Date of Award

Spring 1996

Document Type


Degree Name

Doctor of Philosophy (PhD)


Engineering Management & Systems Engineering

Committee Director

Han P. Bao

Committee Member

Billie M. Reed

Committee Member

Derya Jacobs

Committee Member

Ravi Mukkamala


In this research, algorithms are developed to address the problem of dynamic lot sizing and scheduling in a single level (or single operation) production system. This research deviates from previous research in this area in that it does not have the kind of assumptions regarding the real world production system that normally were made to reduce the complexity of the problem. Specifically, this research explicitly considers finite capacity, multiple items, known deterministic dynamic demand, sequence dependent setup times and setup costs, setup carryover and variable backlogging. The objective is to simultaneously determine the lot size and the sequence of production runs in each period to minimize the sum of setup, inventory, and backlogging costs.

The research here is motivated by observations of a real world production system that has a highly automated operation with sequence dependent setup times. For problems of this kind, optimal solution algorithms do not yet exist and, therefore, heuristic solution algorithms are of interest. Two distinct approaches are proposed to address the problem. The first is a greedy approach that eliminates setups while potential savings are greater than the increase in inventory or backlogging costs incurred. The second approach solves the much easier single item problem optimally for each item and then adapts the solution to account for capacity constraints. An intelligent modification to the second approach is also tried where a "overload penalty" is used between successive runs of the single product optimization algorithms A common component of each approach is a dynamic programming algorithm implemented to determine the optimal sequence of production within each period and across the scheduling horizon. The addition of sequence dependent considerations introduces a traveling salesman type problem to the lot sizing and sequencing decisions.

The algorithms have been tested over several combinations of demand and inventory related cost factors. Specifically the following factors at two levels each have been used: problem size, demand type, utilization, setup cost, backlogging cost, and backlogging limit. The test results indicate that, while the performance of the proposed algorithms appear to be affected by all the factors listed above, overall the regeneration algorithm with "overload penalty" outperforms all of the other algorithms at all factor level combinations.

In summary, the contribution of this research has been the development of three new algorithms for dynamic lot sizing and scheduling of multiple items in a single level production system. Through extensive statistical analysis, it has been shown that these algorithms, in particular the regeneration algorithm with "overload penalty", outperform the conventional scheduling techniques such as no lot sizing and economic manufacturing quantity.