Robust and stochastic approaches to network capacity design under demand uncertainty

This thesis considers the network capacity design problem with demand uncertainty using the stochastic, robust and distributionally robust stochastic optimization approaches (DRSO). Network modeling in itself has found wide areas of application in most fields of human endeavor. The network would normally consist of source (origin) and sink (destination) nodes connected by arcs that allow for flows of an entity from the origin to the destination nodes. In this thesis, a special type of the minimum cost flow problem is addressed, the multi-commodity network flow problem. Commodities are the flow types that are transported on a shared network. Offered demands are, for the most part, unknown or uncertain, hence a model that immune against this uncertainty becomes the focus as well as the practicability of such models in the industry. This problem falls under the two-stage optimization framework where a decision is delayed in time to adjust for the first decision earlier made. The first stage decision is called the "here and now", while the second stage traffic re-adjustment is the "wait and see" decision. In the literature, the decision-maker is often believed to know the shape of the uncertainty, hence we address this by considering a data-driven uncertainty set. The research also addressed the non-linearity of cost function despite the abundance of literature assuming linearity and models proposed for this. This thesis consist of four main chapters excluding the "Introduction" chapter and the "Approaches to Optimization under Uncertainty" chapter where the methodologies are reviewed. The first of these four, Chapter 3, proposes the two models for the Robust Network Capacity Expansion Problem (RNCEP) with cost non-linearity. These two are the RNCEP with fixed-charge cost and RNCEP with piecewise-linear cost. The next chapter, Chapter 4, compares the RNCEP models under two types of uncertainties in order to address the issue of usefulness in a real world setting. The resulting two robust models are also comapared with the stochastic optimization model with distribution mean. Chapter 5 re-examines the earlier problem using machine learning approaches to generate the two uncertainty sets while the last of these chapters, Chapter 6, investigates DRSO model to network capacity planning and proposes an efficient solution technique

A distributionally robust joint chance constrained optimization model for the dynamic network design problem under demand uncertainty

This paper develops a distributionally robust joint chance constrained optimization model for a dynamic network design problem (NDP) under demand uncertainty. The major contribution of this paper is to propose an approach to approximate a joint chance-constrained Cell Transmission Model (CTM) based System Optimal Dynamic Network Design Problem with only partial distributional information of uncertain demand. The proposed approximation is tighter than two popular benchmark approximations, namely the Bonferroni’s inequality and second-order cone programming (SOCP) approximations. The resultant formulation is a semidefinite program which is computationally efficient. A numerical experiment is conducted to demonstrate that the proposed approximation approach is superior to the other two approximation approaches in terms of solution quality. The proposed approximation approach may provide useful insights and have broader applicability in traffic management and traffic planning problems under uncertainty.postprin

Applications of Optimization Under Uncertainty Methods on Power System Planning Problems

This dissertation consists of two published journal paper, both on transmission expansion planning, and a report on distribution network hardening. We first discuss our studies of two optimization criteria for the transmission planning problem with a simplified representation of load and the forecast generation investment additions within the robust optimization paradigm. The objective is to determine either the minimum of the maximum investment requirement or the maximum regret with all sources of uncertainty explicitly represented. In this way, transmission planners can determine optimal planning decisions that are robust against all sources of uncertainty. We use a two layer algorithm to solve the resulting trilevel optimization problems. We also construct a new robust transmission planning model that considers generation investment more realistically to improve the quantification and visualization of uncertainty and the impacts of environmental policies. With this model, we can explore the effect of uncertainty in both the size and the location of candidate generation additions. The corresponding algorithm we develop takes advantage of the structural characteristics of the model so as to obtain a computationally efficient methodology. The two robust optimization tools provide new capabilities to transmission planners for the development of strategies that explicitly account for various sources of uncertainty. We illustrate the application of the two optimization models and solution schemes on a set of representative case studies. These studies give a good idea of the usefulness of these tools and show their practical worth in the assessment of ``what if\u27\u27 cases. We compare the performance of the minimax cost approach and the minimax regret approach under different characterizations of uncertain parameters. In addition, we also present extensive numerical studies on an IEEE 118-bus test system and the WECC 240-bus system to illustrate the effectiveness of the proposed decision support methods. The case study results are particularly useful to understand the impacts of each individual investment plan on the power system\u27s overall transmission adequacy in meeting the demand of the trade with the power output units without violation of the physical limits of the grid. In the report on distribution network hardening, a two-stage stochastic optimization model is proposed. Transmission and distribution networks are essential infrastructures to modern society. In the United States alone, there are there are more than 200,000 miles of high voltage transmission lines and numerous distribution lines. The power network spans the whole country. Such vast networks are vulnerable to disruptions caused by natural disasters. Hardening of distribution lines could significantly reduce the impact of natural disasters on the operation of power systems. However, due to the limited budget, it is impossible to upgrade the whole power network. Thus, intelligent allocation of resources is crucial. Optimal allocation of limited budget between different hardening methods on different distribution lines is explored

Distribution Network Planning and Operation With Autonomous Agents

With the restructured power system, different system operators and private investors are responsible for operating and maintaining the electricity networks. Moreover, with incentives for a clean environment and reducing the reliance on fossil fuel generation, future distribution networks adopt a considerable penetration of renewable energy sources. However, the uncertainty of renewable energy sources poses operational challenges in distribution networks. This thesis addresses the planning and operation of the distribution network with autonomous agents under uncertainty. First, a decentralized energy management system for unbalanced networked microgrids is developed. The energy management schemes in microgrids enhance the utilization of renewable energy resources and improve the reliability and resilience measures in distribution networks. While microgrids operate autonomously, the coordination among microgrid and distribution network operators contributes to the improvement in the economics and reliability of serving the demand. Therefore, a decentralized energy management framework for the networked microgrids is proposed. Furthermore, the unbalanced operation of the distribution network and microgrids, as well as the uncertainty in the operating modes of the microgrids, renewable energy resources, and demand, are addressed. The second research work presents a stochastic expansion planning framework to determine the installation time, location, and capacity of battery energy storage systems in the distribution network with considerable penetration of photovoltaic generation and data centers. The presented framework aims to minimize the capital cost of the battery energy storage and the operation cost of the distribution network while ensuring the security of energy supply for the data centers that serve end-users in the data network as well as the reliability requirements of the distribution network. The third research work proposes a coordinated expansion planning of natural gas-fired distributed generation in the power distribution and natural gas networks considering demand response. The problem is formulated as a distributionally robust optimization problem in which the uncertainties in the photovoltaic power generation, electricity load, demand bids, and natural gas demand are considered. The Wasserstein distance metric is employed to quantify the distance between the probability distribution functions. The last research work proposes a decentralized operation of the distribution network and hydrogen refueling stations equipped with hydrogen storage, electrolyzers, and fuel cells to serve hydrogen and electric vehicles. The uncertainties in the electricity demands, PV generation, hydrogen supply, and hydrogen demands are captured, and the problem is formulated as a Wasserstein distance-based distributionally robust optimization problem. The proposed framework coordinates the dispatch of the distributed generation in the distribution network with the hydrogen storage, electrolyzer, and fuel cell dispatch considering the worst-case probability distribution of the uncertain parameters. The proposed frameworks limit the information shared among these autonomous operators using Benders decomposition

Master production schedule using robust optimization approaches in an automobile second-tier supplier

[EN] This paper considers a real-world automobile second-tier supplier that manufactures decorative surface finishings of injected parts provided by several suppliers, and which devises its master production schedule by a manual spreadsheet-based procedure. The imprecise production time in this manufacturer's production process is incorporated into a deterministic mathematical programming model to address this problem by two robust optimization approaches. The proposed model and the corresponding robust solution methodology improve production plans by optimizing the production, inventory and backlogging costs, and demonstrate the their feasibility for a realistic master production schedule problem that outperforms the heuristic decision-making procedure currently being applied in the firm under study.Funding was provided by Horizon 2020 Framework Programme (Grant Agreement No. 636909) in the frame of the "Cloud Collaborative Manufacturing Networks" (C2NET) project.Martín, AG.; Díaz-Madroñero Boluda, FM.; Mula, J. (2020). Master production schedule using robust optimization approaches in an automobile second-tier supplier. Central European Journal of Operations Research. 28(1):143-166. https://doi.org/10.1007/s10100-019-00607-2S143166281Alem DJ, Morabito R (2012) Production planning in furniture settings via robust optimization. Comput Oper Res 39:139–150. https://doi.org/10.1016/j.cor.2011.02.022Aloulou MA, Dolgui A, Kovalyov MY (2014) A bibliography of non-deterministic lot-sizing models. Int J Prod Res 52:2293–2310. https://doi.org/10.1080/00207543.2013.855336As’ad R, Demirli K, Goyal SK (2015) Coping with uncertainties in production planning through fuzzy mathematical programming: application to steel rolling industry. Int J Oper Res 22:1–30. https://doi.org/10.1504/IJOR.2015.065937Atamturk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper Res 55:662–673. https://doi.org/10.1287/opre.1070.0428Aytac B, Wu SD (2013) Characterization of demand for short life-cycle technology products. Ann Oper Res 203:255–277. https://doi.org/10.1007/s10479-010-0771-5Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23:769–805. https://doi.org/10.1287/moor.23.4.769Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424. https://doi.org/10.1007/PL00011380Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52:35–53. https://doi.org/10.1287/opre.1030.0065Caulkins JJ, Morrison E, Weidemann T (2007) Spreadsheet errors and decision making: evidence from field interviews. J Organ End User Comput 19:1–23Childerhouse P, Towill DR (2002) Analysis of the factors affecting real-world value stream performance. Int J Prod Res 40:3499–3518. https://doi.org/10.1080/00207540210152885Chu SCK (1995) A mathematical programming approach towards optimized master production scheduling. Int J Prod Econ 38:269–279. https://doi.org/10.1016/0925-5273(95)00015-GConlon JR (1976) Is your master production schedule feasible? Prod Invent Manag 17:56–63De La Vega J, Munari P, Morabito R (2017) Robust optimization for the vehicle routing problem with multiple deliverymen. Cent Eur J Oper Res. https://doi.org/10.1007/s10100-017-0511-xDíaz-Madroñero M, Mula J, Jiménez M (2014a) Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions. Int J Prod Res 52:6971–6988. https://doi.org/10.1080/00207543.2014.920115Díaz-Madroñero M, Mula J, Peidro D (2014b) A review of discrete-time optimization models for tactical production planning. Int J Prod Res 52:5171–5205. https://doi.org/10.1080/00207543.2014.899721Díaz-Madroñero M, Peidro D, Mula J (2014c) A fuzzy optimization approach for procurement transport operational planning in an automobile supply chain. Appl Math Model 38:5705–5725. https://doi.org/10.1016/j.apm.2014.04.053Dolgui A, Ben Ammar O, Hnaien F et al (2013) Supply planning and inventory control under lead time uncertainty: a review. Stud Inform Control 22:255–268Dzuranin AC, Slater RD (2014) Business risks all identified? If you’re using a spreadsheet, think again. J Corp Account Finance 25:25–30. https://doi.org/10.1002/jcaf.21936Englberger J, Herrmann F, Manitz M (2016) Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment. Int J Prod Res 54:6192–6215. https://doi.org/10.1080/00207543.2016.1162917Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: an overview. Eur J Oper Res 235:471–483Gharakhani M, Taghipour T, Farahani KJ (2010) A robust multi-objective production planning. Int J Ind Eng Comput 1:73–78. https://doi.org/10.5267/j.ijiec.2010.01.007González JJ, Reeves GR (1983) Master production scheduling: a multiple-objective linear programming approach. Int J Prod Res 21:553–562. https://doi.org/10.1080/00207548308942390Gorissen BL, Yanıkoğlu İ, den Hertog D (2015) A practical guide to robust optimization. Omega 53:124–137. https://doi.org/10.1016/j.omega.2014.12.006Grubbstrom RW, Tang O (2000) An overview of input-output analysis applied to production-inventory systems. Econ Syst Res 12:3–25. https://doi.org/10.1080/095353100111254Grubbström RW, Bogataj M, Bogataj L (2010) Optimal lotsizing within MRP theory. Annu Rev Control 34:89–100. https://doi.org/10.1016/J.ARCONTROL.2010.02.004Haojie Y, Lixin M, Canrong Z (2017) Capacitated lot-sizing problem with one-way substitution: a robust optimization approach. In: In 2017 3rd international conference on information management (ICIM). Institute of Electrical and Electronics Engineers Inc., pp 159–163Kara G, Özmen A, Weber G-W (2017) Stability advances in robust portfolio optimization under parallelepiped uncertainty. Cent Eur J Oper Res. https://doi.org/10.1007/s10100-017-0508-5Kawas B, Laumanns M, Pratsini E (2013) A robust optimization approach to enhancing reliability in production planning under non-compliance risks. OR Spectr 35:835–865. https://doi.org/10.1007/s00291-013-0339-2Kimms A (1998) Stability measures for rolling schedules with applications to capacity expansion planning, master production scheduling, and lot sizing. Omega 26:355–366. https://doi.org/10.1016/S0305-0483(97)00056-XKo M, Tiwari A, Mehnen J (2010) A review of soft computing applications in supply chain management. Appl Soft Comput 10:661–674. https://doi.org/10.1016/j.asoc.2009.09.004Körpeolu E, Yaman H, Selim Aktürk M (2011) A multi-stage stochastic programming approach in master production scheduling. Eur J Oper Res 213:166–179. https://doi.org/10.1016/j.ejor.2011.02.032Kovačić D, Bogataj M (2013) Reverse logistics facility location using cyclical model of extended MRP theory. Cent Eur J Oper Res 21:41–57. https://doi.org/10.1007/s10100-012-0251-xKuchta D (2011) A concept of a robust solution of a multicriterial linear programming problem. Cent Eur J Oper Res 19:605–613. https://doi.org/10.1007/s10100-010-0150-yLage Junior M, Godinho Filho M (2017) Master disassembly scheduling in a remanufacturing system with stochastic routings. Cent Eur J Oper Res 25:123–138. https://doi.org/10.1007/s10100-015-0428-1Lee SM, Moore LJ (1974) Practical approach to production scheduling. Prod Invent Manag J 15:79–92Lehtimaki AK (1987) Approach for solving decision planning of master scheduling by utilizing theory of fuzzy sets. Int J Prod Res 25:1781–1793Li Z, Li Z (2015) Optimal robust optimization approximation for chance constrained optimization problem. Comput Chem Eng 74:89–99. https://doi.org/10.1016/j.compchemeng.2015.01.003Li Z, Ding R, Floudas CA (2011) A Comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed integer linear optimization. Ind Eng Chem Res 50:10567–10603. https://doi.org/10.1021/ie200150pLi Z, Tang Q, Floudas CA (2012) A comparative theoretical and computational study on robust counterpart optimization: II. Probabilistic guarantees on constraint satisfaction. Ind Eng Chem Res 51:6769–6788. https://doi.org/10.1021/ie201651sMula J, Poler R, Garcia-Sabater J, Lario F (2006a) Models for production planning under uncertainty: a review. Int J Prod Econ 103:271–285. https://doi.org/10.1016/j.ijpe.2005.09.001Mula J, Poler R, Garcia JP (2006b) MRP with flexible constraints: a fuzzy mathematical programming approach. Fuzzy Sets Syst 157:74–97. https://doi.org/10.1016/j.fss.2005.05.045Mula J, Poler R, Garcia-Sabater JP (2008) Capacity and material requirement planning modelling by comparing deterministic and fuzzy models. Int J Prod Res 46:5589–5606. https://doi.org/10.1080/00207540701413912Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43:264–281. https://doi.org/10.1287/opre.43.2.264Nannapaneni S, Mahadevan S (2014) Uncertainty quantification in performance evaluation of manufacturing processes. In: 2014 IEEE international conference on Big Data (Big Data). IEEE, pp 996–1005Ng TS, Fowler J (2007) Semiconductor production planning using robust optimization. In: 2007 IEEE international conference on industrial engineering and engineering management. IEEE, pp 1073–1077Peidro D, Mula J, Poler RR, Lario F-C (2009) Quantitative models for supply chain planning under uncertainty: a review. Int J Adv Manuf Technol 43:400–420. https://doi.org/10.1007/s00170-008-1715-yPochet Y, Wolsey LA (2006) Production planning by mixed integer programming. Springer, BerlinPowell SG, Baker KR, Lawson B (2008) A critical review of the literature on spreadsheet errors. Decis Support Syst 46:128–138. https://doi.org/10.1016/j.dss.2008.06.001Rahmani D, Ramezanian R, Fattahi P, Heydari M (2013) A robust optimization model for multi-product two-stage capacitated production planning under uncertainty. Appl Math Model 37:8957–8971. https://doi.org/10.1016/j.apm.2013.04.016Sahinidis NV (2004) Optimization under uncertainty: state-of-the-art and opportunities. Comput Chem Eng 28:971–983. https://doi.org/10.1016/j.compchemeng.2003.09.017Sakhaii M, Tavakkoli-Moghaddam R, Bagheri M, Vatani B (2015) A robust optimization approach for an integrated dynamic cellular manufacturing system and production planning with unreliable machines. Appl Math Model 40:169–191. https://doi.org/10.1016/j.apm.2015.05.005Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21:1154–1157. https://doi.org/10.1287/opre.21.5.1154Supriyanto I, Noche B (2011) Fuzzy multi-objective linear programming and simulation approach to the development of valid and realistic master production schedule. Logist J. https://doi.org/10.2195/lj_proc_supriyanto_de_201108_01Tavakkoli-Moghaddam R, Sakhaii M, Vatani B et al (2014) A robust model for a dynamic cellular manufacturing system with production planning. Int J Eng 27:587–598. https://doi.org/10.5829/idosi.ije.2014.27.04a.09Vargas V, Metters R (2011) A master production scheduling procedure for stochastic demand and rolling planning horizons. Int J Prod Econ 132:296–302. https://doi.org/10.1016/j.ijpe.2011.04.025Wang J, Shu Y-F (2005) Fuzzy decision modeling for supply chain management. Fuzzy Sets Syst 150:107–127Weng ZK, Parlar M (2005) Managing build-to-order short life-cycle products: benefits of pre-season price incentives with standardization. J Oper Manag 23:482–495. https://doi.org/10.1016/j.jom.2004.10.008Werner R (2008) Cascading: an adjusted exchange method for robust conic programming. Cent Eur J Oper Res 16:179–189. https://doi.org/10.1007/s10100-007-0047-6Yu C-S, Li H-L (2000) A robust optimization model for stochastic logistic problems. Int J Prod Econ 64:385–397. https://doi.org/10.1016/S0925-5273(99)00074-