Weird pricing observations for a flight booking

I am going to assume that the itineraries are exactly the same except for the price.

There are many, many ways to cover a given flight itinerary with a valid set of fare components. The computational difficulty in the problem is finding the lowest allowable combination by price.

My guess is that basically the pricing engine in the first instance was not clever enough to find the lowest possible combination of fares covering your journey. (I have to say this is a bit unusual for such a simple journey but mistakes do happen.)

By asking for "ORD [Chicago-O'Hare] BOM [Mumbai]" return, your search engine probably did find a fare covering ORD-BOM-ORD round trip. If the search engine is not particularly intelligent it will stop there. To be fair that is how a travel agent would have priced your fare in the old days.

However, when you asked for a multicity trip the engine may have worked a little bit harder to look at alternatives. For instance, perhaps the engine realized that it could price your itinerary as CHI-NYC [Chicago to New York] (domestic fare component one way), and then use an "open jaw" of NYC-BOM half-return trip and BOM-CHI half-return trip. It might be that the sum of those fares is actually cheaper than the straight round-trip given above. (For example, if there was a sale on from NYC to BOM, you could only take advantage of it by going through NYC and using the NYC-originating fare.)

Fares cannot be combined on one ticket in an arbitrary manner. The way that a fare can be combined with other fares is given within the rules of that particular fare. For example, UA [United Airlines] publishes one particular K-class fare from Chicago to Bombay (called "KKXKEC7N") with the following combination rules:

Category 10: Combinability
   APPLICABLE ADD-ON CONSTRUCTION IS ADDRESSED IN
   MISCELLANEOUS PROVISIONS - CATEGORY 23.
  END-ON-END
    END-ON-END COMBINATIONS PERMITTED. VALIDATE ALL FARE
    COMPONENTS. SIDE TRIPS PERMITTED.
   PROVIDED -
     COMBINATIONS ARE FOR CARRIER UA/AC WITHIN AREA 1
  END-ON-END
    EXCEPT AS PROVIDED ABOVE END-ON-END COMBINATIONS NOT
    PERMITTED WITH INTERNATIONAL FARES FROM/TO SIERRA LEONE/
    GUINEA/LIBERIA. VALIDATE ALL FARE COMPONENTS. SIDE TRIPS
    PERMITTED.
  END-ON-END
    END-ON-END COMBINATIONS PERMITTED. VALIDATE ALL FARE
    COMPONENTS. SIDE TRIPS PERMITTED.
   PROVIDED -
     COMBINATIONS ARE FOR CARRIER UA/LH/LX/OS/SN/AC WITHIN
     AREA 2
     OR FOR CARRIER UA/LH/LX/OS/SN/AC BETWEEN AREA 2/AREA 3
     COMBINATIONS ARE FOR CARRIER UA/NH PUBLISHED FOR TRAVEL
      VIA THE PACIFIC.
  OPEN JAWS
    FARES MAY BE COMBINED ON A HALF ROUND TRIP BASIS
    -TO FORM SINGLE OR DOUBLE OPEN JAWS.
     MILEAGE OF THE OPEN SEGMENT MUST BE EQUAL/LESS THAN
     MILEAGE OF THE LONGEST FLOWN FARE COMPONENT.
   PROVIDED -
     THE OPEN SEGMENT MUST BE
     -BETWEEN AREA 2 AND AREA 3
      -WITHIN AREA 1 OR WITHIN AREA 2 OR WITHIN AREA 3
       COMBINATIONS ARE WITH ANY FARE FOR CARRIER UA/LH/LX/
     OS/SN/AC IN ANY RULE AND TARIFF.
  ROUND TRIPS/CIRCLE TRIPS
    FARES MAY BE COMBINED ON A HALF ROUND TRIP BASIS
    -TO FORM ROUND TRIPS
    -TO FORM CIRCLE TRIPS
     A MAXIMUM OF TWO INTERNATIONAL FARE COMPONENTS
     PERMITTED.
   PROVIDED -
     COMBINATIONS ARE WITH ANY FARE FOR CARRIER UA/LH/LX/OS/
     SN/AC PUBLISHED FOR TRAVEL VIA THE ATLANTIC.
     COMBINATIONS ARE WITH ANY FARE FOR CARRIER UA/NH
      PUBLISHED FOR TRAVEL VIA THE PACIFIC.
 NOTE - THE CITY PAIRS BELOW ARE CONSIDERED THE SAME POINT-
        NYC-EWR

As you can see it quickly becomes a very complex exercise to understand whether two fare components are mutually compatible, let alone three or four! This is why it takes a few moments for the search engine to come back with a price for an uncommon journey.

Travel agents now pay companies such as ITA Software a lot of money to develop fast algorithms for pricing journeys quickly, but as soon as you get into multicity territory it is possible for the pricing system to really struggle to get it right. I often find it takes me a good hour to price a journey involving four or five cities in different countries, and another hour or so to get it booked.