I have a Green Card in USA and it is scheduled to expire in July this year and have been offered a 6-month contract role in Switzerland. Even though the company would need me to start within the next couple of week, I would probably not be back in USA before the expiration of the Green Card. Is this a problem if my Green Card expires while abroad?
I would try to renew the card before you leave but if not USCIS has a procedure for renewing while abroad:
How to Renew a Green Card If You Are Outside the United States
If you are outside the United States and your green card will expire within 6 months (but you will return within 1 year of your departure from the United States and before the card expires), you should file for your renewal card as soon as you return to the United States.
If you are outside of the United States when the card expires and you have not applied for the renewal card prior to your departure, you should contact the nearest U.S. Consulate, USCIS office, or U.S. port of entry before attempting to file Form I-90 for a renewal green card.
Generally the expiration date on the plastic has no bearing on your legal status (unless you have a "conditional" green card). You can use an expired card to enter the US, as long as your status is valid. See page 36 here.
LPRs with expired I-551s may be boarded without penalty provided the card was issued with a 10-year expiration date. A passport is not required
That said, you may want to apply for renewal before you go, or apply for REP. It is required if you stay out of the country for a year or more, but probably won't hurt you even if you stay less.