Document Type


Date of Award

Spring 5-31-2009

Degree Name

Doctor of Philosophy in Industrial Engineering - (Ph.D.)


Mechanical and Industrial Engineering

First Advisor

Sanchoy K. Das

Second Advisor

Reggie J. Caudill

Third Advisor

Athanassios K. Bladikas

Fourth Advisor

George Hanna Abdou

Fifth Advisor

Cheickna Sylla


Many modern supply chains can be described as a series of uncoordinated suppliers. That is each supplier establishes their individual inventory and production policies on both the input and output sides. In these supply links there is minimal coordination between suppliers, and typically only prices and delivery guarantees are contracted. As a consequence, the inventory behavior and associated costs do not exhibit standard patterns. This makes it difficult to model and optimize these chains using classical inventory models. The common approach, therefore, for evaluating uncoordinated supply chains is to use Supply Chain Analytics software. These retrieve operational data from Enterprise Resource Planning (ERP) systems and then characterize the historical inventory performance behavior.

Nearier (2008) developed a joint production inventory model for estimating inventory costs in uncoordinated chains as an alternative to supply chain analytics. They proposed a (Q, R, δ)2 relationship between each pair of sequential suppliers, where Q is the order quantity, R is the reorder level, and δ is the production or consumption rate. In this arrangement each part has two inventory locations: (i) on the output side of the seller, and (ii) on the input side of the buyer. hi this dissertation, the (Q, R, δ)2 model was extended. Three specific research tasks were accomplished in this regard.

First, the inventory estimation accuracy of the original (Q, R, δ)2 model was improved. This was accomplished by deriving a more reliable estimate of the residual inventory at the end of each supply cycle. Further, a more accurate model of the inventory behavior in supply cycles where the seller has no production was developed. A discrete inventory simulation was used to demonstrate a significant improvement in the estimation accuracy, from a 10-30 % error range to within 5% error on average.

Second, a prescriptive model for deriving the optimal Q when reducing inventory costs in a (Q, R, δ)2supply relationship was developed. From simulation studies, it was found that due to differences in production batch sizes, production rates, and replenishment order quantities, the inventory cost function exhibits a non-differentiable step-wise convex behavior. Further, the steps are observed to occur at integer ratios of Q and the buyer's production batch. This behavior makes it difficult to analytically derive the optimal Q, which could occur at one of the step points or any intermediate point. A golden section based search heuristic for efficiently deriving the optimal Q was developed.

Third, the robustness of Q to demand shifts was studied. A demand shift occurs wherever the mean demand jumps to a higher or lower level, similar to a moving average forecast. The demand shift range beyond, which there is significant deterioration in inventory costs and a change in the supply policy Q is justified, was determined Two supply policies were studied: (i) fixed delivery batch and (ii) fixed production period. For each stochastic demand shift behavior, a delivery batch size or production period that minimizes the total cost of both suppliers is selected.



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