Abstract
This work aims to present a methodology to support a company in the automotive business on scheduling the jobs on its final processes. These processes are: (i) checking the final product and (ii) loading the dispatch trucks. These activities are usually found in the outbound area of any manufacturing company. The problem faced is defined as the flow shop problem with precedence constraints, release dates, and delivery times. The major objective is to minimize the latest date a client receives its products. We present a time-indexed integer mathematical model to compute feasible solutions for the presented problem. Moreover, we take advantage of the Lagrangean Relaxation procedure to compute valid lower and upper bounds. The experiments were held based on the company’s premises. As a conclusion, the results showed that the methodology proposed was able to compute feasible solutions for all the instances tested. Also, the Lagrangean Relaxation approach was able to calculate better bounds in a shorter computational time than the Mathematical problem for the more complicated instances.
Highlights
Many companies sort their processes in a sequential way. e sequential standard follows quite well the concept that each process has its suppliers and clients, which may be represented by the previous and the successor processes, respectively.e problem de ned above may be viewed as a ow shop one [1]
We approach a real-world problem that may be equivalent to a ow shop problem with precedence constraints, release dates, and delivery times. e company evaluated in this work, focuses its activities on the car-assembling business
T 3: Results obtained with the linear relaxation and the LR on instances of groups 1 and 2. e Lower Bound (LB)∗values refer to the lower bounds provided by the Lagrangean Relaxation
Summary
Many companies sort their processes in a sequential way. e sequential standard follows quite well the concept that each process has its suppliers and clients, which may be represented by the previous and the successor processes, respectively. Erefore, we de ne this problem as the two-machine ow shop scheduling problem with precedence constraints, release dates and delivery times. We modeled it through a time-indexed formulation which is based on the discretization of the time horizon. 2. The Mathematical Model e two-machine ow shop scheduling problem with precedence constraints, release dates and delivery times is set as ( 2| , , | max ). E precedence constraints applied imply that to each job (truck) ∈ 2 is associated a nonempty set ⊆ 1 such that j can only be processed in M2 a er all clusters belonging to the have been processed in delivery time for each job we consider ∈ 2. The subproblem ( ) is the total weighted completion time scheduling problem on one machine. e completion of a job ∈ 1 is weighted by the sum of penalties applied
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