Optimal Switches in Multi-inventory Systems

Given a switched multi–inventory system we wish to find the optimal schedule of the resets to maintain the system in a safe operating interval, while minimizing a function related to the cost of the resets. We discuss a family of instances that can be solved in polynomial time by linear programming. We do this by introducing a set-covering formulation with a totally unimodular constraint matrix. 1 Problem description Consider the family of continuous time linear multi–inventory system ˙x(t) = Biuc(t) − d(t), i ∈ {1,2} (1) where x(t) ∈ IRn is a vector whose components are the buffer levels, uc(t) ∈ IRm is the controlled flow vector, Bi ∈ Qn×m is the controlled process matrix and d(t) ∈ IRn is the unknown demand. To model backlog x(t) may be less than zero. Controls and demands are bounded within polytopes, i.e., uc(t) ∈ Uc = {u ∈ Rm : u− ≤ u ≤ u+ } d(t) ∈ D = {d ∈ Rn : d− ≤ d ≤ d+ }, where u− c , u+ c , d− , and d+ are assigned vectors. We al...

• Type: Conference
• Year: 2007
• Where: HYBRID
• Authors: Dario Bauso
• Keywords: Continuous Time Linear, HYBRID 2007, Hybrid Systems, Safe Operating Interval, Unimodular Constraint Matrix