Joint capacity, inventory, and demand allocation decisions in manufacturing systems

Abstract

We study the demand, inventory, and capacity allocation problem in production systems with multiple inventory locations and a production facility operating under linear and concave costs. Independent stochastic demand from multiple sources is fulfilled from multiple warehouses that are in turn replenished from a shared production facility with stochastic production lead times. We propose a novel formulation of the demand allocation problem, and show that the optimal customer allocations are not necessarily single-sourced. The new formulation allows the inclusion of additional decisions alongside demand and inventory allocation. Capacity decisions are incorporated under two cost structures: linear and concave. For the concave case, we show that for a given demand and inventory allocation, the optimal capacity of the production facility takes on discrete values within a finite set, which allows the objective to be linearized. We demonstrate numerically that the joint optimization of capacity, inventory, and demand allocation decisions has significant cost savings over a sequential decision and leads to a high utilization of the production facility under linear capacity costs, but relatively low utilization under concave costs. Safety stock, on the other hand, at the distribution centers is relatively low under linear and concave cost.

KEYWORDS:

• Production inventory systems
• demand allocation
• capacity allocation
• inventory management
• economies of scale

Additional information

Notes on contributors

Vedat Bayram

Vedat Bayram is an assistant professor in the Department of Industrial Engineering at TED University, Turkey. He received his Ph.D. from Bilkent University in 2015. His research interests include large-scale optimization and data analytics with applications in disaster management, transportation, logistics, and defense and homeland security.

Fatma Gzara

Fatma Gzara is an associate professor at the Department of Management Sciences at the University of Waterloo, Canada. He received her Ph.D. from McGill University in 2003. Her primary research interests include large-scale optimization and its applications, data analytics, emerging technologies in logistics and distribution, and optimization under uncertainty.

Samir Elhedhli

Samir Elhedhli is professor and chair of the Department of Management Sciences at the University of Waterloo, Canada. He received his Ph.D. from McGill University in 2001. He has research interests in large-scale optimization and data analytics with applications in logistics, supply chains, and service systems design.