Safety stock placement with market selection under load-dependent lead times

Abstract

We study the problem of safety stock placement in a supply chain with market selection decisions. A manufacturer with deterministic, load-dependent lead time supplies multiple warehouses, each serving multiple retailers. Each retailer has access to a set of potential markets with different characteristics. Serving more markets increases revenues, but also increases the manufacturer’s lead time, resulting in higher inventory costs. Adopting the Guaranteed Service Approach, we present a nonlinear mixed-integer programming model and reformulate it to eliminate integer variables related to service times at warehouses. We then propose a successive piecewise linearization algorithm and a mixed-integer conic quadratic formulation to solve the resulting nonlinear binary formulation. Computational experiments show that the successive piecewise linearization algorithm outperforms two state-of-the-art solvers, BARON and CPLEX, which are used to solve instances of the original formulation and the mixed-integer conic quadratic reformulation, respectively. The value of incorporating load-dependent lead times is greatest when capacity is limited relative to available demand. The benefit of integrating market selection and safety stock decisions is greatest when capacity is limited and marginal revenue is relatively low.

Keywords:

• Supply chain management
• load-dependent lead time
• safety stocks
• guaranteed service
• market selection

Additional information

Funding

We acknowledge the support provided by the Research Foundation - Flanders (FWO) for the project with contract number FWO.OPR.2016.0019.01.

Notes on contributors

Foad Ghadimi

Foad Ghadimi works as a Product Analyst at OMP, which is a software and consulting company. He obtained his PhD degree in Business Economics from Ghent University and his bachelors and masters degrees in industrial engineering from Tehran Polytechnic. His doctoral research focused on how to set safety stocks and production capacity in capacitated supply chains with load dependent lead times. His key areas of interest include supply chain management, inventory optimization, and operations research.

Tarik Aouam

Tarik Aouam is professor of operations management at Ghent University, Belgium and an affiliate professor at Africa Business School, Mohammed IV Polytechnic University, Morocco. He held several academic and administrative positions at different universities in the MENA region and has worked in the airline and semiconductor industries in the US. Tarik’s research interests include operations management in general, and the optimization of operations and supply chains in particular. He has been studying models and algorithms for optimizing and coordinating procurement, production, inventory, and transportation decisions within and across firms. His articles have appeared in leading journals, including: Operations Research; European Journal of Operational Research; Omega; International journal of production economics; Journal of the Operations Research Society and Computers and Operations Research. He holds a PhD in industrial engineering from Purdue University (USA) and a Master’s degree in industrial engineering from Kansas State University (USA).

Reha Uzsoy

Reha Uzsoy is Clifton A. Anderson Distinguished Professor in the Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University. He holds BS degrees in Industrial Engineering and Mathematics and an MS in Industrial Engineering from Bogazici University, Istanbul, Turkey. He received his PhD in Industrial and Systems Engineering in 1990 from the University of Florida, and held faculty positions in Industrial Engineering at Purdue University prior to joining North Carolina State University in 2007. His teaching and research interests are in production planning and supply chain management. Before coming to the US he worked as a production engineer with Arcelik AS, a major appliance manufacturer in Istanbul, Turkey. He has also been a visiting researcher at Intel Corporation and IC Delco. He was named Outstanding Young Industrial Engineer in Education in 1997 and a Fellow of the Institute of Industrial Engineers in 2005, and has received awards for both undergraduate and graduate teaching. He is the author of more than 130 refereed journal papers and book chapters, two monographs and three edited books.