Question

How do I calculate the one time adjustment of workforce to support the level production plan?

Problem information:

Month: 1	2	3	4	5	6	7	8	9	10	11	12
Demand: 500	800	1000	1400	2000	3000	2700	1500	1400	1500	2000	1200

Management at the Kerby Corporation has determined the following aggregated demand schedule in Units. An employee can produce an average of 10 units per month. Each worker on the payroll costs $2,000 in regular time wages per month. Undertime is paid at the same rate as regular time. In accordance with the labor contract in force, Kerby Corp does not work overtime or use subcontracting. Kerby can hire and train a new employee for $2,000 and lay off one for $500. Inventory costs $32 per unit on hand at the end of each month. At present, 140 employees are on the payroll and anticipation inventory is zero.

Prepare a production plan that only uses a level workforce and anticipation inventory as its supply options. Minimize the inventory left over at the end of the year. Layoffs, undertime, vacations, subcontracting, backorders and stockouts are not options. The plan may call for a one time adjustment of the workforce before month 1 begins

Answer 1

Total demand = Sum of all monthly demands = 19000

Average demand = 19000 / 12 = 1583

An employee can produce units = 10

Hence, to produce (19000/12) monthly , employees required = 1583 / 10 = 158.3 or 159 (rounded off)

One time hiring (adjustment of workforce) = 159 - 140 = 19 employees

Formulas

• Beginning inventory = Ending inventory of previous month
• Production = 159 * 10 = 1590 across 12 months
• Ending inventory = Production + Beginning inventory of the month - Demand
• Negative ending inventory specifies a stockout has occurred and a negative beginning inventory implies demand being fulfilled for the previous month.
• Also, though anticipation inventory is zero, we get approximately 80 units of inventory at the end as we rounded off employees required to next whole number (From 158.3 to 159).

The production plan is below.

Month	1	2	3	4	5	6	7	8	9	10	11	12
Demand:	500	800	1000	1400	2000	3000	2700	1500	1400	1500	2000	1200	19000
Beginning inventory	0	1090	1880	2470	2660	2250	840	-270	-180	10	100	-310
Production	1590	1590	1590	1590	1590	1590	1590	1590	1590	1590	1590	1590
Ending inventory	1090	1880	2470	2660	2250	840	-270	-180	10	100	-310	80