Stochastic Optimization Models for Supply Chain Management: Integrating Uncertainty into Decision-Making Processes (original) (raw)
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Stochastic programming approaches for risk aware supply chain network design problems
2010
In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these type of problems.
In this work, we proposed a two-stage stochastic programming model for a four-echelon supply chain problem considering possible disruptions at the nodes (supplier and facilities) as well as the connecting transportation modes and operational uncertainties in form of uncertain demands. The first stage decisions are supplier choice, capacity levels for manufacturing sites and warehouses, inventory levels, transportation modes selection, and shipment decisions for the certain periods, and the second stage anticipates the cost of meeting future demands subject to the first stage decision. Comparing the solution obtained for the two-stage stochastic model with a multi-period deterministic model shows that the stochastic model makes a better first stage decision to hedge against the future demand. This study demonstrates the managerial viability of the proposed model in decision making for supply chain network in which both disruption and operational uncertainties are accounted for.
A stochastic model for risk management in global supply chain networks
European Journal of Operational Research, 2007
With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau-Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives.
A stochastic programming approach for supply chain network design under uncertainty
European Journal of Operational Research, 2005
This paper proposes a stochastic programming model and solution algorithm for solving supply chain network design problems of a realistic scale. Existing approaches for these problems are either restricted to deterministic environments or can only address a modest number of scenarios for the uncertain problem parameters. Our solution methodology integrates a recently proposed sampling strategy, the sample average approximation (SAA) scheme, with an accelerated Benders decomposition algorithm to quickly compute high quality solutions to large-scale stochastic supply chain design problems with a huge (potentially infinite) number of scenarios. A computational study involving two real supply chain networks are presented to highlight the significance of the stochastic model as well as the efficiency of the proposed solution strategy.
Risk management for a global supply chain planning under uncertainty: Models and algorithms
AIChE Journal, 2009
In this article, we consider the risk management for mid-term planning of a global multi-product chemical supply chain under demand and freight rate uncertainty. A two-stage stochastic linear programming approach is proposed within a multi-period planning model that takes into account the production and inventory levels, transportation modes, times of shipments, and customer service levels. To investigate the potential improvement by using stochastic programming, we describe a simulation framework that relies on a rolling horizon approach. The studies suggest that at least 5% savings in the total real cost can be achieved compared with the deterministic case. In addition, an algorithm based on the multi-cut L-shaped method is proposed to effectively solve the resulting large scale industrial size problems. We also introduce risk management models by incorporating risk measures into the stochastic programming model, and multi-objective optimization schemes are implemented to establish the tradeoffs between cost and risk. To demonstrate the effectiveness of the proposed stochastic models and decomposition algorithms, a case study of a realistic global chemical supply chain problem is presented. 2009 American Institute of Chemical Engineers
Robust solutions and risk measures for a supply chain planning problem under uncertainty
Journal of the Operational Research Society, 2007
We consider a strategic supply chain planning problem formulated as a two-stage Stochastic Integer Programming (SIP) model. The strategic decisions include site locations, choices of production, packing and distribution lines, and the capacity increment or decrement policies. The SIP model provides a practical representation of real world discrete resource allocation problems in the presence of future uncertainties which arise due to changes in the business and economic environment. Such models that consider the future scenarios (along with their respective probabilities) not only identify optimal plans for each scenario, but also determine a hedged strategy for all the scenarios. We, (1) exploit the natural decomposable structure of the SIP problem through Benders' decomposition, (2) approximate the probability distribution of the random variables using the Generalised Lambda distribution, and (3) through simulations, calculate the performance statistics and the risk measures for the two models, namely the expected-value and the here-and-now.
A review of modelling approaches for supply chain planning under uncertainty
Service Systems and Service …, 2011
Since 1959 in which one of the earliest attempts to address the problem of developing a coordinated link in a supply chain (SC) was performed by [1], managing SC performance has been a main challenge among enterprises. Supply chain planning (SCP), as one of the most important processes within the supply chain management (SCM) concept, has a great impact on firms' success or failure. SCP decision has been greatly influenced by the presence of uncertainty from the intricate nature and dynamic relationship among various stages involved in the SC network. This paper aims to present an extensive review of the existing literature to acquire a deep understanding of modelling approaches used in the area of SCP under uncertainty. The research main objective is to provide a classification framework based on the following elements: problem types, sources of uncertainty, performance measures, and modelling approaches that were exploited by previous researchers. We have conducted a survey of various journal papers dated from 1993 to 2012. In conclusion, some guidelines regarding future areas of research have been identified.
A multi-objective stochastic programming approach for supply chain design considering risk
International Journal of Production Economics, 2008
In this paper, we develop a unified mixed integer linear modelling approach to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under static-dynamic uncertainty strategy. The proposed approach applies to settings in which unmet demand is backordered or lost; and it can accommodate variants of the problem for which the quality of service is captured by means of backorder penalty costs, non-stockout probabilities, or fill rate constraints. This approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the stochastic lot sizing problem, some of which have been previously tackled via ad hoc solution methods and some others that have not yet been addressed in the literature; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds based on piecewise linearisation of the first order loss function. We illustrate the effectiveness and flexibility of the proposed approach by means of a computational study.
Integrating performance and risk aspects of supply chain design processes
Production Planning & Control, 2018
Supply chain design is a complex and relatively poorly structured process, involving choosing many decisional parameters and it usually requires consideration of numerous sources of uncertainty. Many conventional processes of supply chain design involve taking a deterministic approach, using point estimates, on important measures of supply chain effectiveness such as cost, quality, delivery reliability and service levels. Supply chain disruptions are often separately considered as risks, both in the research literature and in practice, meaning that a purely traditional risk management and risk minimization approach is taken. We have developed and applied an approach that combines the intellect and experience of the supply chain designer with the power of evaluation provided by a Monte Carlo simulation model, which uses decision analysis techniques to explicitly incorporate the full spectrum of uncertain quantities across the set of alternative supply chain designs being considered. After defining and setting out the general decision variables and uncertainty factors for 16 distinct supply chain design decision categories, we then apply that approach to combine the decision-makers' heuristics with the probabilistic modeling approach, iteratively, to achieve the best of both elements of such an approach. This novel approach to fully integrating performance and risk elements of supply chain designs is then illustrated with a case study. Finally, we call for further developmental research and field work to refine this approach.