Description

A company obtains a number of bids from vendors for the supply
of a specified number of units of an item. Most of the submitted
bids have prices that depend on the volume of business. A formulation
with 0/1 variables is shown in the original gamslib model BID. Here
we use SOS2 sets (at most two variables can be basic but have to be
adjacent. SOS2 variables are a convenient way to interpolate non-
convex but separable functions.

Small Model of Type : MIP

Category : GAMS Model library

Main file : bidsos.gms

$title Bid Evaluation with SOS2 Sets (BIDSOS,SEQ=163)

$onText
A company obtains a number of bids from vendors for the supply
of a specified number of units of an item. Most of the submitted
bids have prices that depend on the volume of business. A formulation
with 0/1 variables is shown in the original gamslib model BID. Here
we use SOS2 sets (at most two variables can be basic but have to be
adjacent. SOS2 variables are a convenient way to interpolate non-
convex but separable functions.


Bracken, J, and McCormick, G P, Chapter 3. In Selected Applications
of Nonlinear Programming. John Wiley and Sons, New York, 1968,
pp. 28-36.

Keywords: mixed integer linear programming, special ordered sets, micro economics,
          bid evaluation
$offText

Set
   v       'vendors'       / a, b, c, d, e /
   s       'segments'      / nodeal, 0*5   /
   cl      'column labels' / setup, price, q-min, q-max, cost /
   vs(v,s) 'vendor bit possibilities';

Scalar req 'requirements' / 239600.48 /;

Table bid(v,s,cl) 'bid data'
            setup   price   q-min   q-max
   a.1    3855.84  61.150           33000
   b.1  125804.84  68.099   22000   70000
   b.2             66.049   70000  100000
   b.3             64.099  100000  150000
   b.4             62.119  150000  160000
   c.1   13456.00  62.190          165600
   d.1    6583.98  72.488           12000
   e.1             70.150           42000
   e.2             68.150   42000   77000;

* get minimum domains ripple total cost up the segments
* cost will contain the total segment cost

bid(v,'0','cost') = bid(v,'1','setup') + bid(v,'1','q-min')*bid(v,'1','price');
loop((v,s)$bid(v,s,'q-max'),
   bid(v,s,'cost') = bid(v,s - 1,'cost') + (bid(v,s,'q-max') - bid(v,s,'q-min'))*bid(v,s,'price');
);
display bid;

vs(v,s)        = bid(v,s,'q-max');
vs(v,'nodeal') = yes;
vs(v,'0')      = yes;

Variable c 'total cost';

SOS2 Variable pl(v,s) 'purchase level (sos2 type variable)';

Equation
   demand  'demand constraint'
   costdef 'cost definition'
   convex  'convexity definition for segments';

demand..    req =e= sum(vs, bid(vs,'q-max')*pl(vs));

costdef..   c   =e= sum(vs, bid(vs,'cost') *pl(vs));

convex(v).. sum(vs(v,s), pl(vs)) =e= 1;

Model bideval / all /;

option optCr = 0.0;

solve bideval minimizing c using mip;

Parameter rep 'purchase report';
rep(v) = sum(vs(v,s), bid(vs,'q-max')*pl.l(vs));
display rep;