Optimizing Printed Circuit Board Production:
A Case Study

Abstract
This paper focuses on the production of 5 different printed circuit boards (PCBs). The purpose of this paper is to understand the best production model to reach maximum profit. It is understood that there are production capacities that will limit the overall amount of products produce. Through the use of Linear Programming we can determine, based on the current circuit boards sale price, the number of each board type the plant needs to produce. It can also be determined which production capacity would need to be increased in order to increase production numbers. In addition, this paper will look at how the production schedule will alter based on customer demands and changes in sales price.

Optimizing Printed Circuit Board Production
A Case Study ABC Electronics is a manufacturer of printed circuit boards and there is 5 different types the company produces. The Company wants to use Linear Programming to find the best production schedule to maximize profits. For each circuit board (A5464, A2668, G3897, Z9794 and L8687) the company has determined what the profit is for each board type. The profit was calculated by subtracting the material, labor and overhead costs from the selling price (see Appendix A. Individual Profit line). It was also determined the producing minutes for each board during all steps of the process (Laminating, Drilling, Plating, Etching, and Wiring) and the capacity in minutes each step can accommodate (see Appendix A. Laminating, Drilling, Plating, Etching and Wiring Constraint Lines). With all this knowledge in place, the maximum profit production schedule could be determined. The model can also be adjusted to adhere to other variables that could arise.
Discussion
Through the implementation of Linear Programming it can be determined that the best production schedule to maximize profits of PCBs. Producing 45 units of A5464 and 33 units of L8687 will using up all available time capacities for laminating and drilling but produce a maximum profit of $657. Since A5464 and L8687 are more profitable based on the production constraints, it would be in the company’s interest to focus resources on those PCBs and not the other 3 types (see Appendix A. for linear programming analysis). The question now arises which step of the production process should be improved to increase time capacity which intern would increase production capacity. Based on the Linear Program created, laminating and drilling capacities would need to be increased to produce more PCBs. Since there is a slack in the number of etching, plating and wiring minutes these would not be a logical adjustment to increase production numbers (See Appendix A. for slack analysis). ABC Electronics was confronted by a critical customer where they demanded that a minimum 8 units of G3897 be produced. Since the Linear Program was already created for the companies PCB production, a constraint was added for the demanded product. With the production time constraints remaining the same it was determined that to produce the 8 units of G3897, the production of A5464 would drop to 41 units and L8687 would drop to 27 units. The added constraint would decreased the maximum profits by $6 to $651 (See Appendix B. for Analysis breakdown with the 8 unit constraint).
The company then noted an increase in the selling price of the unit G3897, from $26 to $28. This intern increased the profit for G3897 to $12 per unit and caused a shift in the production plan. Now, to maximize profits the optimal production plan would consist of producing 23 units of A5464 and 44 units of G3897. Notice, the production of L8687 went to zero since it would make more sense to focus resources on the higher selling priced item. This change also increased the maximum profit to $712, a $55 dollar increase. Even though the max profit increased the production schedule is still limited by the number of total laminating and drilling minutes (see Appendix C for Analysis breakdown with the increase in selling price).
Conclusion
ABC Electronics was faced with the problem of how many of each 5 units of PCBs should the company produce to maximize profits and when situations occur how it affects the production schedule. Through the use of Linear Programming it could be determined that based on the limited time capacities for each production step the company should produce 45 units of A5464 and 33 units of L8687 for a profit of $657. When the company was faced with a critical customer demanding the production of 8 units of G3897 the production schedule had to adjust to adapt to the new constraint. It was then determined that the company should produce 41 units of A5464 and 27 units of L8687 along with the 8 units of G3897 to maximize profits. With the increase in the selling price of the G3897 unit the production schedule shifted again. The company now needs to produce 23 units of A5464 and 44 units of G3897 to maximize profits. All 3 scenarios are constrained by the laminating and drilling capacities and created a slack in the plating, etching and wiring production steps. It would be suggested to increases the laminating and drilling capacities to further increase production of PCBs and therefore increase the maximum profit.

Appendix A
Linear Program Analysis of PCB Production

Appendix B
Linear Program Analysis with 8 units of G3897 constraint

Appendix C
Linear Program Analysis when G3897 Selling Price Increases