A manager is going to purchase new processing equipment and must decide on the number of spare parts to order with the new equipment. The spares cost $170 each, and any unused spares will have an expected salvage value of $40 each. The probability of usage can be described by this distribution:
Number | 0 | 1 | 2 | 3 |
Probability | .05 | .40 | .20 | .35 |
If a part fails and a spare is not available, 2 days will be needed
to obtain a replacement and install it. The cost for idle equipment
is $550 per day. What quantity of spares should be ordered?
a. Use the ratio method. (Round your answer to 2 decimal
places.)
Service level is , so we need to
order Spares.
b. Use the tabular method.
Cost of Stock out Cs = 550*2 = 1100
Cost of Excess Inventory Ce= 170 - 40 = 130
Service Level = Cs/(Cs+Ce)
Service Level = 1100/(1100+130)
Service Level = 0.8943
Below is the probability table -
Number | Probability | Cumulative Probability |
0 | 0.05 | 0.05 |
1 | 0.4 | 0.45 |
2 | 0.2 | 0.65 |
3 | 0.35 | 1 |
0.8943 lies between, 0.65 and 1, Hence
Number of Spare = 3
2)
Tabular Method -
Below is the calculation performed as per tabular method -
Demand = 0 | Demand = 1 | Demand = 2 | Demand = 3 | ||
Stocking Level | 0.05 | 0.4 | 0.2 | 0.35 | Expected Cost |
0 | 0 | 440 | 440 | 1155 | 2035 |
1 | 6.5 | 0 | 220 | 770 | 996.5 |
2 | 13 | 52 | 0 | 385 | 450 |
3 | 19.5 | 104 | 26 | 0 | 149.5 |
Cost is lowest with 3 spare parts, hence 3 spare parts should be ordered.
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