Cost minimizing planning of container inspection and repair in multiple facilities.

A problem of optimal mid-term or long-term planning of inspection and repair of freight containers in multiple facilities is introduced and investigated. The containers are of different types and quality levels, which define their repair costs and workforce requirements. The objective function includes the total holding, inspection, repair, transportation and rejection costs. We propose a deterministic, time-dependent, integer linear min-cost multi-commodity network-flow formulation. The problem is shown to be polynomially solvable if there is a single facility, a single time period and all the containers are repairable and have to be repaired. It is shown to be NP-hard for three important special cases. The computational results of our experiments on randomly generated instances based on real data show that instances of sizes 3 facilities, 4 container types and up to 9 container quality levels can be solved with CPLEX in 5 minutes on a conventional PC, even for 30 periods, with an optimality gap of less than 3%. This is sufficient for medium-term or weekly planning or for short-term recovery planning. However, there are instances of the same magnitude, but with 360 periods of a considerably longer planning horizon, for which an optimality gap of 28% remained even after 10 hours of CPLEX computation.

Dynamic pricing with demand disaggregation for hotel revenue management

In this paper we present a novel approach to the dynamic pricing problem for hotel businesses. It includes disaggregation of the demand into several categories, forecasting, elastic demand simulation, and a mathematical programming model with concave quadratic objective function and linear constraints for dynamic price optimization. The approach is computationally efficient and easy to implement. In computer experiments with a hotel data set, the hotel revenue is increased by about 6% on average in comparison with the actual revenue gained in a past period, where the fixed price policy was employed, subject to an assumption that the demand can deviate from the suggested elastic model. The approach and the developed software can be a useful tool for small hotels recovering from the economic consequences of the COVID-19 pandemic.