Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Engineering Science (Interdepartmental Program)

First Advisor

Bhaba R. Sarker


This research studies the control mechanism of a supply chain system to operate it efficiently and economically under the just-in-time (JIT) philosophy. To implement a JIT system, kanbans are employed to link different plants' production processes in a supply pipeline. Supply chain models may be categorized into single-stage, multi-stage, and assembly-line types of production systems. In order to operate efficiently and economically, the number of kanbans, the manufacturing batch size, the number of batches, and the total quantity over one period are determined optimally for these types of supply chains. The kanban operation at each stage is scheduled to minimize the total cost in the synchronized logistics of the supply chain. It is difficult to develop a generalized mathematical model for a supply chain system that incorporates all its salient features. This research employs two basic models to describe the supply chain system: a mathematical programming model to minimize the supply chain inventory system cost and a queuing model to configure the kanban logistic operations in the supply pipeline. A supply chain inventory system is modeled as a mixed-integer nonlinear programming (MINLP) that is difficult to solve optimally for a large instance. A branch-and-bound (B&B) method is devised for all versions of it to solve the MINLP problems. From the solution of MINLP, the number of batches in each stage and the total quantity of products are obtained. Next, the number of kanbans that are needed to deliver the batches between two adjacent stages is determined from the results of the MINLP, and kanban operations are fixed to efficiently schedule the dispatches of work-in-process. The new solutions result in a new line configuration as to the number and size of kanbans that led to simpler dispatch schedules, better material handling, reduction in WIP and delivery time, and enhancement of the overall productivity. These models can help a manager respond quickly to consumers' need, determine the right policies to order the raw material and deliver the finished goods, and manage the operations efficiently both within and between the plants.