Temporal and spatial Lagrangean decompositions in multi-site, multi-period production planning problems with sequence-dependent changeovers

Terrazas-Moreno, Sebastian; Trotter, Philipp A.; Grossmann, Ignacio E.

doi:10.1016/j.compchemeng.2011.01.004

Cited by 33 publications

(18 citation statements)

References 8 publications

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“…a source of nonconvexity, there is a duality gap between the solution of the Lagrangean dual problem and the primal problem. Moreover, it has been shown by [19] that the temporal dual bound is at least as tight as the spatial dual bound. Therefore, in this work we focus on the TLD only.…”

Section: Lagrangean Decompositionmentioning

confidence: 99%

“…Upper and lower bounds on the production amounts for each product are enforced in constraints (18) and (19). Figure 5 shows the schematic for the material and inventory balances.…”

Section: Materials and Inventory Balancesmentioning

confidence: 99%

“…For instance, [17] proposed a Bilevel Decomposition algorithm, which involves solving an aggregate formulation in the upper level and a detailed formulation in the lower level with some decisions fixed by the upper level. Lagrangean Decomposition, a particular case of Lagrangean Relaxation [18], has also been investigated by [19] who decomposed their planning problem temporally and spatially in order to solve large instances. A review of methods and decomposition approaches for the integration of planning and scheduling can be found in the work by [20].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Bilevel-Lagrangean Decomposition Scheme for the Integration of Planning and Scheduling of a Network of Batch Plants

Calfa

Agarwal

Grossmann

et al. 2013

Ind. Eng. Chem. Res.

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Motivated by a real-world industrial problem, this work deals with the integration of planning and scheduling in the operation of a network of batch plants. The network consists of single-stage, multiproduct batch plants located in different sites, which can exchange intermediate products in order to blend them to obtain finished products. The time horizon is given and divided into multiple time periods, at the end of which the customer demands have to be exactly satisfied. The planning model is a simplified and aggregate formulation derived from the detailed precedence-based scheduling formulation. Traveling Salesman Problem (TSP) constraints are incorporated at the planning level in order to predict the sequence-dependent changeovers between groups of products, within and across time periods, without requiring the detailed timing of operations, which is performed at the scheduling level. In an effort to avoid solving the full-space, rigorous scheduling model, especially for large problem sizes, two decomposition strategies are investigated: Bilevel and Temporal Lagrangean. We demonstrate that Bilevel Decomposition is efficient for small to medium problem instances and that further decomposition of the planning problem, yielding a hybrid decomposition scheme, is advantageous for tackling a large-scale industrial test case. ysl ill t 0-1 variable to force only one plant l to ship product i to customer l at time period t Notation Planning Model Variablesyg gult 0-1 variable to denote the assignment of group g to unit u of plant l at time period t ygf gult 0-1 variable to denote the first group g assigned to unit u of plant l at time period t ygl gult 0-1 variable to denote the last group g assigned to unit u of plant l at time period t yp iult 0-1 variable to denote the assignment of product i to unit u of plant l at time period t zg gg ult 0-1 variable to denote if group g is followed by group g in unit u of plant l within time period t zzg gg ult 0-1 variable to denote if link between group g and group g in unit u of plant l within time period t is broken zzzg gg ult 0-1 variable to denote a changeover between group g and group g in unit u of plant l across time period t Unit-Specific General Precedence Model VariablesT e iult End time of product i in unit u of plant l at time period t T s iult Start time of product i in unit u of plant l at time period t 4 wp ii ult 0-1 variable to denote changeover between product i and product i in unit u of plant l across time period t xp ii ult 0-1 variable to denote local precedence between product i and product i in unit u of plant l within time period t yp iult 0-1 variable to denote the assignment of product ito unit u of plant l at time period t ypf iult 0-1 variable to denote the first product i assigned to unit u of plant l at time period t ypl iult 0-1 variable to denote the last product i assigned to unit u of plant l at time period t zp ii ult 0-1 variable to denote global precedence between product i and product i in unit u of plant l within time period t

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Section: Lagrangean Decompositionmentioning

confidence: 99%

“…Upper and lower bounds on the production amounts for each product are enforced in constraints (18) and (19). Figure 5 shows the schematic for the material and inventory balances.…”

Section: Materials and Inventory Balancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hybrid Bilevel-Lagrangean Decomposition Scheme for the Integration of Planning and Scheduling of a Network of Batch Plants

Calfa

Agarwal

Grossmann

et al. 2013

Ind. Eng. Chem. Res.

Self Cite

View full text Add to dashboard Cite

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“…Other contributions include methods for accelerating convergence through the use of subgradients (Baker and Sheasby, 1999;Fumero, 2001) and other strategies (Buil, et al 2012). In Terrazas-Moreno et al (2011), an economic interpretation of the multipliers is given, which can benefit from the problem structure to accelerate the convergence. Considering that the dual problem is a high-dimensional nonlinear problem, the shape of its domain and contours is a key to accelerate the convergence, and the interpretation from an economic view may be helpful.…”

Section: Introductionmentioning

confidence: 99%

“…According to the problem structure, temporal and spatial decomposition can be adopted (Terrazas-Moreno, et al 2011). The subgradient optimization is a popular method for updating the multipliers in Lagrangean decomposition (Baker and Sheasby, 1999), although the convergence of the multipliers is the main challenge.…”

Section: Introductionmentioning

confidence: 99%

Optimal supply chain design and management over a multi-period horizon under demand uncertainty. Part II: A Lagrangean decomposition algorithm

Jiang

Rodríguez

Harjunkoski

et al. 2014

Computers & Chemical Engineering

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In Part I (Rodriguez, et al., 2013 an optimization model was proposed to redesign the supply chain of spare parts industry under demand uncertainty in a specified planning horizon. To address large industrial problems, a Lagrangean scheme is proposed to decompose the MINLP of Part I according to the warehouses by dualizing the logic constraints that assign the warehouses to different customers, together with the demand constraints and factory capacity constraints. The subproblems are first approximated by an adaptive piece-wise linearization scheme that provides lower bounds, and the MILP is further relaxed to an LP to improve solution efficiency while providing a valid lower bound. An initialization scheme is designed to obtain good initial Lagrange multipliers, which are scaled to accelerate the convergence. The results from an illustrative problem and two real world industrial problems show that the method can obtain optimal or near optimal solutions in modest computational times.

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Multiechelon supply chain planning with sequence‐dependent changeovers and price elasticity of demand under uncertainty

2012

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An optimization framework is proposed for a multiechelon multiproduct process supply chain planning under demand uncertainty considering inventory deviation and price fluctuation. In this problem, the sequence‐dependent changeovers occur at the production plants, and price elasticity of demand is considered at the markets. Based on the classic formulation of travelling salesman problem (TSP), a mixed‐integer liner programming (MILP) is developed, whose objective function considers the profit, inventory deviations from the desired trajectories and price changes simultaneously. Model predictive control (MPC) approach is adopted to tackle the uncertain issues, as well as the inventory and price maintenance. The applicability of the proposed model and approach was illustrated by solving a supply chain example. Some issues, including length of the control horizon, price elasticity of demand, weights, inventory trajectories, and changeovers, are discussed based on the computational results. © 2012 American Institute of Chemical Engineers AIChE J, 2012

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Temporal and spatial Lagrangean decompositions in multi-site, multi-period production planning problems with sequence-dependent changeovers

Cited by 33 publications

References 8 publications

Hybrid Bilevel-Lagrangean Decomposition Scheme for the Integration of Planning and Scheduling of a Network of Batch Plants

Hybrid Bilevel-Lagrangean Decomposition Scheme for the Integration of Planning and Scheduling of a Network of Batch Plants

Optimal supply chain design and management over a multi-period horizon under demand uncertainty. Part II: A Lagrangean decomposition algorithm

Multiechelon supply chain planning with sequence‐dependent changeovers and price elasticity of demand under uncertainty

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