Date of Award

Spring 2009

Document Type


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 3..0uncoordinated suppliers. That is each supplier establishes their individual inventory 3..0and production policies on both the input and output sides. In these supply links there is 3..0minimal coordination between suppliers, and typically only prices and delivery 3..0guarantees are contracted. As a consequence, the inventory behavior and associated costs 3..0do not exhibit standard patterns. This makes it difficult to model and optimize these chains 3..0using classical inventory 3..0models. The common approach, therefore, for evaluating uncoordinated supply chains is to use Supply Chain 3..0Analytics software. These retrieve operational data from Enterprise Resource Planning 3..0(ERP) systems and then characterize the historical inventory performance 3..0behavior.

Nearier (2008) developed a joint production inventory 3..0model for estimating inventory costs in uncoordinated chains as an alternative to supply chain 3..0analytics. They proposed 3..0a (Q, R, δ)2 relationship between each 3..0pair of sequential suppliers, where Q is the order quantity, R is the reorder level, and δ is the production or 3..0consumption rate. In this arrangement each part has two inventory locations: (i) on the output 3..0side 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 3..0research tasks were accomplished in this regard.

First, 3..0the inventory estimation accuracy of the original (Q, R, δ)2 model was improved. This was 3..0accomplished by deriving a more reliable estimate of the residual inventory 3..0at the end of each supply cycle. Further, a more accurate model of the inventory behavior in supply 3..0cycles where the seller has no production was developed. A discrete inventory simulation 3..0was used to demonstrate a significant improvement in the estimation accuracy, from a 3..010-30 % error range to within 5% error on average.

Second, 3..0a prescriptive model for deriving the optimal Q when reducing inventory costs in a (Q, 3..0R, δ)2supply relationship was developed. From simulation 3..0studies, it was found 3..0that due to differences in production batch sizes, production rates, and replenishment order 3..0quantities, the inventory cost function exhibits a non-differentiable step-wise convex behavior. 3..0Further, the steps are observed to occur at integer ratios of Q and the buyer's production 3..0batch. This behavior makes it difficult to analytically derive the optimal Q, which could 3..0occur at one of the step points or any intermediate point. A golden section based search 3..0heuristic for efficiently deriving the optimal Q was developed.

Third, the robustness of Q to 3..0demand shifts was studied. A demand shift occurs wherever the mean demand jumps to a higher or lower 3..0level, similar to a moving average forecast. The demand shift range beyond, which there is 3..0significant deterioration in inventory costs and a change in the supply policy 3..0Q is justified, was determined Two supply policies were studied: (i) fixed delivery batch and 3..0(ii) fixed production period. For each stochastic demand shift behavior, a 3..0delivery batch size or production period that minimizes the total cost of both suppliers is 3..0selected.