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Mathematical models for a batch scheduling problem to minimize earliness and tardiness
Journal of Industrial Engineering and Management
JIEM
2013-0953
Mathematical Models for a Batch Scheduling Problem to Minimize Earliness and Tardiness
Basar Ogun
?igdem Alabas-Uslu 0
0 Marmara University, Department of Industrial Engineering , Turkey
Purpose: Today's manufacturing facilities are challenged by highly customized products and just in time manufacturing and delivery of these products. In this study, a batch scheduling problem has been addressed to enable on-time completion of customer orders in a lean manufacturing environment. The problem is optimizing the partitioning of product components into batches and scheduling of the resulting batches where each customer order is received as a set of products made of various components. Design/methodology/approach: Three different mathematical models for minimization of total earliness and tardiness of customer orders are developed to provide on-time completion of customer orders and also, to avoid excess final product inventory. The first model is a non-linear integer programming model whereas the second is a linearized version of the first. Finally, to solve larger sized instances of the problem, an alternative linear integer model is presented. Findings: Computational study using a suit set of test instances showed that the alternative linear integer model is able to solve all test instances in varying sizes within quite shorter computer times compared to the other two models. It has also been showed that the alternative model is able to solve moderate sized real-world problems. Originality/value: The problem under study differentiates from existing batch scheduling problems in the literature owing to the inclusion of new circumstances that are present in real-world applications. Those are: customer orders consisting of multi-products made of multi-parts, processing of all parts of the same product from different orders in the same batch, and delivering the orders only when all related products are completed. This research also contributes to the literature of batch scheduling problem by presenting new optimization models.
batch scheduling; earliness and tardiness; mixed integer programming formulation; on-time delivery
1. Introduction
BPM scheduling problem addressed in this study mainly stems from scheduling of a cutting machine in furniture
manufacturing. The short-term production planning problem considers the following input data: customer orders
which consist of a set of products, bill of materials which involves a set of components for each product, due
dates of the customer orders, capacity of BPM (cutting machine) in terms of number of components and finally
process time of BPM. Decision problem is to cluster the components of products into batches that have limited
capacity and also to find a production sequence for these batches. The problem intends to minimize the sum of the
weighted sum of early and late completion times of customer orders by determining optimum composition of
each batch in terms of both type and number of components as well as optimum production sequence of these
batches. To emphasize the importance of on-time completion of customer orders, we have called the problem
BPM-On-time scheduling. One of the differentiating aspect of BPM-On-time scheduling problem arises from its
policy of order of deliveries. According to this policy, a customer order cannot be delivered unless all products
ordered by the same customer are completed. The other aspect is that products are made of several components
and all components of a product belonging to the same customer order must be processed simultaneously because
of technical requirements. In other words, products of a customer order can be partitioned into different batches
but components of a product in the same customer order cannot be partitioned. This constraint is different from
the constraint of incompatible job families considered in the literature since it does not allow processing of jobs
from different job families simultaneously. Existing literature, which is closely related to the completion of
customer orders just in time, focuses on either processing of jobs in batches to minimize due date related objectives
or delivering of completed jobs in batches to minimize inventory and delivery costs. The latter is called batch
delivery and was first introduced by Cheng and Kahlbacher (1993). Batch delivery problem mainly considers
finding optimal partitions of jobs into batches for delivery. In BPM-On-time scheduling problem however, a
customer order is a given set of products and it must be delivered once all the products ordered are completed.
Therefore, BPM-On-time scheduling problem should not be treated in batch scheduling literature as batch delivery.
In this study, we aim to contribute to the literature of batch scheduling by emphasizing the differentiating
constraints of BPM-On-time scheduling problem. We also aim to contribute by suggesting optimization models t (...truncated)