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A manufacturing company is planning to start its operations soon. It produces one model of a

product using a production system with two sequential processes $($process A and process B$).$ Each

process comprises one or more similar machines that run in parallel. Process B can only process the

outputs from Process A that are released to Process B$.$

Below is the key data relating to the two processes:

The sales forecast has determined demand projections over the next four years as follows: Year $1$

$(10,000$ units$),$ Year $2(12,500$ units$),$ Year $3(15,000$ units$),$ and Year $4(17,500$ units$).$ Assume that

daily demand remains stable over the year, and the company operates five days a week with the

normal operating hours being $8$ hours per day.

The company plans to operate all machines at their full capacity within the normal operating hours

and does not want to have any backorder in meeting the annual demand. Overtime can be used in

any year, when needed. The management team is discussing the production capacity plan of the

factory against the projected demand.

Propose a production capacity plan of each process to meet the demand forecast at the lowest total

cost $($which must include the cost of purchasing the machines$)$ over these four years. Note that

currently the company has yet to own any machine.

Explain the logic behind your production plan, i$.$e$.$ the number of machines that the company should

invest in$,$ the amount of overtime units and inventory units $($if any$)$ over the four years.

It is recommended that you use table$($s$)$ in your quantitative analysis to present your answers and

demonstrate your understanding of the relevant operations management theories or concepts.