Solving inventory routing problem with stochastic demand

Abstract

We consider an inventory routing problem with stochastic demand where the demand is expressed in a probabilistic sense and it is dynamic in which the demand is gradually revealed at the end of each period. The problem is known as dynamic and stochastic inventory routing problem (DSIRP). DSIRP distribution network consists of a supplier and a set of retailers is considered. A limited number of single product is assumed to be produced by the supplier and a holding cost per unit product is incurred at both the supplier. The demand is assumed to follow the binomial probability distribution. We adopt an order-up-to level inventory policy and each unit of positive inventory at the retailer is incurred a holding cost, while the unmet demand (stock-out) is penalized. We assumed that the transportation of the product from supplier to the retailers is handled by a third party. The aim of DSIRP is to minimize the total expected cost which includes the inventory cost at supplier, inventory cost at retailers, stockout cost at retailers and transportation cost. The DSIRP is modeled as a Markov decision process (MDP) where the state in period t is represented as the inventory level for all retailers. A hybrid rollout algorithm where a Mixed Integer Linear Programming of the problem is used to obtain the control in each state. We also proposed an Artificial Bee Colony (ABC) algorithm to obtain a feasible and better controls. Computational experiments is conducted using an existing benchmark problem.