• A normal approximation model for safety stock optimization in a two-echelon distribution system

      Desmet, Bram; Aghezzaf, El-Houssaine; Vanmaele, Hendrik (Journal of the Operational Research Society, 2010)
      This paper presents an approximation model for the retailer replenishment lead-times in a two-echelon distribution system, and discusses its implementation for safety stock optimization in a one-warehouse and N-identical retailers system. The model assumes normality of demand and nominal lead times. It takes into account not only the averages of these parameters but also their variances. This approximation model is first tested on a two-echelon, one-warehouse and N-identical retailers system using discrete event simulation. It is then applied to optimize the safety stock in a two-echelon distribution system of a European market leader in the production and distribution of air conditioning equipment. Results of this implementation are analysed and discussed in detail.
    • Optimizing production capacity and safety stocks in general acyclic supply chains

      Ghadimi, Foad; Aouam, Tarik; Vanhoucke, Mario (Computers and Operations Research, 2020)
      This paper addresses the joint optimization of production capacity and safety stocks in supply chains under the guaranteed service approach (GSA). The integrated problem is formulated as a mixed integer nonlinear program (MINLP) and solution procedures are proposed in the cases of general acyclic and spanning tree networks. For general acyclic supply chains, the integrated problem is solved using a Lagrangian decomposition method which iteratively solves capacity planning and safety stock placement subproblems, and adds budget feasibility constraints to strengthen the Lagrangian decomposition lower bound. When the supply chain has a spanning tree structure, an efficient Lagrangian relaxation heuristic dualizes the budget constraint and solves the relaxed problem using a dynamic programming algorithm. Computational experiments on real-world instances show that the Lagrangian decomposition method is able to solve all instances within 0.1% optimality, while a state-of-the-art solver is unable to provide feasible solutions for large instances. In the case of spanning tree networks, the proposed Lagrangian relaxation heuristic finds optimal or near-optimal solutions and greatly improves running time in comparison to the Lagrangian decomposition method. In addition, numerical experiments show that savings can be achieved through joint optimization of capacity and safety stocks.
    • Safety Stock Optimization in Two-Echelon Assembly systems: Normal Approximation Models

      Desmet, Bram; Aghezzaf, El-Houssaine; Vanmaele, Hendrik (International Journal of Production Research, 2010)
      This paper tackles the problem of optimising safety stocks in a two-echelon assembly system. It presents and discusses several approximation models for the assembly lead-time under the assumption of normality of the assembly demand and normality of components’ nominal lead times. These approximation models are subsequently used to optimise safety stocks throughout a two-echelon assembly system. They are then tested on a particular two-echelon N-identical component assembly system. The obtained results are compared with the results of a discrete event simulation. Finally, it is shown that lead-times and safety stock results already obtained for a two-echelon distribution system can also be derived without difficulty from those of two-echelon assembly systems.