Valid inequalities for proportional lot-sizing and scheduling problem with fictitious microperiods

Kaczmarczyk, Waldemar

doi:10.1016/j.ijpe.2019.06.005

Cited by 7 publications

(7 citation statements)

References 25 publications

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“…The valid inequalities for micro-period calendar (Kaczmarczyk, 2020) and the new explicit model for setup operations overlapping multiple periods enable practical applications of models with many short micro-periods (especially in multi-level systems) with dependent demand and several production stages.…”

Section: Discussionmentioning

confidence: 99%

“…When real periods (macro-periods) are split into micro-periods with nonzero demand only at the end of the last micro-period of each macro-period, then inventory lower bound (3) should be replaced by constraints (4) (denoted here as ilbw), which are defined only for macroperiods (Kaczmarczyk, 2020).…”

Section: Valid Inequalitiesmentioning

confidence: 99%

“…Firstly, long periods make it impossible to split production lots into many small transfer lots and, therefore, force long lead times and a high work-inprocess inventory in a multilevel environment (Kaczmarczyk, 2020); i.e., in systems with dependent demand (e.g., Haase, 1994, pp. 15-18) or multi-stage flow lines (e.g., Stadtler and Sahling, 2013).…”

Section: Introductionmentioning

confidence: 99%

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Explicit Modelling of Multi-Period Setup Times in Proportional Lot-Sizing Problem with Constant Capacity

Kaczmarczyk

2021

Preprint

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The planning horizon of small bucket models is often divided into many fictitious micro-periods, with non-zero demand only in the last micro-period of each real (macro-)period. On the one hand, such models ensure schedules with short cycle times and low work-in-process inventory in multilevel systems; on the other, they make setup times that are longer than a single period more likely. This paper presents a new mixed-integer programming model for the case with setup operations that overlap multiple periods. The new model assumes that the capacity is constant in the whole planning horizon and explicitly determines the entire schedule of each changeover. Moreover, a two-level MIP heuristic is presented that uses model-specific cuts to fix a priori some minor decisions. The results of the computational experiments show that the new model and MIP heuristic require a substantially smaller computational effort from a standard MIP solver than the known models.MSC Classification: 90B30 , 90C11

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Section: Discussionmentioning

confidence: 99%

Section: Valid Inequalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Explicit Modelling of Multi-Period Setup Times in Proportional Lot-Sizing Problem with Constant Capacity

Kaczmarczyk

2021

Preprint

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“…They proposed a two-phase heuristic algorithm for this problem. Kaczmarczyk [17] addressed the proportional lot-sizing and scheduling problem with fictitious micro periods. In this regard, they designed a mixed-integer linear programming (MILP) model in which some valid inequalities were utilized.…”

Section: Literature Reviewmentioning

confidence: 99%

Capacitated lot-sizing and production sequence problem with setups complexity

Behnamian,

Fatemi Ghomi,

Karimi

et al. 2022

Scientia Iranica

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This paper considered the multi-product multi-level multi-period capacitated lot-sizing and sequencing problem with setup carry-over and sequence-dependent family setup times and costs. A formulation of the problem was provided as a mixed-integer nonlinear programming model. To propose this formulation, first, the mixed-integer nonlinear of the problem was linearized, and then converted to a mixed-integer linear program. To solve large-size instances of the problem, then, a lower bound was provided. The results confirmed the efficiency of the proposed model compared to previous models in terms of the runtime and the number of defined variables and constraints. Since this problem is NP-hard and adding other factors such as family setups, setup carry over and sequence-dependent setups increase its complexity, in this paper, a genetic algorithm (GA) was applied in large-size dimensions and its results were compared with the proposed lower bound. The numerical results showed that there is no significant difference between the results of the proposed GA and lower bound, and, so, the GA had been able to approach the optimal solution.

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“…Xu et al [21] represented a comprehensive overview and visualisation in the field of supply chain disruption based on several research papers. Kaczmarczyk [22] considered mixed-integer linear programming models of lot-sizing and scheduling problem. However, none of the authors considered shortage problem due to unreliability and solved it using variable backorder price discount in his research models.…”

Section: Literature Reviewmentioning

confidence: 99%

Effects of Unequal Lot Size and Variable Transportation in Unreliable Supply Chain Management

2020

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The effect of unreliable players on the supply chain management with a single-setup-multi-unequal-increasing-delivery-policy (SSMUID) along with a service-dependent demand and investment is discussed in this model. The manufacturer is unreliable which causes an increase of lead time and shortage. For solving the shortage problem and reducing lead time crashing cost (LTCC), an investment is utilized with the variable backorder price discounts. The number of transportation increases due to the new transportation policy and it causes pollution. Besides the fixed transportation and carbon emission cost (FTCEC), a container dependent carbon emission cost is applied. Some investments for setup cost reduction (SCR), ordering cost reduction (OCR), and quality improvement (QI) are considered. The lead time demand follows a normal distribution. The total cost of the supply chain is optimized and the model is tested numerically. The main intent of this study is to solve the shortage problem which occurs due to unreliability of the manufacturer. The study helps to reduce the unreliability issue of the manufacturer. The objective function is solved by using the classical optimization technique. Numerical results show that the discount for partial backorder enhances the profitability of the manufacturer. The sensitiveness of the parameters are discussed through the sensitivity of analysis and some special cases. Managerial insights provide the applicability of this study among different sectors.

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Valid inequalities for proportional lot-sizing and scheduling problem with fictitious microperiods

Cited by 7 publications

References 25 publications

Explicit Modelling of Multi-Period Setup Times in Proportional Lot-Sizing Problem with Constant Capacity

Explicit Modelling of Multi-Period Setup Times in Proportional Lot-Sizing Problem with Constant Capacity

Capacitated lot-sizing and production sequence problem with setups complexity

Effects of Unequal Lot Size and Variable Transportation in Unreliable Supply Chain Management

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