Question

A novelty coffee mug manufacturer produces 5 different designs that

are sold at tourist information kiosks. The demand requirements for the coming

tourist season is as follows:

Design A B C D E

Demand (units) 500 750 600 800 450

The mugs can all be produced in the same workstations, but require different

processing and setup times. The production information is in the following

table:

Design A B C D E

Batch Size (units) 50 50 50 50 50

Setup Time (hr/batch) 2 2 2.5 4 1.5

Processing Time (hr/unit) 0.15 0.15 0.25 0.25 0.10

The company wants to produce all the required mugs in one four-week period.

It currently operates workstations that work 8 hours per day, 5 days per

week, with a capacity cushion of 20%.

(a) Calculate the total time required to produce the mugs to meet the expected

demand.

(b) Calculate the time available (taking into account the capacity cushion)

for 1 workstation.

(c) How many workstations are needed to meet the production requirements?

(d) The company only has 4 workstations available. If it only operates its 4

stations, how many weeks does it need to meet the production requirements?

(e) Operating each workstation costs the company $25/hour for a total of

$1,000 per week (including the capacity cushion). Calculate the total

operating cost to produce the mugs.

(f) Each workstation costs $2,500 to purchase and commission. If the company

acquires the extra number of workstations indicated in part (c),

what would be the cost of production?

(g) If the company has other contracts it needs to satisfy. Working on the

mugs more than 4 weeks means it will have to cancel another contract,

incurring a penalty of $4,500. What should the company do: cancel the

contract or buy the required workstations?

Answer 1

The following data is provided:

Design	Demand (Units)	Batch Size	Setup time (Hr/Batch)	Processing Time (hr/unit)
A	500	50	2	0.15
B	750	50	2	0.15
C	600	50	2.5	0.25
D	800	50	4	0.25
E	450	50	1.5	0.10

Work hours per day = 8 hours

Work days per week = 5 days

Capacity Cushion = 20%

Demand needs to be fulfilled in 4 weeks

Solution for (a)

No. of Batches = Demand/Batch Size

Total setup time = (Setup time * No. of Batches)

Total Processing Time = (Processing time * Demand)

Total Time Required = Total setup time + Total Processing Time

The below table contains the value arrived at using the above formula to arrive at the total time required the expected demand:

Dsign	Demand	Batch Size	No. of Batches	Set up Time (hr/batch)	Total setup time	Processing time (hr/unit	Total Processing Time	Total Time Required
A	500	50	10	2	20	0.15	75	95
B	750	50	15	2	30	0.15	112.5	142.5
C	600	50	12	2.5	30	0.25	150	180
D	800	50	16	4	64	0.25	200	264
E	450	50	9	1.5	13.5	0.10	45	58.5

Based on the above calculations, the total time requied to produce the expected demand is:

Total Time required = Sum of total processing times for all designs = 95+142.5+180+264+58.5=740 hours

Solution for (b)

No. of Batches = Demand/Batch Size

Total setup time = (Setup time * No. of Batches)

Total Processing Time = (Processing time * Demand)

Total Time Required = Total setup time + Total Processing Time

As stated above all the formula reamins the same. However, since we are using the cushion capacity of 20%, the processing time will reduce. Now the processing time will be 20% lower, i.e.if the processing time is T, then, with the utilization of cushion capacity the new processing time will be (T/(120%))

Dsign	Demand	Batch Size	No. of Batches	Set up Time (hr/batch)	Total setup time	Processing time (hr/unit	Total Processing Time	Total Time Required
A	500	50	10	2	20	0.13	62.5	82.5
B	750	50	15	2	30	0.13	93.8	123.8
C	600	50	12	2.5	30	0.21	125	155
D	800	50	16	4	64	0.21	166.7	230.7
E	450	50	9	1.5	13.5	0.08	37.5	51

Based on the above calculations, the total time requied to produce the expected demand using the cushion capacity is :

Total Time required = Sum of total processing times for all designs = 82.5+123.85+155+230.7+51=642.9 hours

Therefore the available time = Time required without capcity cushion - Time required with cushion = 740 - 642.9 = 97.1 hours

Solution for (c)

As given in the question, the demand needs to be met in 4 weeks. When only 1 workstation is used (without cushion), the time required is 740 hours. As given in the question, a work week consists of 5 days of 8 working hours.

Therefore the total number weeks required = 740/8/5= 18.5 weeks

If this demand is to be fulfilled in 4 weeks, then the number of work stations required are (18.5/4) = ~4.6 = 5 workstations.

Solution for (d)

If the company operates with 4 work stations(without capacity cushion) then some setups would happen in parallet indicated by "Setup rounds" column in the below table and the processing time per unit will reduce by 4 times.

Dsign	Demand	Batch Size	No. of Batches	Set up Time (hr/batch)	Setup rounds	Total setup time	Processing time (hr/unit	Total Processing Time	Total Time Required
A	500	50	10	2	3	20	0.0375	18.8	24.8
B	750	50	15	2	4	30	0.0375	28.1	36.1
C	600	50	12	2.5	3	30	0.0625	37.5	45
D	800	50	16	4	4	64	0.0625	50	66
E	450	50	9	1.5	3	13.5	0.025	11.25	15.8

Based on the above calculation the number of weeks required to meet the demand = (24.8+36.1+45+66+15.8)/8/5 = 4.7 weeks

Solution for (e)

Given

Cost per hour per workstation = $25

Cost per week per workstation = $1000

Please find the below calcualtion table considering the 20% capacity cushion

Dsign	Demand	Batch Size	No. of Batches	Set up Time (hr/batch)	Setup rounds	Total setup time	Processing time (hr/unit	Total Processing Time	Total Time Required
A	500	50	10	2	3	20	0.031	15.6	21.6
B	750	50	15	2	4	30	0.031	23.4	31.4
C	600	50	12	2.5	3	30	0.052	31.3	38.8
D	800	50	16	4	4	64	0.052	41.7	57.7
E	450	50	9	1.5	3	13.5	0.021	9.4	13.9

Total production hours required to fulfill the demand = 163.4 hours

Total cost = Rate per hour * Total production hours * No. of workstation = 25*163.4*4 = $16335.42

Solution for (f)

Given

Cost of purchasing and commissioning workstation = $2500

As per solution of question (c), 5 worksations are required. Since the company already has 4 worksations, it required additional 1 worksation which requires $2500 for purchasing and commissioning, bring up the total production cost to $18835.42.

However, the $2500 can be considered capital expenditure, keeping the production cost to $16335.42

Solution for (g)

If the company has to pay a penalty of $4500 upon cancelling other contracts, then the company should purchase the additional workstation. This will eliminate the loss of $4500. The $2500 spent on purchasing and commissioning new workstation can be recovered through future business.