Finite inventory budgets in production capacity and safety stock placement under the guaranteed service approach

Following the guaranteed service approach (GSA), several studies have investigated the interaction between production and inventory decisions in multistage supply systems and developed efficient algorithms to solve the large-scale optimization problems that emerge. These works have largely ignored limited inventory budgets and their effect on production and inventory decisions. In reality, however, firms tend to limit the amount of capital tied-up in inventories, and there is usually a limited amount of storage space at a warehouse or a retailer. This study investigates the problem of production capacity and safety stock placement with both limited capacity and inventory budgets in general acyclic supply chains. This problem allocates capacity to production stages and sets inventory targets at logistics stages, with the objective to minimize the expected total supply chain cost while meeting a target customer service level. The present paper contributes to the GSA literature in several ways. First, we compare guaranteed and chancec-onstraint approaches to model limited inventory budgets and analyze their effect on safety stock placement. Second, we present two new equivalent formulations of the production capacity and safety stock placement problem. Solving these new models using a successive piecewise linear approximation algorithm outperforms existing solution procedures in terms of solution quality and time, in both cases of infinite and finite inventory budgets. Third, taking advantage of the structure of these formulations, we develop a two-phase heuristic, which finds optimal or near-optimal solutions and greatly improves CPU times. Finally, our numerical experiments show that inventory budgets affect production capacity and safety stock placement decisions, increasing both work in process (WIP) and safety stock levels.