A multi-stage stochastic programming approach for managing demand disruptions: insights from the Asafoetida manufacturing industry in India

A novel multi-stage possibilistic stochastic programming approach (with an application in relief distribution planning)

A multi-stage stochastic integer programming approach for locating electric vehicle charging stations

A multi-stage stochastic integer programming approach for a multi-echelon lot-sizing problem with returns and lost sales

From Probabilistic Seasonal Streamflow Forecasts to Optimal Reservoir Operations: A Stochastic Programming Approach

We combine a dynamic programming approach (stochastic optimal control) with a multi-stage stochastic programming approach (MSP) in order to solve various problems in personal finance and pensions. Both optimization methods are integrated into one MSP formulation, making it possible to achieve a solution within a short computational time. The solution takes into account the entire lifetime of an individual, while focusing on practical constraints, such as limits on portfolio composition, limits on the sum insured, inclusion of transaction costs, and taxes on capital gains, during the first years of a contract. Two applications are considered: (A) optimal investment, consumption and sum insured for an individual maximizing the expected utility of consumption and bequest, and (B) optimal investment for a pension saver who wishes to maximize the expected utility of retirement benefits. Numerical results show that among the considered practical constraints, the presence of taxes affects the optimal controls the most. Furthermore, the individual’s preferences, such as impatience level and risk aversion, have even a higher impact on the controlled processes than the taxes on capital gains.

We combine a dynamic programming approach (stochastic optimal control) with a multi-stage stochastic programming approach (MSP) in order to solve various problems in personal finance and pensions. Stochastic optimal control produces an optimal policy that is easy to understand and implement. However, explicit solution may not exist, especially when we want to deal with constraints, such as limits on portfolio composition, limits on the sum insured, an inclusion of transaction costs or taxes on capital gains, which are important issues regularly mentioned in the literature. Both optimization methods are integrated into one MSP formulation, and in a short computational time produce a solution, which takes into account the entire lifetime of an individual with a focus on the practical constraints during the first years of a contract. Two applications are considered: (A) optimal investment, consumption and sum insured for an individual maximizing the expected utility of consumption and bequest, and (B) optimal investment for a pension saver who wishes to maximize the expected utility of retirement benefits. Numerical results show that among the considered practical constraints, the presence of taxes affects the optimal controls the most. Furthermore, the individual's preferences, such as impatience level and risk aversion, have even a higher impact on the controlled processes than the taxes on capital gains.

Food waste and proper methods to deal with it are one of the main challenges of supply chain network management. The majority of studies on how to use mathematical models in the supply chain have focused on goods that are at their peak of freshness as soon as they are produced and deteriorate over time. While some products experience an increase in value at the start of their life cycle, this value eventually reaches its maximum level, and after this point, these products experience a decline in value before being eliminated from the consumption cycle. The objective of this study is to develop a comprehensive inventory–routing model suitable for supply chain networks where products exhibit an increase and decrease in value over time. By considering the randomness and dynamic uncertainty of market demands and the fact that each period has effects on the next period, The proposed model employs a multi-stage stochastic programming (MSSP) approach. By doing so, the model ensures a balanced flow between different components of the network while considering nondeterministic demand under various scenarios that are shown in a tree of scenarios. The utilization of MSSP leads to more reliable solutions compared to deterministic models, making it possible for chain stores to make well-informed decisions in their inventory management and distribution strategies. Ultimately, this approach results in cost savings for chain stores handling such products. This research makes a significant contribution to the existing literature by demonstrating the effectiveness of the proposed model on actual data and highlighting the benefits of using stochastic programming in supply chain optimization.

A multi-stage stochastic programming approach in master production scheduling

Water resources management under multi-parameter interactions: A factorial multi-stage stochastic programming approach

ABSTRACTIn this article, we study the long-term power generation investment expansion planning problem under uncertainty. We propose a bilevel optimization model that includes an upper-level multistage stochastic expansion planning problem and a collection of lower-level economic dispatch problems. This model seeks for the optimal sizing and siting for both thermal and wind power units to be built to maximize the expected profit for a profit-oriented power generation investor. To address the future uncertainties in the decision-making process, this article employs a decision-dependent stochastic programming approach. In the scenario tree, we calculate the non-stationary transition probabilities based on discrete choice theory and the economies of scale theory in electricity systems. The model is further reformulated as a single-level optimization problem and solved by decomposition algorithms. The investment decisions, computation times, and optimality of the decision-dependent model are evaluated by case studies on IEEE reliability test systems. The results show that the proposed decision-dependent model provides effective investment plans for long-term power generation expansion planning.

A risk-based interactive multi-stage stochastic programming approach for water resources planning under dual uncertainties

Capacity planning is a crucial part of global manufacturing strategies in the automotive industry, especially in the presence of volatile markets with high demand uncertainty. Capacity adjustments in machining intensive areas, e.g. body shop, paint shop, or aggregate machining face lead times exceeding a year, making an elaborated decision support indispensable. In this regard, two-stage stochastic programming is a frequently used framework to support capacity and flexibility decisions under uncertainty. However, it does not anticipate future capacity adjustment opportunities in response to market demand developments. Motivated by empirical findings from the automotive industry, we develop a multi-stage stochastic dynamic programming approach where the evolution of demand is represented by a Markov demand model. An efficient multi-stage solution algorithm is proposed and the benefits compared to a rolling horizon application of a two-stage approach are illustrated for different generic manufacturing networks. Especially network structures with limited flexibility might significantly benefit from applying a multi-stage framework.

Wind power trading in pool-based electricity markets is a decision-making problem and is generally modeled using a multi-stage stochastic programming approach because of the implicit uncertainty of wind input. In any stochastic programming approach, representation of random input process is a major issue. Due to uncertainty in wind availability, generated power by wind turbines is stochastic and is represented by possible values with corresponding probability of occurrence or scenarios. Accurate representation of uncertainty generally requires the consideration of large number of scenarios, thus necessitating the need for scenario-reduction techniques. This article presents simplified algorithms for wind power scenario generation and reduction. A time series based auto regressive moving average model is used for scenario generation, and probability distance based backward reduction is used for scenario reduction. The algorithms have been implemented for next-day scenario generation of wind farm located at Barnstable, Massachusetts, USA. The results prove the ability of the proposed algorithms in wind uncertainty modeling. These algorithms can successfully be utilized to generate optimal wind power bids for trading in electricity markets.

The evolving military capability requirements (CRs) must be meted continuously by the multi-stage weapon equipment mix production planning (MWEMPP). Meanwhile, the CRs possess complex uncertainties with the variant military tasks in the whole planning horizon. The mean-value deterministic programming technique is difficult to deal with the multi-period and multi-level uncertain decision-making problem in MWEMPP. Therefore, a multi-stage stochastic programming approach is proposed to solve this problem. This approach first uses the scenario tree to quantitatively describe the bi-level uncertainty of the time and quantity of the CRs, and then build the whole off-line planning alternatives assembles for each possible scenario, at last the optimal planning alternative is selected on-line to flexibly encounter the real scenario in each period. A case is studied to validate the proposed approach. The results confirm that the proposed approach can better hedge against each scenario of the CRs than the traditional mean-value deterministic technique.

We consider an uncapacitated multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We assume a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We consider a multi-stage stochastic integer programming approach relying on scenario trees to represent the uncertain information structure and propose a solution method based on an extension of the stochastic dual dynamic programming algorithm. Our results show that this approach can provide good quality solutions for large-size instances in a reasonable time and significantly outperforms the use of a stand-alone mathematical solver.