project simplex

go backwards in time, starting from the mid sixties, and get hands on with a very small business problem using linear programming on an ibm 7094 computer. the widget problem of alp 3.5 seems ideal since it is explicitly solved there in tableau form. it only takes four iterations and every operation is easily checked against code implementations.

it can be implemented in python first. the trick is to make the python as relevant as possible to f66 on pdp-10 and 7094. the ultimate implementation in 7094 f66 should use simh emulated mag tape to store pfi product form of inverse eta columns for use in ftran and btran.

five activities x1 to x5 and five columns of the tableau

activity x1 is production of unfinished widgets
activity x2 is conversion of unfinished to finished widgets
activity x3 is production of finished widgets from scratch
activity x4 is the use of l1 overtime
activity x5 is the use of l2 overtime

the five rows of the model and its tableau

row 1 is the functional, costs are positive and revenues are negative. functional means objective recast as an equation including the values to be maximized
row 2 is capacity constraint on l1 labor
row 3 is capactiy constraint on l2 labor
row 4 is used to insure that enough unfinished widgets are produced to allow some of them to be converted to finished ones
row 5 is contractual and policy constraints on unfinshed widgets

row equations

u1 - 5.4x1 - 7.3x2 -12.96x3 + 6x4 + 9x5 + 800 = 0
.5x1 + .6x3 - x4 <= 80
.25x1 + .5x2 + .6x3 - x5 <= 40
-x1 + x2 <= 0
100 <= x1 <= 150

where all x >= 0, x4 <= 20, x5 <= 10, u1 is to be maximized

code cold storage area

function feas = isfeas(itr, bh, vtyps) feas = true; for i = 1:5 b = itr(i,11); vt = vtyps(bh(i)); if vt == 1 if b < 0 || b > 1, feas = false; end elseif vt == 2 if b < 0, feas = false; end end end end