List of top Materials, Manufacturing & Industrial Engineering Questions on Production Planning and Control

The activities of a PERT network and their corresponding activity time estimates (in weeks), namely optimistic (\(t_o\)), most likely (\(t_m\)), and pessimistic (\(t_p\)), are given in the table below.

Activity	\(t_o\)	\(t_m\)	\(t_p\)
1-2	2	4	12
1-3	2	4	6
1-4	3	4	11
2-5	3	6	9
3-4	2	5	14
3-5	3	3	3
4-5	3	6	15
5-6	2	5	8

The expected project length is ________ weeks (in integer).

The actual demand for castings in a factory is \(500\) units and \(635\) units for the months of January 2026 and February 2026, respectively. The forecasted demand for January 2026 is \(250\) units and the smoothing constant is \(0.7\). Using the exponential smoothing method, the forecast of the demand for castings in March 2026 is ________ units (in integer).

Four jobs are on order in a factory. As on day 20 of the production calendar, the corresponding due date and work remaining to complete these jobs (in days) are given in the table below.

Job	Due date	Work remaining (in days)
M	26	5
N	24	10
O	28	10
P	31	5

Which job(s) has/have critical ratio less than unity?