All-unit discounts, multi-item inventory model with stochastic demand, service level constraints and finite horizon

Inventory systems are typically described as deterministic or stochastic, single, or multi-item, etc. The model reported in this research combines several such dichotomies, into a single model. It has the objective of deciding the optimal order quantities for a multi-item inventory system over a finite horizon. The demand is probabilistic with service level constraints, and there is an all-unit price break, for orders that exceed a given size. The solution approach uses a goal programming technique, in a mxed integer linear programming formulation. The model is analysed for sensitivity to deviations from the optimal policy, and inaccurate parameter estimation, including the demand distribution. In addition the optimal multi-item policy is compared to an optimal solution derived for each part type separately. Simulation experiments reveal that the model is not sensitive to inaccurate parameters nor to exact estimation of the demand distribution, thus aiding in reducing the control cost. It is also shown that in spite of the computational cost, it is preferable to apply the model as is, instead of dealing with each unit type separately.