Question

7. The Cramer Computer Company has the following projected demand for the next 6 months: Month No. of Working days in Month Demand 2.600 3,100 3,700 4,300 3,500 3,300 There are currently 100 workers, each working a normal 8-hour shift, 5 days a week. They can work an extra 10 hours a week in overtime, but it costs the com- pany an extra $10 per hour in overtime costs. One of the computers takes 5 hours of worker time to produce. They can hire more workers at a cost of $3,000, with an additional cost of $5,000 if they lay off a worker. The company has a policy of not allowing shortages, but they are allowed inventory. Inventory costs $15 per month per unit based on average inventory levels for the month. There are no subcon- tractors for the units. There is a starting inventory of 60 units. Even though they have the "no shortage” policy, if one does happen to occur they charge $150 per unit due to lost profit. Space will only allow them to have 110 workers. If they need more, they need to start a second shift. To do so increases the cost per worker by $1.50 per hour for a shift premium. A second shift also requires hiring support personnel (a supervi- sor, maintenance person, and material handler) at an additional cost of $20,000 per month Given all these conditions, find a satisfactory solution to help them minimize cost. (Hint: Do not look for an optimal solution. Instead try to set up the problem on a spreadsheet and look for patterns toward a good solution.)

Answer 1

Answer :

Note 1 : Since the given problem contains more than 2 variables, it is not solvable linearly. It is a complex problem which requires dynamic solution.

Note 2 : Questions asks to list out the scenarios. It does not ask for optimal solution. Optimal solution cannot be found out because it requires dynamic solution as above discussed, which can be solved in a dedicated software only.

Note 3 : Assumed that current workers = 100, cannot be reduced and they will all produce for their total labour hours.

Note 4 : Rank of Cost Elements

a) Overtime Cost = $10/hour

Therefore Overtime Cost per unit = $10/hour x 5 hours per unit = $50 per unit = Rank 2

b) Inventory Holding Cost = $ 15 per unit per month = Rank 1

c) Extra Labour Cost (Hiring) = $ 3000/labour for hiring

Normal Labour Hours per month = 8 hours per day x 5 days x 4 weeks = 160 Hours

No. of Units produced in 160 Hours = 160Hours / 5 hours per unit = 32 units

Hiring Cost per unit = $ 3000/ 32 units = $ 93.75 per unit = Rank 3

d) Extra Labour Cost (Layoffs) = $ 5000/labour for layoff

Normal Labour Hours per month = 8 hours per day x 5 days x 4 weeks = 160 Hours

No. of Units produced in 160 Hours = 160Hours / 5 hours per unit = 32 units

Layoff Cost per unit = $ 5000/ 32 units = $ 156.25 per unit = Rank 5

e) Shortage cost = $ 150 per unit = Rank 4

Note 5: Inventory Holding cost is Rank 1 only till 3 months. After 3 months of holding the inventory, it becomes higher per unit ($15 x 4 = $ 60 per unit) than overtime cost to produce the unit.

Note 6: Second Shift : As per given problem this is not required, since going to shift Premium involves the following costs

a) Support Personnel cost = $ 20,0000 per month (if 200 units are produced, per unit cost = $ 100)

b) Shift Premium Cost = $ 1.50 per labour hour = $ 7.50 per unit ( 5 LHR is required per unit)

c) Hiring Cost = $ 93. 75 per unit

Moroever the given problem can be mitigated with combination of overtime, excess inventory, extra workers, shortage alone. There is no such significant shortage that a second shift would be required.

Tables :

Month	No. of Working Days	No. of Workers	No. of Labor Hours @8 LHR/worker	Demand units	No. of Labour Hours required @5 LHR/unit	Excess/Deficit LHR
1	20	100	16000	2600	13000	3000
2	21	100	16800	3100	15500	1300
3	21	100	16800	3700	18500	-1700
4	22	100	17600	4300	21500	-3900
5	19	100	15200	3500	17500	-2300
6	20	100	16000	3300	16500	-500

Scenario 1: With same workforce/no overtime
Month	Excess/Deficit LHR	Excess/deficit units produced in units	Running Inventory Level in units	Inventory Holding Cost @$15/unit	Shortage Cost	Total Cost
0	-	-	60	900	-	900
1	3,000	600	660	9,900	-	9,900
2	1,300	260	920	13,800	-	13,800
3	(1,700)	(340)	580	8,700	-	8,700
4	(3,900)	(780)	(200)	-	30,000	30,000
5	(2,300)	(460)	(660)	-	99,000	99,000
6	(500)	(100)	(760)	-	114,000	114,000
			GT	33,300	243,000	276,300

Scenario 2: With same workforce and overtime
Month	Excess/Deficit LHR	Excess/deficit units produced	Running Inventory Level	Required Overtime	Inventory Holding Cost	Overtime cost	Total Cost
0	-	-	60	-	900	-	900
1	3,000	600	660	-	9,900	-	9,900
2	1,300	260	920	-	13,800	-	13,800
3	(1,700)	(340)	580	-	8,700	-	8,700
4	(3,900)	(780)	(200)	(1,000)	-	10,000	10,000
5	(2,300)	(460)	(660)	(3,300)	-	33,000	33,000
6	(500)	(100)	(760)	(3,800)	-	38,000	38,000
				GT	33,300	81,000	114,300

Scenario 3: With increased workforce/no overtime/no layoffs
Month	No. of Working Days	No. of Workers	No. of Labor Hours @8 LHR/worker	Demand units	No. of Labour Hours required @5 LHR/unit	Excess/Deficit LHR	Excess/deficit units produced	Running Inventory Level	Inventory Holding Cost	Hiring Cost	Total Cost
0	-	-	-	-	-	-	-	60	900	-	900
1	20	100	16000	2600	13000	3000	600	660	9,900	-	9,900
2	21	100	16800	3100	15500	1300	260	920	13,800	-	13,800
3	21	100	16800	3700	18500	-1700	(340)	580	8,700	-	8,700
4	22	110	19360	4300	21500	-2140	(428)	152	2,280	30,000	32,280
5	19	110	16720	3500	17500	-780	(156)	(4)	60	-	60
6	20	100	16000	3300	16500	-500	(100)	(104)	(1,560)	-	(1,560)
								GT	34,080	30,000	64,080

Note : Additionally a Shortage Cost of $ 600 will be incurred in month 5 for shortage of 4 units, in addition to the Total Cost.