Consider a production system with four stations in series. The processing time at each station is exponentially distributed with a mean of $24$mins. Assume job interarrival times are exponential. The profit per unit is $$10$ and the holding cost is $$1.$

$4$StationLine.png

Please provide the final numerical solution, not including any text, for each of the sections and then upload your full calculations as a pdf file in the last section below.

Question $3\mathrm{.}1$ WIP Level $-$ CONWIP

Q$3\mathrm{.}1$ WIP Level $-$ CONWIP

$2$ Points

Grading comment:

What is the WIP level required to achieve a throughput of $2$ jobs per hour, assuming that the line is run under the CONWIP discipline?

Question $3\mathrm{.}2$ Profit $-$ CONWIP

Q$3\mathrm{.}2$ Profit $-$ CONWIP

$2$ Points

Grading comment:

What is the profit of this CONWIP system?

Question $3\mathrm{.}3$ WIP Level $-$ Push

Q$3\mathrm{.}3$ WIP Level $-$ Push

$2$ Points

Grading comment:

Suppose that we are running the line as a push system, instead of a CONWIP line. What will be the average WIP in the system if we release at the same rate of $2$ jobs$/$hour to the system?

Question $3\mathrm{.}4$ Profit $-$ Push

Q$3\mathrm{.}4$ Profit $-$ Push

$2$ Points

Grading comment:

What is the profit of the Push system?

Question $3\mathrm{.}5$ CONWIP Benefits

Q$3\mathrm{.}5$ CONWIP Benefits

$5$ Points

Grading comment:

Explain the observed difference in profits between push and CONWIP systems and describe further benefits of one system over the other.