Inventory systems are aimed at maximizing customer service level for a given budget. In this thesis, a continuous review (Q, r) replenishment model is formulated, validated and applied. Three different stock-out criteria are used to measure the customer service level and minimize the expected number of stock-outs. The value of inventory (VOI) approach is used to determine the budget constraint. The resulting nonlinear optimization problem, where the stock out measure is minimized subject to the VOI for single-echelon multi-item and multi-echelon problems, is solved using the Lagrangian methodology. Approximation of the tail of the normal distribution by an exponential function allowed for an explicit solution for Q. Newton’s iterative approach is used to solve for r. The validat...[ Read more ]

Inventory systems are aimed at maximizing customer service level for a given budget. In this thesis, a continuous review (Q, r) replenishment model is formulated, validated and applied. Three different stock-out criteria are used to measure the customer service level and minimize the expected number of stock-outs. The value of inventory (VOI) approach is used to determine the budget constraint. The resulting nonlinear optimization problem, where the stock out measure is minimized subject to the VOI for single-echelon multi-item and multi-echelon problems, is solved using the Lagrangian methodology. Approximation of the tail of the normal distribution by an exponential function allowed for an explicit solution for Q. Newton’s iterative approach is used to solve for r. The validation is conducted (i) theoretically by showing that well known models can be recovered from the proposed model when the stock out cost is null and (ii) numerically by comparing the results of the proposed model with two existing models. Sensitivity analysis to the various parameters is conducted and shows that the model is robust. The model allows for economic tradeoff analysis between additional investment (i.e., increase in VOI) and reduction in stock outs.