A bi-objective location-inventory model with capacitated transportation and lateral transshipments

We integrate location and inventory decisions in a three-echelon distribution network model with multiple products, capacitated in-house fleet and proactive transshipments between depots. The problem was originally motivated by the real-life case of a leading company in consumers’ household goods. The company offers a wide range of products which are different from demand pattern and shortage viewpoints. One of the product groups has seasonal trend with possibly lost sales during high seasons and backlog in low seasons, while the others lack any seasonal trend and get backlogged if any shortage occurs. A two-step process consisting of a new practical customer classification framework and a new mathematical model is developed. Total profit and customers’ dissatisfaction in the form of a new service-level measure are considered as the objective functions. To study the effects of transportation capacity on the network’s performance, a second scenario with inclusion of third-party transportation resources is presented. Due to unavailability or insufficiency of required objective data about production capacities and demands, they are assumed to be imprecise (i.e. possibilistic). After converting the original fuzzy model to its equivalent crisp formulation, an interactive solution procedure is applied to deal with the trade-off between the conflicting objectives. Useful managerial insights are also derived from the numerical experiments.