Multi-stage Stochastic Programming Approach Research Articles

Green and reliable medical device supply chain network design under deep dynamic uncertainty: A novel approach in the context of COVID-19 outbreak

Conditions governing industrial activities during and after global shocks with societal and economic transformations such as the COVID-19 pandemic have led to the loss of effectiveness of conventional approaches to dealing with uncertainties. The occurrence of sharp fluctuations in the essential parameters has left decision-makers in an unpredictable situation. Therefore, proactive efforts should be made to develop current approaches for adapting to new conditions. This paper establishes a strategic, tactical, and operational decision-making framework under the COVID-19 outbreak by developing a new uncertainty type called deep dynamic uncertainty. In the first step, a Mixed-Integer Linear Programming (MILP) model is proposed for the green and reliable closed-loop supply chain network design. The proposed model allows the decision-maker (DM) to manage and control co2emissions and e-waste generation. In the second step, a new three-step algorithm called Augmented Adjustable Column-Wise Robust Optimization (AACWRO) is first proposed. Then, by combining the proposed column-wise uncertainty with multi-stage stochastic programming (MSSP) approach, deep dynamic uncertainty is theorized for modeling the demand uncertainty under pandemic conditions. The model's performance under deep dynamic uncertainty has been carefully investigated based on the real ventilator and infusion pump supply chain network in Iran. The model under deep dynamic uncertainty, while maintaining tractability and adjustability, provides flexibility in entering data into the problem and significantly increases the coverage of modeling uncertainties. The results clearly demonstrate the efficiency of the proposed approach. The model under deep dynamic uncertainty at all levels of conservatism has on average 42.96% lower cost and 32% higher stability than the MSSP model.

A multi-stage stochastic programming approach for an inventory–routing problem considering life cycle

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.

Hydropower preventive maintenance scheduling in a deregulated market: A multi-stage stochastic programming approach

Hydropower preventive maintenance scheduling in a deregulated market: A multi-stage stochastic programming approach

Toward circular economy for pomegranate fruit supply chain under dynamic uncertainty: A case study

Food security is a fundamental prerequisite of human survival. This study focuses on providing a novel bi-objective model for the design of a green closed-loop pomegranate supply chain based on the value chain. To maximize the benefits of circular economy, we propose a thermochemical conversion process and develop a novel hybrid risk-neutral and risk-averse multi-stage stochastic programming (RNRAMSSP) approach to cope with supply uncertainty. We employ the expected value of perfect information (EVPI) and value of stochastic solution (VSS) to validate the proposed approach. For the VSS metric, we define a novel measure to compare the worst-case cost of the stochastic and deterministic model solutions. To demonstrate the applicability of the proposed model, we provide a real case study in Iran. Based on the VSS metric, the risk-neutral and risk-averse stochastic model solutions save up to 1% and 1.76% in the worst-case cost, respectively, compared to the deterministic model.

Large-scale financial planning via a partially observable stochastic dual dynamic programming framework

The multi-stage stochastic programming (MSP) approach is widely used to solve financial planning problems owing to its flexibility. However, the size of an MSP problem grows exponentially with the number of stages, and such problem can easily become computationally intractable. Financial planning problems often consider planning horizons of several decades, and thus, the curse of dimensionality can become a critical issue. Stochastic dual dynamic programming (SDDP), a sampling-based decomposition algorithm, has emerged to resolve this issue. While SDDP has been successfully implemented in the energy domain, few applications of SDDP are found in the finance domain. In this study, we identify the major obstacle in using SDDP to solve financial planning problems to be the stagewise independence assumption and propose a partially observable SDDP (PO-SDDP) framework to overcome such limitations. We argue that the PO-SDDP framework, which models uncertainties using discrete-valued partially observable Markov states and introduces feasibility cuts, can properly address large-scale financial planning problems.

A multi-stage stochastic programming approach for pre-positioning of relief supplies considering returns

A dynamic pre-positioning problem is proposed to efficiently respond to victims’ need for relief supplies under uncertain and dynamic demand in humanitarian relief. The problem is formulated as a multi-stage stochastic programming model that considers pre-positioning with the dynamic procurement and return decisions about relief supplies over a time horizon. To validate the advantages of dynamic pre-positioning, three additional pre-positioning strategies are presented: pre-positioning with one-time procurement and without returns, pre-positioning with one-time procurement and returns, and pre-positioning with dynamic procurement and without returns. Using data from real-world disasters in the United States in the Emergency Events Database, we present a numerical analysis to study the applicability of the proposed models. We develop a sample average approximation approach to solving the proposed model in large-scale cases. Our main contribution is that we integrate dynamic procurement and return strategies into pre-positioning to decrease both costs and shortage risks in uncertain and dynamic contexts. The results illustrate that dynamic pre-positioning outperforms the other three strategies in cost savings. It also indicates that a higher return price is particularly helpful for decreasing unmet demand. The proposed models can help relief agencies evaluate and choose the solutions that will have the greatest overall effectiveness in the context of different relief practices.

The impact of transshipment on an integrated platelet supply chain: A multi-stage stochastic programming approach

This paper presents a multi-stage stochastic optimization model to minimize total cost under centralized control for a multi-echelon platelet supply chain which takes into account transshipment, demand uncertainty, stock age information, two types of supply, and three types of patients. The objective is to study the impact of transshipment between hospitals on performance improvement using a multi-stage stochastic framework to capture dynamic demand so as to explore approaches to improve an integrated platelet supply chain. Applicability of the model is tested through a real-world platelet supply chain with one blood center, three collection facilities, and five hospitals. The proposed multi-stage stochastic model is shown to perform better than a two-stage stochastic program in handling random daily demand and it also shows transshipment helps with alleviating shortage and wastage and reallocating stock at hospitals to improve system cost efficiency. Further, sensitivity analysis indicates that recruiting more apheresis platelet donors at hospitals and maintaining an initial inventory level that is close to the daily demand of hospitals are efficient strategies to improve performance of the platelet supply chain. In addition, we observed that imposing a FIFO issuing policy is not necessary for achieving optimal performance. These findings suggest that administrators and decision makers can improve cost efficiency in the platelet supply chain by implementing transshipment between hospitals, recruiting more donors, maintaining a suitable inventory level, and making collection and production plans in a shorter stage length.

A stochastic dual dynamic integer programming based approach for remanufacturing planning under uncertainty

ABSTRACT We seek to optimize the production planning of a three-echelon remanufacturing system under uncertain input data. We consider a multi-stage stochastic integer programming approach and use scenario trees to represent the uncertain information structure. We introduce a new dynamic programming formulation that relies on a partial nested decomposition of the scenario tree. We then propose a new approximate stochastic dual dynamic integer programming algorithm based on this partial decomposition. Our numerical results show that the proposed solution approach is able to provide near-optimal solutions for large-size instances with a reasonable computational effort.

Multistage Stochastic Programming for VPP Trading in Continuous Intraday Electricity Markets

The stochastic nature of renewable energy sources has increased the need for intraday trading in electricity markets. Intradaymarkets provide the possibility to the market participants to modify their market positions based on their updated forecasts. In this paper, we propose a multistage stochastic programming approach to model the trading of a Virtual Power Plant (VPP), comprising thermal, wind and hydro power plants, in the Continuous Intraday (CID) electricity market. The order clearing in the CID market is enabled by the two presented models, namely the Immediate Order Clearing (IOC) and the Partial Order Clearing (POC). We tackle the proposed problem with a modified version of Stochastic Dual Dynamic Programming (SDDP) algorithm. The functionality of our model is demonstrated by performing illustrative and large scale case studies and comparing the performance with a benchmark model.

Modeling and optimization of bioethanol production planning under hybrid uncertainty: A heuristic multi-stage stochastic programming approach

When making planning decisions, fluctuation in both product demand and yield for the bioethanol plant denotes an important factor to affect the results. In this paper, a mixed multi-stage stochastic optimization model is proposed to solve the production planning problem of a bioethanol plant with multiple raw materials simultaneously considering uncertain demand and yield. The multi-source uncertainty is described as a multi-layer hybrid scenario tree model according to the historical statistics. Due to the diversity of pretreatment approach in the bioethanol production process, the yield of saccharification liquid is different. At each node of the scenario tree, the uncertainty of demand is expressed by probability. The uncertain scenarios of the yield are integrated at each node of demand to form a mixed scenario tree. To improve the solution efficiency, a heuristic algorithm based on fast forward selection is designed to simplify the decomposition of the large-scale hybrid scenario tree in the mixed multi-stage stochastic programming problem. The effectiveness of the proposed model is verified by a practical case. The results show that the proposed approach performs better than the two-stage stochastic programming and the deterministic approaches, and the algorithm can significantly reduce the computational efforts.

A Multi-Stage Stochastic Programming Approach for Dynamic Pre-Positioning of Relief Supplies Considering Return

A Multi-Stage Stochastic Programming Approach for Dynamic Pre-Positioning of Relief Supplies Considering Return

Design of control strategies to help prevent the spread of COVID-19 pandemic

This paper proposes control strategies to allocate COVID-19 patients to screening facilities, health facilities, and quarantine facilities for minimizing the spread of the virus by these patients. To calculate the transmission rate, we propose a function that accounts for contact rate, duration of the contact, age structure of the population, susceptibility to infection, and the number of transmission events per contact. Moreover, the COVID-19 cases are divided into different groups according to the severity of their disease and are allocated to appropriate health facilities that provide care tailored to their needs. The multi-stage fuzzy stochastic programming approach is applied to cope with uncertainty, in which the probability associated with nodes of the scenario tree is treated as fuzzy variables. To handle the probabilistic model, we use a more flexible measure, Me measure, which allows decision-makers to adopt varying attitudes by assigning the optimistic-pessimistic parameter. This measure does not force decision-makers to hold extreme views and obtain the interval solution that provides further information in the fuzzy environment. We apply the proposed model to the case of Tehran, Iran. The results of this study indicate that assigning patients to appropriate medical centers improves the performance of the healthcare system. The result analysis highlights the impact of the demographic differences on virus transmission, and the older population has a greater influence on virus transmission than other age groups. Besides, the results indicate that behavioral changes in the population and their vaccination play a key role in curbing COVID-19 transmission.

A multi-stage stochastic programming approach to epidemic resource allocation with equity considerations.

Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals. We define two new equity metrics, namely infection and capacity equity, and explicitly consider equity for allocating treatment funds and facilities over multiple time stages. We also study the multi-stage value of the stochastic solution (VSS), which demonstrates the superiority of the proposed stochastic programming model over its deterministic counterpart. We apply the proposed formulation to control the Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and fair resource-allocation strategies. Our model balances the proportion of infections over all regions, even without including the infection equity or prevalence equity constraints. Model results also show that allocating treatment resources proportional to population is sub-optimal, and enforcing such a resource allocation policy might adversely impact the total number of infections and deaths, and thus resulting in a high cost that we have to pay for the fairness. Our multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

Stochastic Market Operation for Coordinated Transmission and Distribution Systems

This paper proposes a three-stage unit commitment model for the market operation of transmission and distribution coordination under the uncertainties of renewable generation and demand variations. The first stage is for the independent system operator (ISO) that determines the commitment decisions of the transmission-level generators and the distribution-level system reconfiguration; the second stage optimizes the transmission economic dispatch; then distribution system operators (DSOs) in the third stage perform their economic dispatch and exchange information with the ISO at the boundary nodes. Between the transmission and distribution networks, not only conventional thermal generators but renewables and variable demands are considered, which are tackled via a multi-stage stochastic programming approach. The model adopts a convexified AC branch flow formulation in the distribution system. We devise a generalized nested L-shaped algorithm to solve the proposed framework in an efficient manner. Numerical experiments on multi-scale test systems corroborate the efficacy of this strategy.

A Multi-Stage Stochastic Programming Approach to Epidemic Resource Allocation with Equity Considerations

Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals. We define two new equity metrics, namely infection and capacity equity, and explicitly consider equity for allocating treatment funds and facilities over multiple time stages. We also study the multi-stage value of the stochastic solution (VSS), which demonstrates the superiority of the proposed stochastic programming model over its deterministic counterpart. We apply the proposed formulation to control the Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and fair resource-allocation strategies. Our model balances the proportion of infections over all regions, even without including the infection equity or prevalence equity constraints. Model results also show that allocating treatment resources proportional to population is sub-optimal, and enforcing such a resource allocation policy might adversely impact the total number of infections and deaths, and thus resulting in a high cost that we have to pay for the fairness. Our multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

A Multistage Stochastic Programming Approach to the Optimal Surveillance and Control of the Emerald Ash Borer in Cities

Emerald ash borer (EAB), a wood-boring insect native to Asia and invading North America, has killed untold millions of high-value ash trees that shade streets, homes, and parks and caused significant economic damage in cities of the United States. Local actions to reduce damage include surveillance to find EAB and control to slow its spread. We present a multistage stochastic mixed-integer programming (M-SMIP) model for the optimization of surveillance, treatment, and removal of ash trees in cities. Decision-dependent uncertainty is modeled by representing surveillance decisions and the realizations of the uncertain infestation parameter contingent on surveillance as branches in the M-SMIP scenario tree. The objective is to allocate resources to surveillance and control over space and time to maximize public benefits. We develop a new cutting-plane algorithm to strengthen the M-SMIP formulation and facilitate an optimal solution. We calibrate and validate our model of ash dynamics using seven years of observational data and apply the optimization model to a possible infestation in Burnsville, Minnesota. Proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. Our comparative analysis shows that the M-SMIP model outperforms six different heuristic approaches proposed for the management of EAB. Results from optimally solving our M-SMIP model imply that under a belief of infestation, it is critical to apply surveillance immediately to locate EAB and then prioritize treatment of minimally infested trees followed by removal of highly infested trees. Summary of Contributions: Emerald ash borer (EAB) is one of the most damaging invasive species ever to reach the United States, damaging millions of ash trees. Much of the economic impact of EAB occurs in cities, where high-value ash trees grow in abundance along streets and in yards and parks. This paper addresses the joint optimization of surveillance and control of the emerald ash borer invasion, which is a novel application for the INFORMS society because, to our knowledge, this specific problem of EAB management has not been published before in any OR/MS journals. We develop a new multi-stage stochastic mixed-integer programming (MSS-MIP) formulation, and we apply our model to surveillance and control of EAB in cities. Our MSS-MIP model aims to help city managers maximize the net benefits of their healthy ash trees by determining the optimal timing and target population for surveying, treating, and removing infested ash trees while taking into account the spatio-temporal stochastic growth of the EAB infestation. We develop a new cutting plane methodology motivated by our problem, which could also be applied to other stochastic MIPs. Our cutting plane approach provides significant computational benefit in solving the problem. Specifically, proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. We calibrate and validate our model using seven years of ash infestation observations in forests near Toledo, Ohio. We then apply our model to an urban forest in Burnsville, Minnesota, that is threatened by EAB. Our results provide insights into the optimal timing and location of EAB surveillance and control strategies.

Optimisation of medical equipment replacement using stochastic dynamic programming

In this paper, the medical equipment replacement strategy is optimised using a multistage stochastic dynamic programming (SDP) approach. The outcome is an optimal path which shows whether to keep an existing piece of medical equipment (defender) or replace it with a more economical alternative (challenger). We assume that each decision can result in a number of different possible outcomes, each with a known probability. Contrary to deterministic dynamic programming, the state at the next stage is not completely determined by the state and policy decision at the current stage. Instead, the next stage depends on the operation and maintenance cost which is modelled as a stochastic variable. A Keep-Replace sequence of the highest returns (lowest costs) is the result of solving the problem using forward decision making. The benefit of the SDP solution versus that of keeping medical equipment until the end of its expected life is investigated for three scenarios: (1) no revenue for the defender and the challenger, (2) equal revenues for both, and (3) higher revenue for the challenger. The percentage of benefits relative to the current acquisition cost for the three scenarios are 616.9%, 728.2%, and 789.29%, respectively. Each percentage represents the relative difference between the equipment life cycle cost of the optimal sequence and that of the conventional sequence.

Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties

Job scheduling incorporated with material ordering can better meet practical needs and lead to overall cost reduction. In this paper, we present a stochastic approach for this joint optimization problem, considering uncertainties in job processing times and resource consumptions. We formulate this integrated problem as a multistage stochastic mixed-integer program involving endogenous uncertainties. Several theoretical properties that can reduce the model size are studied. Based on this, a branch-and-bound exact algorithm and a sampling-based approximate method are designed as solution algorithms. The effectiveness of the integrated scheduling approaches and the efficiency of the proposed solution algorithms are evaluated via numerical experiments. It is shown that our approach can greatly reduce the overall cost compared with the traditional separate production planning approach, especially when production resources are not very restricted.

A multi-stage stochastic programming approach for supply chain risk mitigation via product substitution

Trends like globalization, shorter product life-cycles, and cost reduction strategies in the global business environment have exposed many supply chains to various risks. Disruptions are one of the supply chain risks that can interrupt product flow, delay customer deliveries, and reduce supply chain revenues considerably. Prior planning for disruptions could greatly alleviate these consequences. A method to cope with disruptions is to use product substitution in the case of a product shortage. In this research, the supply chain of a livestock-drug distribution company in Iran, facing demand disruptions, has been chosen as a case study. For this purpose, a multi-stage stochastic integer programming model is proposed and solved using a customized progressive hedging algorithm. Moreover, the effect of uncertainty on the supply chain performance is measured using the value of the stochastic solution (VSS) and the expected value of perfect information (EVPI) metrics. Based on the different instances of the problem solved, the VSS metric shows that modeling and solving the proposed stochastic model could enhance the company profit by about 3.27 percent on average. In addition, the EVPI metric demonstrates that planning and investing in proactive demand management could enhance the profit up to 9.42 percent. Finally, analyses indicate that when dealing with increased demand uncertainty levels, the importance of using the proposed method increases as the profitability of the company decreases.

A multistage stochastic programming approach for preventive maintenance scheduling of GENCOs with natural gas contract

A preventive maintenance scheduling problem is studied on behalf of generation companies (GENCOs) with natural gas power plants, while taking into account their signed natural gas contracts and the opportunities of purchasing and selling natural gas in the spot market. This paper considers the uncertain prices of both natural gas and electricity in the spot market, and proposes a multistage stochastic mixed integer programming (MSMIP) model seeking the optimal operations regarding maintenance outage scheduling and natural gas trading. Large-scale MSMIP problems suffer not only the curse of dimensionality, but also computational difficulties with both discrete and continuous variables at each stage. To this respect, this paper leverages the progressive hedging algorithm based on scenario-based decomposition to solve large MSMIP problems. The solutions obtained from the algorithm exhibit promising quality under our numerical studies. Due to the independence among all the subproblems after the decomposition, the algorithm is amenable to parallel computing, which leads to faster convergence as demonstrated in the numerical results. Computational experiments also show that it is beneficial to use MSMIP while considering both maintenance planning and natural gas contracting. In addition, the results also indicate the GENCOs with a larger number of small generators perform better than those with a smaller number of big generators.