Question $33$: Capacity planning

MicroControl Limited produces three different types of micro controllers $($A$,$ B$,$ C$)$ to prevent industrial equipment to overheat. Each unit is processed by a machine that production manager has identified as process bottleneck. The plant operates on two $8-$hour shifts, $5$ days per week, $52$ weeks per year. Table $3$ provides the time standards at the bottleneck, lot sizes, and demand forecasts for the three units. Because of demand uncertainties, the operations manager obtained three demand forecasts $($pessimistic$,$ expected, and optimistic$).$ The manager believes that a $20$ percent capacity cushion is best.

Table $3$: Capacity information for the company

$\backslash$table$[[$TIME STANDARD,DEMAND FORECAST$],[$Component$,\backslash$table$[[$Processing$],[($hr$/$unit$)]],\backslash$table$[[$Setup$],[($hr$/$lot$)]],\backslash$table$[[$Q Lot Size$],[($units$/$lot$)]],$Pessimistic,Expected,Optimistic,,,,,,$],[$A$,0\mathrm{.}05,1\mathrm{.}0,60,16,000,16,000,26,000,,,,,,],[$B$,0\mathrm{.}30,4\mathrm{.}1,80,11,000,12,000,18,000,,,,,,],[$C$,0\mathrm{.}05,8\mathrm{.}3,100,16,000,23,000,35,000,,,,,,]]$

a$.$ How many machines are required to meet minimum $($pessimistic$)$ demand, expected demand, and maximum $($optimistic$)$ demand?

b$.$ How many machines are required if the operations manager decides to double lot sizes?

$8$ N$37$

c$.$ If the operations manager has three machines and believes that the plant can reduce setup time by $25$ percent through process improvement initiatives, does that plant have adequate capacity to meet all demand scenarios without increasing lot sizes?

an $39$

The operations manager at MicroControl Limited believes that pessimistic demand has a probability of $20$ percent, expected demand has a probability of $50$ percent, and optimistic demand has a probability of $30$ percent. Currently, new machines must be purchased at a cost of $500,000$ a piece, the price charged for each control unit is $110,$ and the variable cost of production is $50$ per unit.

$[$Hint$]$: since the price and variable cost for each control unit are the same, the profit maximizing product mix will be the same as the mix that maximizes the total number of units produced.

a$.$ Draw a decision tree for this problem.

$q38$

If the oplant can reduce setup capacity to meet all demand scenarios without increasing lot sizes?