Process flexibility in homogeneous production–inventory systems with a single-period demand

ABSTRACT

Most studies of process flexibility have considered a make-to-order setting, whereas in practice, production systems usually have a make-to-stock environment. In this article, we investigate the process flexibility in homogeneous production–inventory systems with a single-period demand. We formulate the capacitated multi-product production–inventory system as a convex optimization model with an implicit objective function, which is then transformed into a network flow problem. We develop optimality conditions for the production decision problem based on concepts such as the flow position and the influencing set of each product node in the associated network for any given flexibility design. We further characterize the optimal production decision with an analytical approach for dedicated and completely flexible systems and two numerical algorithms for production systems with general flexibility designs.

 We then investigate the popular long chain design in homogeneous production–inventory systems with a comprehensive numerical study, showing that its performance is more sensitive to the asymmetry in initial product inventory than the system cost structure. However, the long chain design is still capable of achieving most of the benefits gained from a completely flexible design in a make-to-stock environment unless the asymmetry in product initial inventory is too high.

KEYWORDS:

• Process flexibility
• production–inventory system
• maximum flow
• convex optimization

Notes

1 In a system with limited flexibility, only some (instead of all) types of products can be produced in more than one plants.

2 A two-flexibility design refers to a production flexible system where each plant is capable of manufacturing two types of products. Each product can be produced by two plants, but the entire process structure could form more than one cycle.

3 Here we assume that g( · ) is first-order differentiable. If the function is non-differentiable at some point Γ_j or Γ_j + Δ_j, we define g′( · ) as the left derivative for Δ_j ⩽ 0 and the right derivative for Δ_j ⩾ 0.

Additional information

Funding

This work was partially supported by the National Science Foundation (Grant CMMI 1265671) and the National Science Foundation of China (Grants 71210002 and 71332005).

Notes on contributors

Wancheng Feng

Wancheng Feng was born in February 1990. He is currently pursuing a Ph.D. degree in the Department of Industrial Engineering, Tsinghua University, Beijing, China. His research focuses on process flexibility, logistics system analysis, and smart warehouse design and management.

Zuo-Jun Max Shen

Zuo-Jun Max Shen is the Chancellor’s Professor in the Department of Industrial Engineering and Operations Research and the Department of Civil and Environmental Engineering at University of California, Berkeley. He is also an honorary professor at Tsinghua University and a Center Director at the Tsinghua-Berkeley Institute at Shenzhen. He received his Ph.D. from Northwestern University. He has been active in the following research areas: integrated supply chain design and management, design and analysis of optimization algorithms, energy systems, and transportation system planning and optimization. He is currently on the editorial/advisory board for several leading journals. Dr. Shen received the CAREER award from the National Science Foundation in 2003.