A Two-Stage Modeling and Solution Framework for Multisite Midterm Planning under Demand Uncertainty

Abstract

A two-stage, stochastic programming approach is proposed for incorporating demand uncertainty in multisite midterm supply-chain planning problems. In this bilevel decision-making framework, the production decisions are made "here-and-now" prior to the resolution of uncertainty, while the supply-chain decisions are postponed in a "wait-and-see" mode. The challenge associated with the expectation evaluation of the inner optimization problem is resolved by obtaining its closed-form solution using linear programming (LP) duality. At the expense of imposing the normality assumption for the stochastic product demands, the evaluation of the expected secondstage costs is achieved by analytical integration yielding an equivalent convex mixed-integer nonlinear problem (MINLP). Computational requirements for the proposed methodology are shown to be much smaller than those for Monte Carlo sampling. In addition, the cost savings achieved by modeling uncertainty at the planning stage are quantified on the basis of a rolling horizon simulation study.

Mid-term supply chain planning under demand uncertainty: customer demand satisfaction and inventory management

“…The variables of this model can be partitioned into two categories (Gupta and Maranas, 2000) based on whether the corresponding tasks need to be carried out before or after demand realization. The production variables model activities such as raw material consumption, capacity utilization and final product production.…”

“…Consequently, these constitute the supply-chain variables which can be fine-tuned in a "wait-and-see" setting after realization of the actual demand. This classification of variables naturally extends to the constraints of the problem (Gupta and Maranas, 2000) and results in the following two-stage formulation. …”

“…In view of this, incorporation of demand uncertainty in midterm planning of multisite supply chains having (semi)continuous processing attributes is discussed in Gupta and Maranas (2000) through a two-stage stochastic programming framework. In this paper, the trade-off involved between inventory depletion and production costs in the face of uncertainty is captured in a probabilistic framework through chance-constraints.…”

“…Next, the key elements of the proposed solution methodology are discussed briefly. The details of the analysis can be found in Gupta and Maranas (2000). The main part of the paper proposes a chance-constraint based approach for capturing the trade-off between customer shortage and production costs.…”

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AbstractThis paper utilizes the framework of midterm, multisite supply chain planning under demand uncertainty (Gupta and Maranas, 2000) to safeguard against inventory depletion at the production sites and excessive shortage at the customer. A chance constraint programming approach in conjunction with a two-stage stochastic programming methodology is utilized for capturing the trade-off between customer demand satisfaction (CDS) and production costs.

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