Modelling and solving a novel gardener problem under an emergency order and stochastic storage space

The objective of this research is to determine the optimum order quantity such that the expected total profit will be maximised while some constraints such as the service level and stochastic storage space will be satisfied in the gardener problem. The main contribution is to utilise the emergency order in case of shortage, in order to achieve more profits where the demand is more than the on hand inventory. In this case, the vendor should pay the cost of customer waiting time to receive the required products either purchasing the products or losing the sale condition. As the proposed problem is NP-hard, using meta-heuristic method is our methodology for solving. Two meta-heuristic algorithms, namely differential evolution and invasive weed optimisation, are utilised to solve the problem in which their parameters are tuned. Finally, some numerical experiments and statistical comparisons are performed to evaluate the applicability of both proposed model and the algorithms. The computational results show that the proposed differential evolution has a desirable performance in favour of the expected total profits.