Integrating shelving technology selection and storage assignment under uncertainty: a two-stage mathematical programming approach

The primary objective of this study is to select appropriate shelving technology while minimising intra warehouse transportation costs under probabilistic demand conditions. This research introduces four key innovations: integrating shelving technology selection and storage location assignment problem for the first time, considering capacity as a probabilistic variable to enhance realism, incorporating a multi-period framework, and allowing replenishment. Since predicting required capacity deterministically for shelving technology selection is impractical, capacity is modelled as a probabilistic variable. The next step involves allocating items to this technology. The problem is designed as multi-periodic, where, in each period, some orders are dispatched to customers, and some items are stored in the system. The problem ensures that sufficient space is always available for incoming items, forming a combined warehouse design and item allocation problem for shelving technology. Failure to address these integrative issues can lead to suboptimal solutions. A two-stage programming approach is employed to solve the model. Given the probabilistic nature of required capacity, the problem is solved under both continuous and discrete conditions, and a comparison between these approaches is conducted to determine the most effective solution method.