python - PuLP - relative allocation constraint

Question

I have a bucket and list of items with a packsize where a packsize is a collection of units.

bckdf=pd.DataFrame.from_dict({0:{'Bucket_Type': 'Veg', 'Capacity':1000},
                        1:{'Bucket_Type': 'Non-Veg', 'Capacity':500}}).T

items=pd.DataFrame.from_dict({'item_no': {0: '123', 1: '456', 2: '789'},
 'item_description': {0: 'Buffet Malabar Paratha 300 gm',
  1: 'Mc Cain French Fries Value Pk 750 Gm',
  2: 'Yummies Veg Sticks 320 gm Pouch'},
 'volume': {0: 0.0714286, 1: 0.214286, 2: 0.0357143}})

I need to fit in minimum 900 units in the bucket, while ensuring that more or less equal number of packs are put in the bucket for each item. Everytime, i choose 1 pack, I use up volume of that pack which I formulated as a cost.

prob = LpProblem("LP_Problem", LpMaximize)

buckettype = bckdf[bckdf['Bucket_Type']=='Veg']['Bucket_Type']
capacity = bckdf.set_index(['Bucket_Type'])['Capacity'].to_dict()
itemlist=items['item_no']
combos = [(w,b) for w in buckettype for b in itemlist]
costs = makeDict((buckettype, itemlist),[items['volume']])

itemqtydict = LpVariable.dicts("Combo",(buckettype, itemlist), 0, None, LpInteger)
## Objective function
prob += lpSum([(itemqtydict[w][b]) for (w,b) in combos])
prob += lpSum([(itemqtydict[w][b])*costs[w][b] for (w,b) in combos])>=900
prob += lpSum([(itemqtydict[w][b])*costs[w][b] for (w,b) in combos])<=bckdf[bckdf['Bucket_Type']=='Veg']['Capacity'].values[0]

status=prob.solve(pulp.PULP_CBC_CMD(timeLimit=5,msg=1, gapRel=1))

How do I build in constraint where

more or less equal number of packs are put in the bucket

Answer 1

You basically already have it with

prob += lpSum([(itemqtydict[w][b])*costs[w][b] for (w,b) in combos])>=900

Here you're constraining the cost of the items in the bucket to be equal to or greater than 900.

But if you want just the number of items to be greater then you can use;

prob += lpSum([(itemqtydict[w][b])] for (w,b) in combos])>=900