Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing

Rossi, Roberto; Kilic, Onur A.; Tarim, Ş. Armağan

doi:10.1016/j.omega.2014.08.003

Cited by 53 publications

(63 citation statements)

References 39 publications

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Order By: Relevance

“…Under this strategy, the timing of orders and order-up-to-levels are expected to be determined at the beginning of the planning horizon, while associated order quantities are decided upon only when orders are issued. As illustrated in Rossi et al (2015), this strategy provides a cost performance which is close to the optimal "dynamic uncertainty" strategy. However, optimal (s, S) parameters cannot be immediately derived from existing mathematical programming models operating under a static-dynamic uncertainty strategy, such as Tarim and Kingsman (2006), and Rossi et al (2015).…”

Section: Minlp Approximation Of Scarf 'S G T (Y) Functionmentioning

confidence: 76%

Computing non-stationary (s, S) policies using mixed integer linear programming

Xiang¹,

Rossi²,

Martín-Barragán³

et al. 2018

European Journal of Operational Research

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This paper addresses the single-item single-stocking location stochastic lot sizing problem under the (s, S) policy. We first present a mixed integer non-linear programming (MINLP) formulation for determining near-optimal (s, S) policy parameters. To tackle larger instances, we then combine the previously introduced MINLP model and a binary search approach. These models can be reformulated as mixed integer linear programming (MILP) models which can be easily implemented and solved by using off-the-shelf optimisation software.Computational experiments demonstrate that optimality gaps of these models are around 0.3% of the optimal policy cost and computational times are reasonable.

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Section: Minlp Approximation Of Scarf 'S G T (Y) Functionmentioning

confidence: 76%

Computing non-stationary (s, S) policies using mixed integer linear programming

Xiang¹,

Rossi²,

Martín-Barragán³

et al. 2018

European Journal of Operational Research

Self Cite

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“…Moreover, Özen et al [20] develop a non-polynomial dynamic programming algorithm to solve the same problem. Recently, Tunç et al [36] reformulate the problem as MIP by using alternative decision variables and Rossi et al [24] propose an MIP formulation based on the piecewise linear approximation of the total cost function, for different variants of this problem.…”

Section: Literature Reviewmentioning

confidence: 99%

Stochastic lot sizing problem with controllable processing times

Koca

Yaman

Aktürk

2015

Omega

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a b s t r a c tIn this study, we consider the stochastic capacitated lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function as it may reflect increasing marginal costs of larger reductions and may be more appropriate when the resource life, energy consumption or carbon emission are taken into consideration. We consider this problem under static uncertainty strategy and α service level constraints. We first introduce a nonlinear mixed integer programming formulation of the problem, and use the recent advances in second order cone programming to strengthen it and then solve by a commercial solver. Our computational experiments show that taking the processing times as constant may lead to more costly production plans, and the value of controllable processing times becomes more evident for a stochastic environment with a limited capacity. Moreover, we observe that controllable processing times increase the solution flexibility and provide a better solution in most of the problem instances, although the largest improvements are obtained when setup costs are high and the system has medium sized capacities.

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“…[29] developed a new approximation algorithm for multi-period stochastic lotsizing inventory models with positive order lead times. [30] proposed a MILP model for non-stationary stochastic lotsizing problem where lost sales are considered. [31] applied a multiple-stage stochastic programming approach for joint stochastic single-item CLSP and pricing problem with backlogging.…”

Section: Ml-clsp Modelmentioning

confidence: 99%

A novel fuzzy stochastic multi-objective linear programming for multi-level capacitated lot-sizing problem: a real case study of a furniture company

Sahebjamnia

Jolai

Torabi

et al. 2015

Int J Adv Manuf Technol

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This paper develops a fuzzy stochastic multiobjective linear programming model for a multi-level, capacitated lot-sizing problem (ML-CLSP) in a mixed assembly shop. The proposed model aims to minimize the total cost consisting of total variable production cost, inventory cost, backorder cost, and setup cost while maximizing the resource utilization rate simultaneously. To cope with inherent mixed fuzzy stochastic uncertainty associated with input data, e.g., the demand and process-related parameters, they are treated as fuzzy stochastic parameters. We conducted a numerical example from literature to illustrate the efficiency of the proposed method against other ones. To validate the expediency of the proposed ML-CLSP and solution method, a real case study was executed in a furniture company. The results demonstrate the usefulness of the proposed model and its solution approach.

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Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing

Cited by 53 publications

References 39 publications

Computing non-stationary (s, S) policies using mixed integer linear programming

Computing non-stationary (s, S) policies using mixed integer linear programming

Stochastic lot sizing problem with controllable processing times

A novel fuzzy stochastic multi-objective linear programming for multi-level capacitated lot-sizing problem: a real case study of a furniture company

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