On the relationship of capacitated production/inventory models to manufacturing flow control models

Authors:
Michael C. Fu;Jian-Qiang Hu
Affiliations:
College of Business and Management and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA;Department of Manufacturing Engineering, Boston University, Boston, MA 02215, USA
Venue:
Operations Research Letters
Year:
1995

Citing 5
Cited 0

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Abstract

Characterizing and determining optimal operating policies for production/inventory systems are of paramount importance. Perhaps two of the most important practical factors which make this a difficult problem are the randomness of demand and the finiteness of production capacity. In the traditional inventory literature of operations research and management science, it has been shown that a modified base-stock policy is optimal for a periodic review model; results exist that can be used to estimate the single parameter that characterizes the optimal policy. On the other hand, research found in the control systems community casts the problem in the framework of manufacturing flow control - where inventory is monitored continuously and the production rate is also controlled continuously - and has shown that the optimal policy can also be characterized by a single parameter called the hedging point. Our view is that these two models and approaches solve essentially the same problem, albeit one in discrete time and the other in continuous time. In this paper, we compare the two approaches and discuss various beneficial implications that result from correspondences between the two approaches. For example, both systems have fundamental connections to processes of a single-server queue: one to the discrete-time process of system time, and the other to the continuous-time process of the workload process. Finally we also tackle the problem of stochastic capacity in the context of both approaches.