 1957;Dandy et al 1984;Braga et al 1985;Mahmoud 2006;Luo et al 2007;Hsu et al 2008;Chou et al 2013) and heuristic optimisation methods (Savic and Walters 1997;Deb 2001). Linear programming is popular because of its assured convergence to a globally optimum solution but is limited to using only convex and linear objective functions, linear constraints and continuous decision variables (Mahmoud 2006).…”

Optimizing system capacity expansion schedules for groundwater supply

“…Their model considers the conjunctive operation and expansion schedule of an integrated water resources system including groundwater wells, reservoirs, desalination plants and shipping water. Mahmoud [2006] applies an optimization model to determine the optimal expansion schedules of a desalination plant. Mahmoud integrates objective space dynamic programming (OSDP) and mixed integer programming to solve the capacity expansion problem.…”

“…Incrementally expanding water resource capacity is a cost‐effective strategy that satisfies increasing water demand [ Braga et al , 1985; Rosegrant and Cai , 2002; Jenkins et al , 2004; Pulido‐Velazquez et al , 2006]. Optimizing capacity expansion has become a significant issue in water resources management [ Voivontas et al , 2003; Mahmoud , 2006]. However, previous investigations cannot effectively solve the groundwater capacity expansion problem under fully dynamic conditions.…”

“… Voivontas et al [2003] and Mahmoud [2006] studied optimal capacity expansion for a surface water system. Voivontas et al [2003] developed a capacity expansion model of an integrated water resource management for islands.…”