Browsing by Subject "Multi-stage stochastic programming"

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Open Access
Fair allocation of in-kind donations in post-disaster phase
(2024-05) Varol, Zehranaz
Disaster response aims to address the immediate needs of the affected populations quickly in highly uncertain circumstances. In disaster relief supply chains, the demand comes from disaster victims (typically considered as internally dis-placed populations), while the supply mostly consists of in-kind donations. This dissertation focuses on finding a fair mechanism to distribute a scarce relief item among a set of demand points under supply uncertainty. Primary concerns, restrictive elements, and unknown parameters change throughout the response phase, which substantially affects the structure of the underlying problems. Thus, the first part of this study provides a temporal classification of disaster response (e.g., into subphases) based on evolving features of demand and supply. As the next step, a donation management problem is structured considering the characteristics of a selected subphase. We first focus on the deterministic donation management problem, which is formulated as a multi-criteria multi-period location-inventory problem with service distance constraints. A set of mobile facilities, called points of distribution (PoDs), is used to distribute the collected supply. In particular, two decisions are made for every period of the planning horizon: (i) where to locate a limited number of mobile PoDs and (ii) what quantity to deliver to each demand node from each PoD. We consider three criteria. The first two involve the so-called deprivation cost, which measures a population’s “suffering” due to a shortage. The third objective is related to the total travel time. Two resulting vectorial optimization models are solved using the ε-constraint method, and the corresponding Pareto frontiers are obtained. Computational results are presented that result from applying the proposed methodological developments to an instance of the problem using real data as well as a generated one. Finally, the stochastic counterpart of the problem is addressed with the aim of minimizing a deprivation cost-based objective. The uncertain supply parameters are integrated into the model using a multi-stage stochastic programming (MSSP) approach. The MSSP model is tested on a real data set to assess and evaluate possible policies that can be adopted by decision-makers. Two matheuristic approaches are employed to handle the exponential growth of the scenario trees: a rolling horizon algorithm and a scenario tree reduction algorithm. A set of computational experiments is performed to evaluate the performance of the proposed methodologies. Overall, the results show that the proposed algorithms can better support the decision-making process when fairness is of relevance.
Open Access
Master production scheduling under uncertainty with controllable processing times
(2009) Körpeoğlu, Ersin
Master Production Schedules (MPS) are widely used in industry especially within Enterprise Resource Planning (ERP) Software. MPS assumes infinite capacity, fixed processing times and a single scenario for demand forecasts. In this thesis, we questioned these assumptions and considered a problem with finite capacity, controllable processing times and finally and most importantly, several demand scenarios instead of just one. We used a multi-stage stochastic programming approach in order to come up with maximum expected profit given the demand scenarios. We used controllable processing times, which are feasible in most of the scheduling practice in industry, to achieve a flexibility in capacity usage. We provided a non-linear mixed integer programming formulation for our problem. Afterwards, we analyzed two sub-problems to simplify the structure of the objective function and suggested alternative linearizations. We considered easier cases of our problem, proposed sufficient conditions for optimality and established the computational complexity status for two special cases. We conducted three experiments, to test computational performance of the formulations, to analyze the profit performance of the multi-stage solutions and finally, to analyze the effect of controllability on profit. Our computational studies show that one of the proposed formulations solves large instances in a very small amount of time. The second experiment suggests that the performance of multi-stage solutions is significantly better than the one of solutions obtained using single scenario strategies in terms of relative regret. Finally, the third experiment shows that controllability significantly increases the performance of multi-stage solutions.
Open Access
Multi-period supplier selection under price uncertainty
(Palgrave Macmillan, 2014) Şen, A.; Yaman, H.; Güler, K.; Körpeoğlu, E.
We consider a problem faced by a procurement manager who needs to purchase a large volume of multiple items over multiple periods from multiple suppliers that provide base prices and discounts. Discounts are contingent on meeting various conditions on total volume or spend, and some are tied to future realizations of random events that can be mutually verified. We formulate a scenario-based multi-stage stochastic optimization model that allows us to consider random events such as a drop in price because o. The most favoured customer clauses, a price change i. The spot market or a new discount offer. We propose certainty-equivalent heuristics and evaluat. The regret of using them. We use our model for three bidding events of a large manufacturing company. The results show that considering most favored customer clauses in supplier offers may create substantial savings that may surpas. The savings from regular discount offers.
Open Access
Multi-stage airline scheduling problem with stochastic passenger demand and non-cruise times
(Elsevier, 2018) Şafak, Ö.; Çavuş, Ö.; Aktürk, Selim
We propose a three-stage stochastic programming model which determines flight timing, fleeting and routing decisions while considering the randomness of demand and non-cruise times. Our model differs from the existing two-stage stochastic models by considering not only flight timing and potential passenger demand, but also expected operational expenses, such as fuel burn and carbon emission costs. We include aircraft cruise speed decisions to compensate for non-cruise time variability so as to satisfy the time requirements of the passenger connections. We handle nonlinear functions of fuel and emission costs associated with cruise speed adjustments by utilizing mixed integer second order cone programming. Because the three-stage stochastic model leads to a large decision tree and can be very time-consuming to solve optimally, we suggest a scenario group-wise decomposition algorithm to obtain lower and upper bounds for the optimal value of the proposed model. The lower and upper bounds are obtained by solving a number of group subproblems, which are similar to proposed multi-stage stochastic model defined over a reduced number of scenarios. We suggest a cutting plane algorithm, along with improvements, to efficiently solve each group subproblem. In the numerical experiments, we provide a significant cost savings over two-stage stochastic programming and deterministic approaches.
Open Access
Multi-stage stochastic programming for demand response optimization
(Elsevier, 2020-02-19) Şahin, Munise Kübra; Çavuş, Özlem; Yaman, Hande
The increase in the energy consumption puts pressure on natural resources and environment and results in a rise in the price of energy. This motivates residents to schedule their energy consumption through demand response mechanism. We propose a multi-stage stochastic programming model to schedule different kinds of electrical appliances under uncertain weather conditions and availability of renewable energy. We incorporate appliances with chargeable and dischargeable batteries to better utilize the renewable energy sources. Our aim is to minimize the electricity cost and the residents’ dissatisfaction. We use a scenario groupwise decomposition (group subproblem) approach to compute lower and upper bounds for instances with a large number of scenarios. The results of our computational experiments show that the approach is very effective in finding high quality solutions in small computation times. We provide insights about how optimization and renewable energy combined with batteries for storage result in peak demand reduction, savings in electricity cost and more pleasant schedules for residents with different levels of price sensitivity.
Open Access
Risk-averse multi-stage mixed-integer stochastic programming problems
(2019-01) Mahmutoğulları, Ali İrfan
Risk-averse multi-stage mixed-integer stochastic programming problems form a class of extremely challenging problems since the problem size grows exponentially with the number of stages, they are non-convex due to integrality restrictions, and their objective functions are nonlinear in general. In this thesis, we first focus on such problems with an objective of dynamic mean conditional value-at-risk. We propose a scenario tree decomposition approach to obtain lower and upper bounds for their optimal values and then use these bounds in an evaluate-and-cut procedure which serves as an exact solution algorithm for such problems with integer first-stage decisions. Later, we consider a risk-averse day-ahead scheduling of electricity generation or unit commitment problem where the objective is a dynamic coherent risk measure. We consider two different versions of the problem: adaptive and non-adaptive. In the adaptive model, the commitment decisions are updated in each stage, whereas in the non-adaptive model, the commitment decisions are fixed in the first-stage. We provide theoretical and empirical analyses on the benefit of using an adaptive multi-stage stochastic model. Finally, we investigate the trade off between the adaptivity of the model and the computational effort to solve it for risk-averse multi-stage production planning problems with an objective of dynamic coherent risk measure. We also conduct computational experiments in order to verify the theoretical findings and discuss the results of these experiments.
Open Access
Shelter site location under multi-hazard scenarios
(Elsevier, 2019) Özbay, Ekmel; Çavuş, Özlem; Kara, Bahar Y.
Natural disasters may happen successively in close proximity of each other. This study locates shelter sites and allocates the affected population to the established set of shelters in cases of secondary disaster(s) following the main earthquake, via a three-stage stochastic mixed-integer programming model. In each stage, before the uncertainty in that stage, that is the number of victims seeking a shelter, is resolved, shelters are established, and after the uncertainty is resolved, affected population is allocated to the established set of shelters. The assumption on nearest allocation of victims to the shelter sites implies that the allocation decisions are finalized immediately after the location decisions, hence both location and allocation decisions can be considered simultaneously. And, when victims are allocated to the nearest established shelter sites, the site capacities may be exceeded. To manage the risk inherit to the demand uncertainty and capacities, conditional value-at-risk is utilized in modeling the risk involved in allocating victims to the established shelter sites. Computational results on Istanbul dataset are presented to emphasize the necessity of considering secondary disaster(s), along with a heuristic solution methodology to improve the solution qualities and times.