MM584 CONTINUOUS ASSESSMENT 2020-21

The Challenge:

In a manufacturing system, after rough castings are manufactured, they must pass through a finishing department. Castings are made ready for the finishing process in the warehouse with an interarrival rate uniformly distributed within the interval 12020 minutes. There are three types of castings in the system: 20% of the castings are of Type 1, 25% is of Type 2 and the remaining are of Type 3. The finishing work consists of 7 steps carried out in order. The time interval it takes to perform each step for each type of casting is given in Table 1. The step times are uniformly distributed within the given intervals in the table. At most two castings are processed at each finishing station at one time.

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Step 1: Casting is brought in from the warehouse. Step 2: Loading the casting onto first finishing station. Step 3: Carry out first finishing process.

Step 4: Loading the casting onto second finishing station. Step 5: Carry out second finishing process.

Step 6: Unloading the casting from the second finishing station. Step 7: Casting is taken back to the warehouse.

The castings are very heavy so for steps 1,2,4,6 and 7, a crane is used. There is only one crane in the manufacturing system, and it is used also by other departments. The other departments require to use the crane with an interarrival time distributed exponentially with average 60 minutes. For each request, the duration of the time the other departments use the crane is a uniformly distributed random variable in the interval 2010 minutes. Requests coming from the other departments to use the crane have higher priority than those coming from the finishing department.

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Table 1: Times required for completing each step for each type of casting

	Type 1	Type 2	Type 3
Step 1	123 minutes	123 minutes	123 minutes
Step 2	103 minutes	103 minutes	103 minutes
Step 3	8020 minutes	5015 minutes	6520 minutes
Step 4	157 minutes	157 minutes	157 minutes
Step 5	11030 minutes	9020 minutes	13010 minutes
Step 6	104 minutes	104 minutes	104 minutes
Step 7	123 minutes	123 minutes	123 minutes

Points to be addressed in this CA:

The description of the system is deliberately vague. You must make assumptions about the system structure and inventory controls and provide justifications for your assumptions.