Question

2. Consider two identical machines in parallel. Four items have to be pro- duced items 2 3 50 50 60 60 Q 200 200 300 300 20 20 30 70 2000 2500 800 0 (a) Find the optimal rotation schedule assuming that the cycle lengths of the two machines have to be the same. Compute the total average cost per unit time. (b) Find the optimal rotation schedules of the two machines assuming the cycle lengths of the two machines do not have to be the same (determine which items have to be combined with one another on the same machine to obtain the best result). Compute the average cost per unit time and compare the result with the result found under (a).

Answer 1

Given:-

Items 1 2 3 4 Q 200 200 300 300 hj 2 2 60 2 30 2000 2500 800 70

where,

Dj is demand for item j

Qj is production rate of item j

hj is inventory holding cost for item j

cj is setup cost for item j

Optimal Cycle length is given by:-

エー 12 3-1

The ideal time is given by:-

0-20 Q,

Therefore. Idle time = .48X = 0.595 Months

Total avg cost per unit time is calculated as given below

=

(b) Total avg cost per unit time is

2155

2599

1627

2213

Hence, Machine 3 will do better as avg. cost per unit time is lower for machine 3.