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Access Type

Open Access

Document Type


Degree Program

Industrial Engineering & Operations Research

Degree Type

Master of Science (M.S.)

Year Degree Awarded


Month Degree Awarded



Inventory control, Service levels, Fill rate


The level of customer satisfaction largely depends on manufacturer’s ability to respond to customer orders with promptness. The swiftness with which the manufacturers are able to meet customer demand is measured by the service level. There are two service level measures typically used. The first one is type 1 service level which denotes the probability of not stocking out over a planning period. The other is fill rate which denotes the proportion of demand satisfied with the existing inventory. We review the rich and diverse literature available on inventory cost optimization under these service level constraints. Subsequently two optimization models are developed for the two different types of service level measures. The goal is to determine the safety stock values for all products in a multi product inventory required to achieve aggregate type 1 and type 2 service levels at the minimum inventory cost. For both the models we also maintain a minimum threshold for individual type 1 and type 2 service level for every product. The models are solved using Lagrangian relaxation techniques.

The models are computationally solved in Microsoft Excel. We then carry out discrete event simulation to validate the results and to test the performance of the models. To provide the decision makers with an idea of variability in the service levels and the related risks associated with it on an immediate finite horizon planning scale we also carry out simulation for a time span of one, two and four years.

The results obtained show desired type 1 and type 2 service levels for products with under both infinite and finite planning horizons.


First Advisor

Ana Muriel

Second Advisor

Hari Balasubramanian