Example of Calculation of Tool Number

A production industry contains a machine having two tool types for three products. The cost of the idle tool (PT) in two consecutive operations is 348 units and 342 units correspondingly and cost of idle tool of types 1, 2 are 150 units and 140 units correspondingly. Calculate tool number if utilization of tool of types 1, 2 for first operation is 0.4, and 0.6 whereas for second operation it is 0.7 and 0.4 correspondingly.

Solution

Given data:

For first operation: Φ₁ = 0.4, Φ₂ = 0.6, P = 348 unit, P₁ = 150 unit, P₂ = 140 unit

For second operation: Φ₁ = 0.7, Φ₂ = 0.4, P = 342 unit, P₁ = 150 unit, P₂ = 140 unit

Suppose number of tool of type 1 is N1 and number of tool of type 2 is N₂

Using Equation

For first operation:

Equation 1

348 = 150 * N₁ * (1 - 0.4) + 140 * N₂ * (1 - 0.6)       

For second operation:

Equation 2

342 = 150 * N₁ * (1 - 0.7) + 140 * N₂ * (1 - 0.4)    

After solving Eqs. (2) and (3), it is found that

N₁ = 2 and N₂ = 3.