Bun splitting: an online cutting problem with defects from the food industry

ABSTRACT

In this article we address an online cutting problem with defects that arises in the food industry originally proposed by Glass and van Oostrum ([2010]. “Bun Splitting: A Practical Cutting Stock Problem.” Annals of Operations Research 179: 15–33): the Bun Splitting Problem. The problem involves splitting buns that are baked in large trays into package-size blocks while removing defective buns. Removing defective buns results in small blocks of buns that need to be assembled into package-size blocks at the subsequent packing phase. The primary objective in this splitting process is the minimisation of packing time; however, reducing the number of small blocks awaiting assembly is also a secondary concern. In this study, we relax simplifying assumptions imposed in the previous work to allow for multiple defects in the tray, production switchovers between different package sizes as well as a general defect distribution on the tray. We solve the resulting online cutting problem using a dynamic programming-based algorithm and demonstrate that the algorithm is capable of producing locally optimal solutions in a real-time production environment. We also discuss how the same approach can be adopted to other cutting problems with defects from various industries.

KEYWORDS:

• Cutting stock problem
• dynamic programming
• defects
• optimisation
• food industry

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Bahadır Durak

Bahadır Durak received both his B.S. degree in 2007 and his M.S. degree in 2010 in Industrial Engineering from Middle East Technical University, Ankara, Turkey. He completed his Ph.D. degree in Industrial and Systems Engineering from Yeditepe University, Istanbul, Turkey in 2018. Upon receiving his Ph.D. degree, he joined the Research and Development Center of OBASE Software and Consulting, Inc. in Istanbul where he has been developing optimisation-based decision support systems for the retail industry. His research interests include problems in the areas of retail, human capital management, e-commerce and the solution of these problems using mathematical modelling, machine learning, deep learning and natural language processing.

Dilek Tuzun Aksu

Dilek Tuzun Aksu completed her B.S. degree in Industrial Engineering at Boğaziçi University in 1992 and received her Ph.D. in the same field from Lehigh University in 1998. After graduating from Lehigh, she joined the Research and Development group within the Information Services Division at United Airlines. During her six-year tenure at United, she lead a range of R&D projects in the areas of inventory planning, supply chain management, scheduling and manpower planning. Since 2005, she has been a full-time faculty member of the Industrial and Systems Engineering Department at Yeditepe University in Istanbul, Turkey. In addition to her academic work, she also serves as a consultant for the R&D Center at Obase Software and Consulting, Inc. Her primary research interests include mathematical modelling and combinatorial optimisation with particular emphasis on problems in airline and airport operations, routing and public transportation, disaster management and manufacturing as well as data analytics applications in retail operations.