Abstract
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.
Highlights
Production planning, sequencing, and scheduling are key operations performed by enterprises, and any circumstances or events that affect them strongly influence the supply chain operation in which they are embedded
By continuing with the future research lines indicated by these authors, our study considers many periods when modeling and running experiments to solve the lot-sizing and scheduling problem (LSSP). e base model proposed bears in mind stock coverage constraints, which are typical in the studied automotive supply chain industry context. e proposed novel mixed integer linear program (MILP) contemplates an objective function based on the assembly line and allows idle times among molds, which is a fundamental characteristic for real cases and has been ignored by former studies
In order to give the reader a clear insight of the input data parameter values and the output data results once implemented the proposed MILP, we include an example of a small dataset size. e input data for the base LSSP model are presented at https://bit.ly/3p3IFqo. e small dataset of the base model is characterized by having 2 machines, 4 tools, 6 parts, and 3 periods. e results obtained with the decision variables in the MILP model for lot sizing and scheduling on parallel flexible injection machines are presented in Tables 6 and 7
Summary
Production planning, sequencing, and scheduling are key operations performed by enterprises, and any circumstances or events that affect them strongly influence the supply chain operation in which they are embedded. All these three planning levels are characterized by the decision-making time horizon in accordance with three decision-making levels: strategical, tactical, and operational. Our aim is to solve a lot-sizing and scheduling problem with a sequence-dependent setup on parallel flexible machines. To this end, a mixed integer linear program (MILP) model is proposed 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. We consider setup common operators to extend the proposed basic MILP model
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