A bilevel programming framework for enterprise-wide process networks under uncertainty

Ryu, Jun-Hyung; Dua, Vivek; Pistikopoulos, Efstratios N.

doi:10.1016/j.compchemeng.2003.09.021

Cited by 125 publications

(43 citation statements)

References 19 publications

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“…in the solution of decentralised decision makers. The presence of uncertainty in bilevel problems has been addressed before for the linear case (Ryu et al 2004). Uncertainty is considered unstructured, taking any value between its bounds.…”

Section: Qp|qp Bilevel Programming Problemmentioning

confidence: 99%

“…Applications of bilevel and multilevel programming include design optimisation problems in process systems engineering (Clark 1990;Clark and Westerberg 1990); design of transportation networks (LeBlanc and Boyce 1985); agricultural planning (Fortuny-Amat and McCarl 1981); management of multi-divisional firms (Ryu et al 2004) and hierarchical decision-making structures (Fortuny-Amat and McCarl 1981). These multilevel problems are classified accordingly to the number of levels and the type of their cost functions and variables: if the problem has two levels, where both cost functions are affine functions and the variables are continuous, the problem is classified as a linear BLPP; if at least one of these functions has a quadratic expression, it is a quadratic BLPP; adding uncertainty to the formulations results in a BLPP with uncertainty; on the other hand, if binary and continuous variables coexist in the same bilevel problem formulation, it corresponds to a mixed integer BLPP.…”

Section: Introductionmentioning

confidence: 99%

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Parametric global optimisation for bilevel programming

et al. 2006

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We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower's) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader's) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.

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Section: Qp|qp Bilevel Programming Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parametric global optimisation for bilevel programming

et al. 2006

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“…However, the literature of bilevel approaches to inventory problems is rather scarce. The most relevant references include [6] and [14], where two different production and delivery planning problems are investigated in extended supply chain, with the goal of constructing plans that are locally optimal for the individual parties as well. In [17], the problem of coordinated planning in a supply chain under hard service time requirements is investigated, where a central coordinating agency allocates desired response times to the individual parties.…”

Section: Bilevel Approachmentioning

confidence: 99%

Inventory control in supply chains: Alternative approaches to a two-stage lot-sizing problem

Kovács

Egri

Kis

et al. 2013

International Journal of Production Economics

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The principal challenge of inventory control in supply chains is that the interacting autonomous enterprises have to plan their production and logistics under information asymmetry, driven by different, often conflicting objectives. In this paper, four different computational approaches are investigated to cope with this challenge: decomposition, integration, coordination, and bilevel programming. The four approaches are applied to solving the same two-stage economic lot-sizing problem, and compared in computational experiments. The prerequisites of the approaches are analyzed, and it is shown that the profits realized and the costs incurred at the different parties largely depend on the solution approach applied. This research also resulted in a novel coordination mechanism, as well as a new algorithm for the bilevel optimization approach to the investigated lot-sizing problem. A specific goal of this study is to highlight the so far less recognized application potential of the coordination and the bilevel optimization approaches for controlling inventories in a supply chain.

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“…Since then, hierarchical decision making has found application to numerous practical problems across various disciplines, such as economics, management, agriculture, transportation and engineering [19,39,48,53,65]. Of particular interest are hierarchical systems in parameter estimation [59,66], environmental policies in biofuel production [10] and chemical equilibria [21,22].…”

Section: Introductionmentioning

confidence: 99%

Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development

Kleniati

Adjiman

2014

J Glob Optim

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We present a global optimization algorithm, Branch-and-Sandwich, for optimistic bilevel programming problems that satisfy a regularity condition in the inner problem. The functions involved are assumed to be nonconvex and twice continuously differentiable. The proposed approach can be interpreted as the exploration of two solution spaces (corresponding to the inner and the outer problems) using a single branch-and-bound tree. A novel branching scheme is developed such that classical branch-and-bound is applied to both spaces without violating the hierarchy in the decisions and the requirement for (global) optimality in the inner problem. To achieve this, the well-known features of branch-and-bound algorithms are customized appropriately. For instance, two pairs of lower and upper bounds are computed: one for the outer optimal objective value and the other for the inner value function. The proposed bounding problems do not grow in size during the algorithm and are obtained from the corresponding problems at the parent node.Keywords Bilevel programming · Nonconvex inner problem · Branch and bound

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A bilevel programming framework for enterprise-wide process networks under uncertainty

Cited by 125 publications

References 19 publications

Parametric global optimisation for bilevel programming

Parametric global optimisation for bilevel programming

Inventory control in supply chains: Alternative approaches to a two-stage lot-sizing problem

Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development

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