Question

HSS Ltd. manufactures decorative tins that hold various food products such as popcorn, cookies, and candies. The finished tins are sold to food packaging companies that fill the tins. In making the actual tin, minus the lid, there are three steps involved: Step 1: Lithography, Step 2: Molding/Sealing, and Step 3: Assembly.

Table 1 lists the required processing times and set up times at each of the steps. The demand greatly exceeds capacity for these decorative tins. There is unlimited space for buffer inventory between these steps.

Table 1: Processing Times and Set-up Times for Tin Manufacturing

Process step	1 Lithography	2 Molding / Sealing	3 Assembly
Set up time	50 min	0	20 min
Activity time	2 min/tin	3 min/tin	1 min/tin

What is the maximum amount of tins the Assembly step can produce per hour with a batch size of 100 tins?

24 tins/hour

20 tins/hour

None of the above

50 tins/hour

100 tins/hour

What is the maximum amount of tins the Assembly step can produce per hour if the batch size becomes 60 tins?

None of the above

60 tins/hour

25 tins/hour

30 tins/hour 45 tins/hour

What is the process capacity in tins per hour with a batch size of 100 tins?

20 tins/hour

24 tins/hour

60 tins/hour

50 tins/hour None of the above

What batch size should be used in order to minimize inventory without sacrificing flow rate?

100 tins

None of the above

125 tins

50 tins 20 tins

Management is considering the purchase of a new lithography machine. Model 1 will reduce the set up time of Lithography by 10 minutes. Model 2 will reduce the activity time of the Lithography machine by 0.1 minute but setup time will remain unchanged at 50 minutes. Which model will increase the process capacity (meaning, the capacity of the entire process) the most with a batch size of 100 tins?

Both models

Model 2

Model 1

Neither model

None of the above

Answer 1

Q1 : 50 tins/hour

Capacity of a step is given by below formula

Capacity = Batch Size/(Setup time + Processing Time* Batch Size)

For batch size = 100, capacity of assembly step is

Capcaity= 100/(20+1*100) = 100/120 = 0.8333 tins/minute = 0.8333*60 tins/hour = 50 tins/hour

Q2 : 45 tins/hour

Capacity of a step is given by below formula

Capacity = Batch Size/(Setup time + Processing Time* Batch Size)

For batch size = 60, capacity of assembly step is

Capcaity= 60/(20+1*60) = 60/80 = 0.75 tins/minute = 0.75*60 tins/hour = 45 tins/hour

Q3 : 20 tins/hour

Maximum amount of tins that can be produced is given by the capacity of the bottleneck. The bottleneck is the step with the lowest capacity. Capacity of a step is given by below formula

Capacity = Batch Size/(Setup time + Processing Time* Batch Size)

For lithography we have Capacity = 100/(50+2*100) = 100/250 = 0.4 tins/minute = 0.4*60 tins/hour = 24 tins/hour

For molding we have Capacity = 100/(0+3*100) = 100/300 = 0.3333 tins/minute = 0.3333*60 tins/hour = 20 tins/hour

For Assembly Step we have Assembly = 100/(20+1*100) = 100/120 = 0.8333 tins/minute = 0.8333*60 tins/hour = 50 tins/hour

We can see that the capacity of molding process is the least and hence this is the bottleneck which determines the process capacity. Thus process capacity is 20 tins/hour

Q4 : 50 tins

The flow rate is the minimum of process capacity and demand. The process capacity is 0.3333 tins per minute or 20 tins per hour. Thus flow rate = 20 tins/hour or 20/60 = 0.333 tins per minute

Target Batch Size = [Capacity * Total Setup Time]/[1-(Capacity*Processing Time)]

Setting the capacity of lithography as 0.3333/ minute we get

Target Batch Size = [0.3333*50]/[1-(0.3333*2)] = 16.6666/(1-0.6666) = 16.6666/3.3334 = 50 tins

Setting the capacity of assembly as 0.3333/ minute we get

Target Batch Size = [0.3333*20]/[1-(0.3333*1)] = 6.6666/(1-0.3333) = 6.6666/0.6667 = 10 tins

To ensure that flow rate does not fall below 0.333 per minute, we need to select the maximum of above batch size calculated. Hence target batch size to minimize inventory without decreasing flow rate is 50 tins.