A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a ‘first come first served’ queue discipline. Breakdowns occur on an average of $$3$$ per day with a range of zero to eight. The maintenance crew can service an average of $$6$$ machines per day with a range of zero to seven. The mean waiting time for an item to be serviced would be

An electronic equipment manufacturer has decided to add a component sub-assembly operation that can produce $$80$$ units during a regular $$8$$-hour shift. This operation consists of three activities as below .

For line balancing the number of work stations required for the activities $$M, E$$ and $$T$$ would respectively be

For a product, the forecast and the actual sales for December $$2002$$ were $$25$$ and $$20$$ respectively. If the exponential smoothing constant $$(\alpha )$$ is taken as $$0.2,$$ then forecast sales for January $$2003$$ would be

In $$PERT$$ analysis a critical activity has