Question

1. For the Red Tomato Garden Tools example, consider the following situation:

The company has a Six month aggregate production planning procedure in place. The following factors are considered for planning.

The planners use a 160 hour-month for planning purposes. The average labor wage is assumed to be $18.00 per hour. Overtime wage rate is 2.0 times that of regular wage. Federal regulations stipulate that overtime for a worker cannot be more than 15 hours a month.

The demand is forecasted and past data shows that they have a very good forecasting system. The forecasts for the next six months, May through October 2016, are available: 2500, 3000, 4000, 3800, 3500, and 2800.

The inventory at the end of April is 600. The company would like to have an inventory of at least 500 units at the end of the planning period.

In April 2016, the plant has a workforce of 85 people. Assume that it takes 5 labor hours to produce one unit.

Material and production costs are $35 per unit. When they buy mowers from their seller, it costs them $150 a piece.

Any shortage in satisfying the demand (stock-out) is compensated in the next month. Inventory costs are $10 per unit per month, and stock-out cost is $40 a unit.

Develop an Aggregate Production Planning model, to plan for the horizon starting from May. Define your coefficients and variables. Write down the model with all the coefficients and variables.

Use a table to display the workforce level, no. of workers hired and laid-off, amount produced, overtime hours, and units bought from supplier, for each month. . You can use it for EXCEL Solver.

Answer 1

Month	Demand	Regular Time Production	No of Workers	Hired	Layoff	Overtime	Inventory	Stockout
							600
May	2500	2720	85	0	0	0	820	0
June	3000	2720	85	0	0	0	540	0
July	4000	3200	100	15	0	255	0	5
August	3800	3552	111	11	0	255	2	0
September	3500	3552	111	0	0	0	54	0
October	2800	3200	100	0	11	46	500	0
Total	19600	18944				556
Regular monthly production=		85*160/5	2720
Overtime units=	85*15/5=		255
Output of one worker a month=		160/5	32	units
Costs
Month	Material and production	Holding Cost	Labor cost	Overtime	Stockout
May	95,200.00	8,200.00	244,800.00	0.00
June	95,200.00	5,400.00	244,800.00	0.00	0.00
July	120,925.00	0.00	288,000.00	45,900.00	0.00
August	133,245.00	20.00	319,680.00	45,900.00	200.00
September	124,320.00	540.00	319,680.00	0.00	0.00
October	113,610.00	5,000.00	288,000.00	8,280.00	0.00
	$682,500.00	$19,160.00	$1,704,960.00	$100,080.00	$200.00
Total	$2,506,900.00