Design and Analysis of a Non Linear Optimization Inventory Model for Uncertain Quantity

This paper considers a continuous review policy with controllable lead time and the partial backordering under the circumstance of uncertain quantity received. A Non Linear Programming Model is constructed with service level constraint. An optimal inventory control approach by the Lagrange multiplier method is applied. The lead time crashing cost is considered as an exponential function of lead time, while the order processing cost and lost sales rate are considered as logarithmic functions of capital investment. The objective of this study is to minimize the total relevant cost by simultaneously optimizing the order quantity, lost sales rate and order processing cost.

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