Document Type


Publication Date

Fall 2019


Timothy Anderson

Course Title

Operations Research

Course Number

ETM 540


Mathematical optimization, Paint industry and trade -- Management, Operations research, Production planning


This project will consider a linear product mix optimization problem for a fictional paint company, Paints-R-Us. Paints-R-Us is a wholesale paint manufacturer located in the Pacific Northwest. The Global Production Manager, Steve Brush, has been tasked with maximizing Paints-R-Us’s profit in the upcoming quarter. Steve Brush oversees the global production plan, and in collaboration with the production planners will develop a production plan which optimizes the profits that Paints-R-Us can create in the quarter accounting for the following criteria:

• Demand in the given quarter for each of the 5 paint types that Paints-R-Us produces • The warehousing storage capacity for the production facility • The throughput rate of the 5 paint types that Paints-R-Us manufactures on the 5 operating production lines that Paints-R-Us operates. • The delivery requirements of specific paints on specific days per pre planned customer orders.

The output that Steve must produce is a production schedule for each production line during the quarter which maximizes the profit that the business can achieve. The production plan is decided by the upcoming demand. Steve believes more profit can be achieved through a production schedule that is derived through linear programming. However, the challenge is mathematically representing the production process and constraints. Steve has brought together his production planners to develop the model that will generate the production schedule which accommodates for committed demand and maximizes profit.

The Northwest facility has booked orders for the next 90-days, all of which must be fulfilled by the specified delivery date. Additionally, there is additional market demand that is filled through on-demand sales. Paints-R-Us must have a production plan which meets their booked order requirements and doesn’t exceed the forecasted total on-demand sales projections for any of their 5 product lines.

Each of the 5 production lines have a unique production rate for the number of barrels of different paints they can produce per day. Some production lines are restricted on the types of paint that they can produce, and some production lines can create certain types of paint at a faster rate than other paints. The supply chain can provide the required raw materials to meet the maximum paint production rate for the quarter. The production plan feeds supply chain planning and thus is not a constraint for production planning purposes.

Another factor that Steve must consider is for any production line to switch to a different paint, the production line must be shutdown for a day. This shutdown is so that the production line can be cleaned and set up for the production of the new paint type.

Finally, Paints-R-Us has warehousing constraints. Their production plan must account for the amount of expected sales per day and ensure that paint production beyond the daily paint demand doesn’t exceed Paints-R-Us’s warehousing capacity.

Steve and his production planning team have partnered with local PSU Graduate students to build a model which can product the optimized production schedule and can also be easily adapted for future quarters or for longer forecast periods.


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