Solving the Guaranteed-service Time Inventory Model for Real-world Supply Chains by Implementing It in Commercial Optimisers

The guaranteed service time inventory (GSTI) model aims to satisfy customers’ demand in an assured time. As multi-echelon supply chains (SC) grow in size and complexity, there is a need to develop exact algorithms to compute the amount of safety stock to deliver products to customers in the guaranteed service time. This work proposed an algorithm to minimise the safety stock in real–world SCs in minutes. The application reads the data set provided in [31]; then a continuous initial solution is computed in seconds using the software library (IPOpt); finally, that solution is used as the initial solution to run the branch–and–cut (B&C) algorithm implemented in a state-of–the–art commercial solver. In the proposed application, the GSTI model is modified to be implemented in commercial solvers when the demand is normally distributed. The reader can download the application's source code from [24] to analyse the results of the 38 instances. The application computes an integer solution to each of the 38 SCs; in the worst case, it takes 150 min to find the solution. Seventeen instances are solved optimally, and the worst gap between the actual and best solution is about 24% in three instances. The biggest instance is solved in less than 10 min, but other smaller ones are solved in a longer time because of the echelons’ structure (degree and depth). Thus, the time to compute a solution does not depend on the size of the SC but on its structure. The findings indicate that by using a state-of–the–art commercial solver (based on the B&C method) and running it with powerful computer capabilities, real–world SCs can be solved with techniques that return optimal solutions.