ISE$301$ Modelling and Optimization II $-$ Assignment $2$

$(100$p$)$ An assembly line has three serial workstations. For the assembly line to work properly,

these workstations must all function properly. To increase the reliability of the assembly line,

extra workers may be added to each workstation. It costs $$400$ to add an extra worker to

workstation $1,$ $$200$ to workstation $2,$ and $$600$ to workstation $3.$ As a function of the number of

added workers $($a maximum of two workers may be added to each system$),$ the reliability of each

workstation is given in table below. Use dynamic programming to maximize the probability that

the assembly line will work properly, given that $$1200$ is available for extra workers.

a$)(20$p$)$ Clearly indicate stages, states, decisions, and the recursion relation.

b$)(20$p$)$ Show your manual calculations for all $f$ values.

c$)(10$p$)$ State the optimal strategy that maximizes the reliability of the assembly line. $($Note

that multiple strategies may exist.$)$

d$)(50$p$)$ Implement the problem on Excel $($include Excel screenshots in your answer sheet$).$

Submit Excel as a separate file.

$(5$p$)$ Adherence to submission rules:

See Blackboard page before preparing your submission.