Can some one help!

Hello All, I have been asked to do a project that seems to be baffling me. It's not really the php which is the hard part, but the mathematical problem behind the project that is causing me to have a headache! Imagine an ecommerce site where a user can pick 5 products (it must be 5) from a possible 60. That's the easy bit. The project that I have to do is to do with the way the order is dealt with. Imagine the company has a warehouse (the attached layout) where the yellow boxes are bins of 1 product in each (A1 would be the bin with all products A1 in). P1, P2, and P3 are stations where pickers (people who pack each order) receive the order. I have to build some PHP that shows the picker the optimum way around the warehouse to pick up all the 5 products, and then return him to the starting station. I hope there is a bright spark out there that can solve this easier than I have (my way requires calculating all the possible ways of picking up the 5 products and then calculating the shortest route from a stored database, but it would require 780 sql statements, that just isn't going to work!) Here are the rules that I have to follow: An Order Picking slip for a complete order is printed at 1 of 3 packing locations (P1, P2, or P3). A picker must start at one of these packing locations, collect all products required for that order then return back to the start position to deposit all items for packing. Note: a.. A picker can only move one square at a time (& not diagonally) b.. Pickers cannot walk through bin locations! c.. A picker can only access a bin location when standing directly at the side. e.g. A picker standing at 'X' can access locations B8 or C8 from this position. A picker standing at 'Y' cannot access any locations. I live in hope! Hamish

Attachment: [application/vnd.ms-excel] warehouse layout.xls