Stochastic Mixed-integer Model Research Articles

Comparative study of robust optimization model of multimaterial emergency logistics in an uncertain environment

AbstractGiven the significance of objective functions in alleviating human suffering within the humanitarian relief supply chain, it is imperative to consider both logistics costs and the cost of deprivation as ideal targets. This study investigates a multimaterial single‐cycle stochastic mixed integer model, integrating uncertainties about post‐disaster demand, supply survival, and road networks. An innovative heuristic approach is used to solve the stochastic facility location problem, which minimizes unfulfilled requests and response times in lexicographic order. This research also compares the cost‐minimization model of the pre‐positioning problem to an alternative model that maximizes demand satisfaction under resource constraints. Empirical validation through numerous case studies and solutions confirms the effectiveness and feasibility of the alternative model. The results of our experiments consistently demonstrate that the best solution provided by the alternative model not only satisfies the minimum cost model but also surpasses the conventional problem, without compromising performance. Consequently, it is crucial to avoid the cost‐minimization approach at the expense of human suffering.

A stochastic mixed-integer model to support foodbank resources prepositioning during the prelude to a natural disaster

A stochastic mixed-integer model to support foodbank resources prepositioning during the prelude to a natural disaster

A stochastic mixed-integer model to support foodbank resources prepositioning during the prelude to a natural disaster

A stochastic mixed-integer model to support foodbank resources prepositioning during the prelude to a natural disaster

A two-stage ambiguous stochastic program for electric vehicle charging station location problem with valet charging service

This paper introduces a new charging service mode that is emerging in the market for electric vehicles called the valet charging service. Through this service mode, a company provides free valet charging services to users that are far away from charging stations, and users can request the fee-based service when they are unwilling to charge electric vehicles themselves. The valet charging service is a new service mode that promises to alleviate users’ worries regarding the lack of nearby charging stations. However, whether such a mode truly benefits a specified system remains open to careful study. We build the charging station locating and sizing model with the valet charging service under demand uncertainty. We first formulate this problem as a two-stage stochastic mixed-integer model (TSMIP). Then, considering that the demand probability distribution is difficult to estimate, we reformulate TSMIP into a risk-averse two-stage stochastic mixed-integer model (RTSMIP) with the ambiguity set. Next, we propose an SAA-based hybrid-cut L-shaped algorithm to solve this model. By comparing the total cost of the system with and without the valet charging service under different scenarios through hypothetical numerical experiments and a realistic case study in Shanghai, meaningful insights are provided that include identifying the conditions in which the valet charging service works well and how it influences the location and capacity of charging stations. These insights provide some understanding of this new service mode that can help companies make rational decisions.

Long-term renewable electricity planning using a multistage stochastic optimization with nested decomposition

Renewable energy plays a key role in mitigating climate change and promoting the energy transition. In this context, we address two crucial consequences for planning the electricity transition: (a) substantially more complex uncertainties in variable renewable energy and (b) a requirement to co-ordinate extensive transmission investment with the newly located generating facilities. These features combine to present a major modelling challenge both for countries that have a liberalized electricity market, where long terms plans are needed to support subsidy policies, as well as for those countries which have retained central planning. This paper develops a new multistage stochastic mixed-integer model which uses a new decomposition algorithm based on stochastic dual dynamic integer programming, with a two-phase acceleration method. The scalability of the approach is demonstrated by application to China’s electric power requirements and it performs well in terms of computational tractability and policy insights.

Improving the sustainability of a reverse supply chain system under demand uncertainty by using postponement strategies.

In recent decades, issues of resource depletion and waste piling have grown at an alarming rate, which are happening in the cases of product wastes with significant residual values, such as e-waste. To address these issues, stakeholders have focused to develop a reverse supply chain (RSC) system that can sustain profitable takeback, reuse, and recycling operations in the long-term. Such a system requires efficiency in handling complex operations involving various players while being responsive to demand uncertainty and changes. One way in realizing these capabilities is by incorporating postponement concepts to the integrated RSC network, allowing the delay of operations susceptible to demand uncertainty. This study pioneers the formulation of a two-stage stochastic mixed-integer model of a multi-player RSC with speculation-postponement strategies. The sample average approximation method is used to solve and verify the proposed model that has an uncertain demand. Various speculation-postponement strategies, namely, disassembly, reconditioning, and reassembly strategies are developed to configure forecast and demand-driven RSC operations, including the purchasing, product takeback, production planning, inventory, and item speculation decisions. Numerical examples of the notebook computer RSC demonstrate that utilizing the right operation postponement can increase the network's flexibility, allowing better economic performances even under high demand uncertainty risks and stricter environmental regulations. In various cases, the RSC performs better with speculation-postponement strategies than without postponement strategy, demonstrating the proposed model's superiority. This study can provide insight to decision-makers to improve RSC sustainability through postponement. Moreover, the model is generic and can be applied to other products as well.

A Study on the Optimal Inventory Allocation for Clinical Trial Supply Chains

With increasing competition in the pharmaceutical industry, pharmaceutical companies pay more attention to improving the efficiency of clinical trial supply chains to reduce the drug supplying cost, which takes up a considerable part of the total research and development expense. To improve the efficiency of clinical trial supply chains, this study investigates the inventory levels of clinical drugs in each period at a distribution center and clinics considering the reverse replenishment, transshipment, and generalized stockout cost. The inventory allocation problem in clinical trial supply chains is formulated as a rolling horizon-based two-stage stochastic mixed-integer model where the minimal operational cost constitutes the underage cost at the production planning level of clinical trial supply chains. An algorithm extending Benders decomposition is proposed as the solution approach. We also derive several structural results and develop the reformulation method and row generation strategy to improve the efficiency of the optimization process. The effectiveness of our approach is demonstrated in the numerical experiment.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

We develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

Airline Re-Fleeting Managing Revenues and Maintenance Operations

Abstract Airline re-fleeting, also known as Demand Driven Dispatch, is the reassignment of aircraft to flights close to departure to improve operating profitability. It swaps aircraft of different sizes on flight legs to change capacity in response to demand. Schedules are usually fixed many months ahead of the departure date, with limited information about demand. Demand driven dispatch makes capacity flexible again, changing aircraft assignments nearer to departure. Using more detailed and reliable demand information to better match capacity supplied with quantity demanded, revenues may be increased and operating costs decreased. Previous research on demand driven dispatch have not incorporated or significantly simplified key issues such as revenue management and maintenance operations; making changes few days in advance to the day of operations may dramatically influence aircraft airworthiness if available flying hours until maintenance are not considered. The focus of this paper is on the integration of demand driven dispatch, revenue management and maintenance operations in an airline network environment. A stochastic mixed integer model is proposed to solve the fleet re-assignment problem while considering aircraft maintenance requirements. Stochastic demand is considered to model demand predictions. Realistic computational experiments drawn from IBERIA, the major Spanish airline, are presented.

Benders’ decomposition for concurrent redesign of forward and closed-loop supply chain network with demand and return uncertainties

This paper attempts to design a reverse supply chain network (SCN), add it to an existing multi-product forward SCN and simultaneously redesign the existing forward supply chain (SC). The problem considers uncertainty on products demand and and also returned products in multi-period context. Benders’ decomposition is applied to solve the stochastic mixed-integer model to optimality. The scenarios are generated based on the demand distribution function using Cholesky’s factorization method to consider correlation among different products’ demands. To decrease the computational effort, the number of scenarios is reduced using k-means clustering algorithm. The method is tested on a cell phone SC.

Supply chain design under quality disruptions and tainted materials delivery

Events such as the 2008 Heparin tragedy, in which patients lost their lives due to tainted pharmaceuticals, highlight the necessity for supply chain designers and planners to consider the risk of even low probability incidents in supply chains. The goal of this research is to design a single-period, single-product supply chain model with capacitated facilities to hedge against the possibility of sending tainted materials to consumers. Given that our mixed-integer stochastic model is NP-hard, we develop efficient heuristic and metaheuristic algorithms to obtain acceptable solutions. Computational experience is presented and discussed.

An accelerated scenario updating heuristic for stochastic production planning with set-up constraints in sawmills

In this article we propose an accelerated scenario updating heuristic to solve a real-world large-scale multi-stage stochastic mixed-integer model. Motivated from challenges we are facing in sawmills, the model corresponds to multi-period, multi-product production planning including setup constraints, with random yield and demand. While addressing real-life size instances of the problem, the resulting large-scale multi-stage stochastic mixed-integer model cannot be solved by commercial optimisation packages. Moreover, as the production planning model is a mixed-integer program without any special structure, developing decomposition and cutting plane algorithms to obtain good approximate solutions in reasonable time is not straightforward. We propose a successive approximation heuristic inspired from scenario updating heuristic which has been proposed for multi-stage stochastic models with partial recourse. The latter solves the problem by considering only a subset of scenarios which is updated at each iteration. We modify the scenario updating heuristic in two directions: (1) we modify the bounds on the optimal solution so as to make them valid for multi-stage stochastic models with full recourse, and (2) we propose a new scenario selection rule so as to increase the rate of convergence and the quality of solution. Computational experiments for a real-world large-scale sawmill production planning model verify the effectiveness of the proposed solution strategy in finding quickly good approximate solutions.

A scenario decomposition approach for stochastic production planning in sawmills

This study considers a real world stochastic multi-period, multi-product production planning problem. Motivated by the challenges encountered in sawmill production planning, the proposed model takes into account two important aspects: (i) randomness in yield and in demand; and (ii) set-up constraints. Rather than considering a single source of randomness, or ignoring set-up constraints as is typically the case in the literature, we retain all these characteristics while addressing real life-size instances of the problem. Uncertainties are modelled by a scenario tree in a multi-stage environment. In the case study, the resulting large-scale multi-stage stochastic mixed-integer model cannot be solved by using the mixed-integer solver of a commercial optimization package, such as CPLEX. Moreover, as the production planning model under discussion is a mixed-integer programming model lacking any special structure, the development of decomposition and cutting plane algorithms to obtain good solutions in a reasonable time-frame is not straightforward. We develop a scenario decomposition approach based on the progressive hedging algorithm, which iteratively solves the scenarios separately. CPLEX is then used for solving the sub-problems generated for each scenario. The proposed approach attempts to gradually steer the solutions of the sub-problems towards an implementable solution by adding some penalty terms in the objective function used when solving each scenario. Computational experiments for a real-world large-scale sawmill production planning model show the effectiveness of the proposed solution approach in finding good approximate solutions.

Stochastic hydro-economic modeling for optimal management of agricultural groundwater nitrate pollution under hydraulic conductivity uncertainty

In decision-making processes, reliability and risk aversion play a decisive role. This paper presents a framework for stochastic optimization of control strategies for groundwater nitrate pollution from agriculture under hydraulic conductivity uncertainty. The main goal is to analyze the influence of uncertainty in the physical parameters of a heterogeneous groundwater diffuse pollution problem on the results of management strategies, and to introduce methods that integrate uncertainty and reliability in order to obtain strategies of spatial allocation of fertilizer use in agriculture. A hydro-economic modeling approach is used for obtaining the allocation of fertilizer reduction that complies with the maximum permissible concentration in groundwater while minimizes agricultural income losses. The model is based upon nonlinear programming and groundwater flow and mass transport numerical simulation, condensed on a pollutant concentration response matrix. The effects of the hydraulic conductivity uncertainty on the allocation of nitrogen reduction among agriculture pollution sources are analyzed using four formulations: Monte Carlo simulation with pre-assumed parameter field, Monte Carlo optimization, stacking management, and mixed-integer stochastic model with predefined reliability. The formulations were tested in an illustrative example for 100 hydraulic conductivity realizations with different variance. The results show a high probability of not meeting the groundwater quality standards when deriving a policy from just a deterministic analysis. To increase the reliability several realizations can be optimized at the same time. By using a mixed-integer stochastic formulation, the desired reliability level of the strategy can be fixed in advance. The approach allows deriving the trade-offs between the reliability of meeting the standard and the net benefits from agricultural production. In a risk-averse decision making, not only the reliability of meeting the standards counts, but also the probability distribution of the maximum pollutant concentrations. A sensitivity analysis was carried out to assess the influence of the variance of the hydraulic conductivity fields on the strategies. The results show that the larger the variance, the greater the range of maximum nitrate concentrations and the worst case (or maximum value) that could be reached for the same level of reliability.

Risk conscious solution of planning problems under uncertainty by hybrid multi-objective evolutionary algorithms

Abstract We consider the risk conscious solution of planning problems with uncertainties in the problem data. The problems are formulated as two-stage stochastic mixed-integer models in which some of the decisions (first-stage) have to be made under uncertainty and the remaining decisions (second-stage) can be made after the realization of the uncertain parameters. The uncertain model parameters are represented by a finite set of scenarios. The risk conscious optimization problem under uncertainty is solved by a stage decomposition approach using a multi-objective evolutionary algorithm which optimizes the expected scenario costs and the risk criterion with respect to the first-stage decisions. The second-stage scenario decisions are handled by mathematical programming. Results from numerical experiments for two real-world problems are shown.

An efficient hybrid self-learning method for stochastic cellular manufacturing problem: A queuing-based analysis

This paper addresses a new version of Stochastic Mixed-Integer model to design cellular manufacturing systems (CMSs) under random parameters described by continues distributions. In an uncertain environment processing time, part demand, product mix, inter-arrival time and etc. may change over the period of time. Thus, during planning horizon since any of the parameters of the problem may vary widely, design decisions may be in effect. So, in this research to overcome such drawback, it’s assumed that processing time for parts on machines and arrival time for parts to cells are stochastic and described by continues distribution which yields more flexibility to analyze manufacturing framework. In such case, there are some approaches such as stochastic programming (SP), robust optimization (RO) and queuing theory which can formulate and analyze this problem. In this paper, it’s assumed that each machine works as a server and each part is a customer where servers should service to customers. Therefore, formed cells define a queue system which can be optimized by queuing theory. In this way, by optimizing a desired queue system measurement such as maximizing the probability that a server is busy, the optimal cells and part families will be formed. To solve such a stochastic and non-linear model, an efficient hybrid method based on new combination of genetic algorithm (GA) and simulated annealing (SA) algorithm will be proposed where SA is a sub-ordinate part of GA under a self-learning rule (SLR) criterion. This integrative combination algorithm is compared against global solutions obtained from branch-and-bound algorithm and a benchmark heuristic algorithm existing in the literature. Also, sensitivity analysis will be performed to illustrate behavior of the model.