# Shopping Cart Optimisation

The bid is about providing a solution in theory only to optimisation of a shopping cart. No coding needed. Standard notion such as Sigma for Sum may be used. The problem is stated below.

A shopping cart consists of m items which are supplied by up to n suppliers. The cart appears on a Reverse Auction website, so suppliers bid on the price of each item in the cart. The buyer wants the lowest price for the whole cart.

Each supplier has a delivery charge, so there are n delivery charges, but only one delivery applies per order.

The total of the shopping cart (ie the final buying price) must be optimised by selecting the best supplier bids and factoring the delivery charges.

In the case of no delivery charges, the problem is very easy, as simple the best price is taken for each item and then the sum taken.

But since delivery charges vary, the best price for the item will not provide the total cost. Also there is just one charge for the whole order per supplier, so the charge cannot just be added to the item price since it applies for all items supplied by that supplier. ie if m items exist and r are supplied by suppliers already supplying siomething for the cart, then we have n-r delivery charges, eg 3 suppliers for the cart means 3 delivery charges.

Example: A cart has 4 items and 3 suppliers bid for the cart, ie they want to sell the items. If Seller 1 can supply items 1,2; Seller 2 can supply items 2,3,4; Seller 3 can supply also 1,2; then we have a total of six possibilities as follows for the totals:

{T1,T2,T3,T4,T5,T6}=

{S1,S1,S2,S2}+{D1+D2},{S1,S2,S2,S2}+{D1+D2},{S1,S3,S2,S2}+{D1+D2+D3},{S3,S1,S2,S2}+{D1+D2+D3},{S3,S2,S2,S2}+{D2+D3},{S3,S3,S2,S2}+{D3+D2}

Hence the lowest Total would be taken from the six possible totals.

## Deliverables

1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done.

2) Deliverables must be in ready-to-run condition, as follows (depending on the nature of the deliverables):

a) For web sites or other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment.

b) For all others including desktop software or software the buyer intends to distribute: A software installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request.

3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement).

## Platform

The work is part of mathematics and requires skills in that area. It is part of Auction Theory or Operational Research.

A solution should be produced so that converting into code is possible, ie the explicit calculations need to be showed, and not simply a high theory stated and then therefore ....

Om arbejdsgiveren:
( 97 bedømmelser ) westcliff, United Kingdom

Projekt ID: #3329774

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