ORIGINAL PAPER Storage-yield analysis of surface water reservoirs: the role of reliability constraints and operating policies S. Jamshid Mousavi • Hosein Alizadeh • Kumaraswamy Ponnambalam Published online: 24 June 2014 Ó Springer-Verlag Berlin Heidelberg 2014 Abstract Stochastic optimization methods are used for optimal design and operation of surface water reservoir systems under uncertainty. Chance-constrained (CC) opti- mization with linear decision rules (LDRs) is an old approach for determining the minimum reservoir capacity required to meet a specific yield at a target level of reli- ability. However, this approach has been found to overes- timate the reservoir capacity. In this paper, we propose the reason for this overestimation to be the fact that the reli- ability constraints considered in standard CC LDR models do not have the same meaning as in other models such as reservoir operation simulation models. The simulation models have fulfilled a target reliability level in an average sense (i.e., annually), whereas the standard CC LDR models have met the target reliability level every season of the year. Mixed integer nonlinear programs are presented to clarify the distinction between the two types of reli- ability constraints and demonstrate that the use of seasonal reliability constraints, rather than an average reliability constraint, leads to 80–150 % and 0–32 % excess capacity for SQ-type and S-type CC LDR models, respectively. Additionally, a modified CC LDR model with an average reliability constraint is proposed to overcome the reservoir capacity overestimation problem. In the second stage, we evaluate different operating policies and show that for the seasonal (average) reliability constraints, open-loop, S-type, standard operating policy, SQ-type, and general SQ-type policies compared to a model not using any operation rule lead to 190–460 % (200–550 %), 100–200 % (80–300 %), 0–90 % (0–60 %), 30–90 % (0–20 %), and 10–90 % (0–10 %) excess capacity, respectively. 1 Introduction Reservoir yield can be defined as a constant amount of reliably available water over a specific period of time (typically 1 year). Water resources engineering has long used the storage-yield-reliability analysis for reservoir systems design and operation. The analysis deals with estimating either the required capacity of the reservoir to provide a specific yield at a certain level of reliability or the yield from a constructed reservoir of known capacity, in both cases assuming stationary inflows. The chance-constrained (CC) approach is an explicit stochastic optimization method for storage-yield-reliability analysis of reservoir systems (ReVelle et al. 1969, ReVelle and Kirby 1970; Eastman and ReVelle 1973; ReVelle and Gundelach 1975; Gundelach and ReVelle 1975; Houck 1979; Houck et al. 1980; Joeres et al. 1981). This approach has also been extended to reliability programming, where reliability levels are considered as unknown decision variables (Simonovic and Marino 1980, 1981, 1982). In CC models, the deterministic equivalent of chance constraints S. J. Mousavi (&) Department of Civil and Environmental Engineering, Amirkabir University of Technology (Polytechnic of Tehran), 424 Hafez Ave., P.O. Box: 15875-4413, Tehran, Iran e-mail: jmosavi@aut.ac.ir H. Alizadeh School of Civil Engineering, Iran University of Science and Technology, Narmak, P.O. Box: 1684613114, Tehran, Iran e-mail: alizadeh@iust.ac.ir K. Ponnambalam Department of Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada e-mail: ponnu@uwaterloo.ca 123 Stoch Environ Res Risk Assess (2014) 28:2051–2061 DOI 10.1007/s00477-014-0910-7