The “Hub” and “Wheel” Scheduling Problems

We pursue the analysis of the Hub Operation Scheduling Problem (HOSP) over the finite and infinite horizons. The demand is assumed deterministic and stationary. We deduce the minimum fleet size V_T that satisfies all demands for 1 ≤ T ≤ ∞, as well as the optimal schedule that minimizes lost sales for a given fleet size smaller than V_T. Reintroducing the costs of empties and of delayed sales or, equivalently, the cost of empties and the gains from shipments, we resolve the issues of optimal allocation and optimal schedule over a horizon T ≤ ∞. Finally, we generalise the above results—still under the assumption of deterministic, stationary demands—first to the case in which each city communicates with its two “adjacent” cities (this is the “Wheel” problem) and then to the general network problem in which each terminal may communicate with any other terminal.