A Lagrangian heuristic for bid evaluation in e-procurement auctions

e-Procurement is an Internet based business process for sourcing direct or indirect materials. This paper considers a procurement scenario of a buyer procuring large quantities of a single good. The suppliers submit nonconvex piecewise linear supply curves as their bids. Such bids enable the suppliers to effectively express their economies of scale and transportation constraints. The buyer imposes a business rule of limiting the winning suppliers within a preferred range. The bid evaluation problem faced by the buyer is to select the winning suppliers and their trading quantities, such that the cost of procurement is minimized while satisfying the supply, demand, and business constraints. The bid evaluation problem is NP-hard even for a simple special case. In this paper, the problem is formulated as a mixed integer linear programming problem and we propose a Lagrangian relaxation based heuristic to find a near optimal solution. The computational experiments performed on representative data sets show that the proposed heuristic produces a feasible solution with negligible optimality gap.