Johnsons algorithm for scheduling n jobs on two machines in the deterministic case has a natural extension to the stochastic case as long as the job times are exponentially distributed.

We take a and b as the expected rates on machines A and B $($A $=1$ B $=$ by are expected times$)$

Johnson's rule using expected values then implies that i is before i $+1$ if ai bi ai$+1$ bi$+1,$ i$.$e$.,$ process in order of decreasing values of expected rate differences.

Applying the above methodology find the optimal sequence for the following problem:

Two law students, John and Marsha, are planning an all$-$nighter to prepare for their law boards the following day. Between them they have one set of materials in the following five subjects: contracts, torts, civil law, corporate law, and patents. Based on their previous experience, they estimate that they will need the following amount of time $($in hours$)$ with each set of material

Contracts

Marsha

$1\mathrm{.}2$

$1\mathrm{.}8$

Torts

$2\mathrm{.}2$

$0\mathrm{.}8$

Civil

$0\mathrm{.}7$

$3\mathrm{.}1$

Corporate

$0\mathrm{.}5$

$1\mathrm{.}1$

Patents

$1\mathrm{.}5$

$2\mathrm{.}3$

John

If the times required by John and Marsha are exponentially distributed random variables with expected times given in table. Find the optimal sequence.