Marc & John Inc.

General company presentation :

Marc & John Inc. is a medium-size business that operates in North York. It produces 4 types of plywood and sells mostly in the province of Ontario. The production is based on the forecast of the demand for the next eight (8) weeks. They review their plan at the beginning of each week. The master production plan has been prepared for the next eight (8) weeks. The company prepares this plan every Friday based on revised forecast demand, availability of machines, and inventory levels.

The four products they produce are plywood panels composed of many layers of pine wood, covered by a thin layer of maple wood, cherry wood, walnut wood or mahogany wood finish. These panels measure 4 x 8 feet and are inch thick. The production is made a lot-for lot and can be stored and used later to meet the demand.

Forecast of the demand:

Before establishing the master production plan which will start next week, the company has calculated in its inventory the following quantities of finished plywood: 1200 of maple, 600 of walnut, and 800 of mahogany finish. Furthermore, the inventory log indicates that the cherry panels are BO (backorder) for a quantity of 100. Safety stock must also be rebuilt at the end of the 8 weeks. The safety stock available at the end of the 8 weeks must be equal to the average weekly demand for each product.

Production costs and available capacity:

The production plant operates 24 hours a day but the company wants to avoid having employees work weekends because the salaries are 50% higher than the weekly salaries. The company works with two production lines and each line must be operated by 5 workers. Each worker works 8 hours per day at an hourly rate of $20.

The cost or raw materials (wood and glue) are $12, $12,50, $12,50, and $13 respectively for the Maple, walnut, mahogany, and cherry panels. The company has also established the sales prices for each wood type (in the same order as costs): $25, $28, $28, and $32.

The production rate for each production line is 10 panels per hour. However, to change from one wood finish to another, the production line must stop for 12 hours. This causes hundreds of dollars in set-up costs. The set-up costs consist of the salary for 5 operators plus $200 in raw material loss. At this moment, beginning of week 1, the first production line is set to produce maple panels and the second one to produce walnut panels.

Employment and commercial policies:

The corporation has promised not to lay off any employees in the next 6 months. Contreplaqu Inc. has also guaranteed that each employee hired works 40 hours per week.

Every customer requests that his order (s) be delivered on time. In the event that an order is late, the company will have to pay a penalty of $2 per unit per late week. The products made in advance and kept in inventory cost $0.50 per panel per week.

Here is the detailed forecast for the next 8 weeks, per product type:

Week	1	2	3	4	5	6	7	8
Maple	900	1000	1100	1300	1400	1100	1000	1000
Cherry	300	400	500	600	700	600	500	400
Walnut	100	200	300	300	400	300	200	200
Mahogany	200	200	300	400	400	400	300	200

QUESTION: For the four products: produce which product has the lowest cost using Aggregation planning to cover the needs for the next 8 weeks. The company wishes to reduce setups as much as possible. No more than 9 setups can be done over the 8 week period. The salary unused must still be paid since the company promised to pay 40 hours per employee hired. (Add as a penalty: penalty = total hours of salary unused).