bidsos.gms : Bid Evaluation with SOS2 Sets

**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.

**Reference**

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

**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
$offText
Set
v 'vendors' / a, b, c, d, e /
s 'segments' / nodeal, 0*5 /
cl 'column labels' / setup, price, q-min, q-max ,cost /
vs(v,s) 'vendor bit possibilities';
Scalar req 'requirements' / 239600.48 /;
Table bid(v,s,cl) 'bid data'
setup price q-min q-max
a.1 3855.84 61.150 33000
b.1 125804.84 68.099 22000 70000
b.2 66.049 70000 100000
b.3 64.099 100000 150000
b.4 62.119 150000 160000
c.1 13456.00 62.190 165600
d.1 6583.98 72.488 12000
e.1 70.150 42000
e.2 68.150 42000 77000;
* get minimum domains ripple total cost up the segments
* cost will contain the total segment cost
bid(v,'0','cost') = bid(v,'1','setup') + bid(v,'1','q-min')*bid(v,'1','price');
loop((v,s)$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;
```