Interval-parameter robust optimization for environmental management under uncertainty

2009 ◽  
Vol 36 (4) ◽  
pp. 592-606 ◽  
Author(s):  
Y.P. Li ◽  
G.H. Huang
Keyword(s):  
Stochastic Programming ◽  
Robust Optimization ◽  
Decision Makers ◽  
Interval Parameter ◽  
Two Stage ◽  
Uncertainty Interval ◽  
Second Stage ◽  
Programming Framework ◽  
Different Levels

In this study, an interval-parameter robust optimization (IPRO) method is developed through incorporating techniques of interval-parameter programming and robust optimization within a two-stage stochastic programming framework. The IPRO improves upon the two-stage stochastic programming methods by allowing uncertainties presented as both intervals and random variables to be handled in the optimization system. Moreover, in the modeling formulation, penalties are exercised with the recourse against any infeasibility, and robustness measures are introduced to examine the variability of the second-stage costs that are above the expected level. The IPRO is generally suitable for risk-aversive planners under high-variability conditions. The developed method is applied to a case of long-term waste management under uncertainty. Interval solutions under different robustness levels have been generated. They cannot only be used for analyzing various policy scenarios that are related to different levels of economic penalties when the pre-regulated waste allocation allowances are violated, but also help decision makers to analyze the interrelationships between the penalties and their variabilities.

scholarly journals Optimization of Ecological Water Supplement Scheme for Improved Suitable Habitat Area for Rare Migratory Birds in Nature Reserves Using Interval-Parameter Fuzzy Two-Stage Stochastic Programming Model

2020 ◽  
Vol 17 (20) ◽  
pp. 7562
Author(s):  
Xianrui Liao ◽  
Chong Meng ◽  
Zhixing Ren ◽  
Wenjin Zhao
Keyword(s):  
Stochastic Programming ◽  
Migratory Birds ◽  
Programming Model ◽  
Decision Makers ◽  
Fuzzy Membership ◽  
Interval Parameter ◽  
Two Stage ◽  
Target Value ◽  
Habitat Area ◽  
Optimization Schemes

The optimization of ecological water supplement scheme in Momoge National Nature Reserve (MNNR), using an interval-parameter two-stage stochastic programming model (IPTSP), still experiences problems with fuzzy uncertainties and the wide scope of the obtained optimization schemes. These two limitations pose a high risk of system failure causing high decision risk for decision-makers and render it difficult to further undertake optimization schemes respectively. Therefore, an interval-parameter fuzzy two-stage stochastic programming (IPFTSP) model derived from an IPTSP model was constructed to address the random variable, the interval uncertainties and the fuzzy uncertainties in the water management system in the present study, to reduce decision risk and narrow down the scope of the optimization schemes. The constructed IPFTSP model was subsequently applied to the optimization of the ecological water supplement scheme of MNNR under different scenarios, to maximize the recovered habitat area and the carrying capacity for rare migratory water birds. As per the results of the IPFTSP model, the recovered habitat areas for rare migratory birds under low, medium and high flood flow scenarios were (14.06, 17.88) × 103, (14.92, 18.96) × 103 and (15.83, 19.43) × 103 ha, respectively, and the target value was (14.60, 18.47) × 103 ha with a fuzzy membership of (0.01, 0.83). Fuzzy membership reflects the possibility level that the model solutions satisfy the target value and the corresponding decision risk. We further observed that the habitat area recovered by the optimization schemes of the IPFTSP model was significantly increased compared to the recommended scheme, and the increases observed were (5.22%, 33.78%), (11.62%, 41.88%) and (18.44%, 45.39%). In addition, the interval widths of the recovered habitat areas in the IPFTSP model were reduced by 17.15%, 17.98% and 23.86%, in comparison to those from the IPTSP model. It was revealed that the IPFTSP model, besides generating the optimal decision schemes under different scenarios for decision-makers to select and providing decision space to adjust the decision schemes, also shortened the decision range, thereby reducing the decision risk and the difficulty of undertaking decision schemes. In addition, the fuzzy membership obtained from the IPFTSP model, reflecting the relationship among the possibility level, the target value, and the decision risk, assists the decision-makers in planning the ecological water supplement scheme with a preference for target value and decision risk.

scholarly journals Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Ke Shang ◽  
Felix T. S. Chan ◽  
Stephen Karungaru ◽  
Kenji Terada ◽  
Zuren Feng ◽  
...  
Keyword(s):  
Mathematical Programming ◽  
Robust Optimization ◽  
Comparative Studies ◽  
Complex Model ◽  
Orienteering Problem ◽  
Two Stage ◽  
Second Stage ◽  
Robust Model ◽  
Uncertainty Set

In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage orienteering problem with stochastic weights.

scholarly journals Two-stage treatment of hip periprosthetic joint infection complicated with retroperitoneal urinary bladder defect

2021 ◽  
Vol 27 (5) ◽  
pp. 587-591
Author(s):  
S.T. Ivanian ◽  
◽  
S.V. Basov ◽  
N.O. Gritsuk ◽  
V.A. Pronin ◽  
...  
Keyword(s):  
Urinary Bladder ◽  
Hip Arthroplasty ◽  
Joint Infection ◽  
Long Term Results ◽  
Sustained Remission ◽  
Two Stage ◽  
Second Stage ◽  
Short And Long Term ◽  
Type 3

emphasize the importance of preoperative preparation and well-coordinated work of related specialists using a specific clinical instance. Case report Reported is a successful experience of two-stage treatment of the patient with hip PJI complicated with urinary bladder defect. A 40-year old male patient diagnosed with left-sided deep hip PJI Tsukayama type 3 was treated at department of infection surgery, Rostov Regional Clinical Hospital No. 2 in January 2019. Total hip arthroplasty performed in 2008 was complicated by migration of acetabulum component. A retroperitoneal bladder defect (pressure ulcer) was detected during the first stage of resection arthroplasty and placement of an antibacterial spacer. Urological procedure was performed in a delayed manner due to technical difficulties of implant removal, prolonged and traumatic procedure, and high blood loss. With the patient's condition stabilized cystoscopy and bilateral ultrasound guided percutaneous nephroureterostomy were performed. Prolonged antibacterial aetiotropic treatment was administered. The second stage of surgical treatment included revision hip arthroplasty using a tailored acetabular component and a standard revision femoral component performed at 6 months of debridement. Results Short- and long-term results were good with sustained remission achieved. Patient could walk unassisted using a cane and had a satisfactory ROM in the left hip with HHS scored 76.255. Conclusion Multiple disciplinary teamwork is appropriate for treatment of deep PJI with much coherence, coordinated efforts and expertise from diverse professionals.

Stochastic progamming in the mid-term operations planning of an oil refinery

2012 ◽  
Author(s):  
Leonardo Nascimento ◽  
Helder Venceslau ◽  
Adilson Xavier ◽  
Virgílio Ferreira Filho ◽  
Leonidas Sakalauskas ◽  
...  
Keyword(s):  
Stochastic Programming ◽  
Crude Oil ◽  
Economic Efficiency ◽  
Decision Makers ◽  
Oil Refinery ◽  
Oil Refining ◽  
Production Plan ◽  
Two Stage ◽  
Operations Planning ◽  
The Impact

Oil refining is a series of processes that aim to separate the crude oil into pre-standardized fractions. The way these processes can be combined result in a variety of schemes where each one can be used as a production plan. This work presents a methodology, based upon stochastic programming (SP), that support the decision makers in the mid-term operations planning of an oil refinery. Results generated by running a multi-period two-stage SP model are used to measure the impact on the economic efficiency when not considering the randomness of the demand and the receipt of crude oil.

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