General lot-sizing and scheduling for perishable food products

General lot-sizing and scheduling is a well-studied problem in the literature, but for perishable or time-sensitive products is less investigated. Also, most of studies on perishable product supply chains focus on strategic and tactical decision levels rather than operational decision level and integrated operational and tactical decision levels. We focus on a general lot-sizing and scheduling problem faced by perishable food products. The lifespan and shelf life are two important key features of perishable products that are considered in the problem. This problem can be described as a multi-product, multi-parallel line, multi-period general lot-sizing and scheduling problem with sequence dependent change over time. The objective function is sum of production costs, inventory holding costs, waste costs, and lifespan related cost function. We apply two mixed-integer programming based heuristics to solve generated instances. The heuristics are compared in terms of solution quality and computational time. Also, the sensitivity analysis is presented to analyze the effects of parameters’ changes.

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A Novel MILP Model for the Production, Lot Sizing, and Scheduling of Automotive Plastic Components on Parallel Flexible Injection Machines with Setup Common Operators

Complexity ◽

10.1155/2021/6667516 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

Beatriz Andres ◽

Eduardo Guzman ◽

Raul Poler

Keyword(s):

Supply Chain ◽

Lot Sizing ◽

Mixed Integer ◽

Computational Time ◽

Scheduling Problem ◽

Automotive Supply Chain ◽

Milp Model ◽

Plastic Components ◽

Automotive Supply ◽

Lot Sizing And Scheduling

In this article, a mixed integer linear program (MILP) model is proposed for the production, lot sizing, and scheduling of automotive plastic components to minimize the setup, inventory, stockout, and backorder costs, by taking into account injection molds as the main index to schedule on parallel flexible injection machines. The proposed MILP considers the minimum and maximum inventory capacities and penalizes stockout. A relevant characteristic of the modeled problem is the dependence between mold setups to produce plastic components. The lot sizing and scheduling problem solution results in the assignment of molds to machines during a specific time period and in the calculation of the number of components to be produced, which is often called lot size, following a sequence-dependent setup time. Depending on the machine on which the mold is setup, the number of units to be produced will be distinct because machines differ from one another. The stock coverage, defined in demand days, is also included in the MILP to avoid backorders, which is highly penalized in the automotive supply chain. Added to this, the proposed model is extended by considering setup common operators to respond to and fulfill the constraints that appear in automotive plastic enterprises. In this regard, the MILP presented solves a lot-sizing and scheduling problem, emerged in a second-tier supplier of a real automotive supply chain. Finally, this article validates the MILP by performing experiments with different sized instances, including small, medium, and large. The large-sized dataset is characterized by replicating the amount of data used in the real enterprise, which is the object of this study. The goodness of the model is evaluated with the computational time and the deviation of the obtained results as regards to the optimal solution.

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Study on column generation for the lot-sizing and scheduling problem with sequencedependent setup time

MATEC Web of Conferences ◽

10.1051/matecconf/201818906002 ◽

2018 ◽

Vol 189 ◽

pp. 06002

Author(s):

Dandan Zhang ◽

Canrong Zhang

Keyword(s):

Lot Sizing ◽

Setup Time ◽

Mixed Integer ◽

Scheduling Problem ◽

Optimal Solutions ◽

Sequence Dependent ◽

Sequence Dependent Setup Time ◽

Capacitated Lot Sizing ◽

Sequence Dependent Setup ◽

Lot Sizing And Scheduling

The capacitated lot-sizing and scheduling problem with sequence-dependent setup time and carryover setup state is a challenge problem in the semiconductor assembly and test manufacturing. For the problem, a new mixed integer programming model is proposed, followed by exploring its relative efficiency in obtaining optimal solutions and linearly relaxed optimal solutions. On account of the sequence-dependent setup time and the carryover of setup states, a per-machine Danzig Wolfe decomposition is proposed. We then build a statistical estimation model to describe correlation between the optimal solutions and two lower bounds including the linear relaxation solutions, and the pricing sub-problem solutions of Danzig Wolfe decomposition, which gives insight on the optimal values about information regarding whether or not the setup variables in the optimal solution take the value of 1, and the information is further used in the branch and select procedure. Numerical experiments are conducted to test the performance of the algorithm.

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Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources

RAIRO - Operations Research ◽

10.1051/ro/2021084 ◽

2021 ◽

Author(s):

Willy Alves de Oliveira Soler ◽

Maristela Oliveira Santos ◽

Maria do Socorro Nogueira Rangel

Keyword(s):

Lot Sizing ◽

Computational Study ◽

Mixed Integer ◽

Optimization Models ◽

Scheduling Problem ◽

Production Lines ◽

Commodity Flow ◽

Scarce Resources ◽

Computational Performance ◽

Lot Sizing And Scheduling

The purpose of this paper is to propose mathematical models to represent a lot sizing and scheduling problem on multiple production lines that share scarce resources and to investigate the computational performance of the proposed models. The main feature that differentiates this problem from others in the literature is that the decision on which lines to organize should be taken considering the availability of the necessary resources. The optimization criterion is the minimization of the costs incurred in the production process (inventory, backlogging, organization of production lines, and sequence-dependent setup costs). Nine mixed integer optimization models to represent the problem are given and, also, the results of an extensive computational study carried out using a set of instances from the literature. The computational study indicates that an efficient formulation, able to provide high quality solutions for large sized instances, can be obtained from a classical model by making the binary production variables explicit, using the facility location reformulation as well as the single commodity flow constraints to eliminate subsequences. Moreover, from the results, it is also clear that the consideration of scarce resources makes the problem significantly more difficult than the traditional one.

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Extended Model Formulation of the Proportional Lot-Sizing and Scheduling Problem with Lost Demand Costs

Decision Making in Manufacturing and Services ◽

10.7494/dmms.2011.5.1.49 ◽

2011 ◽

Vol 5 (1) ◽

pp. 49-56

Author(s):

Waldemar Kaczmarczyk

Keyword(s):

Lot Sizing ◽

Valid Inequalities ◽

Mixed Integer ◽

Extended Model ◽

Scheduling Problem ◽

Scheduling Problems ◽

Model Formulation ◽

Mip Models ◽

Planning Problems ◽

Lot Sizing And Scheduling

We consider mixed-integer linear programming (MIP) models of production planning problems known as the small bucket lot-sizing and scheduling problems. We present an application of a class of valid inequalities to the case with lost demand (stock-out) costs. Presented results of numerical experiments made for the the Proportional Lot-sizing and Scheduling Problem (PLSP) confirm benefits of such extended model formulation.

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