Supplier pricing and lot sizing when demand is price sensitive

The problem of co-ordination between a vendor and a buyer is formulated as a two-person fixed threat bargaining game. The vendor decides on his lot size and the price schedule he is to offer to the buyer. The buyer decides upon his lot size and the selling price in the market. We have characterized Pareto efficient solutions and the Nash bargaining solution for the problem. We have also proposed two pricing schedules for the vendor who is supplying to a large population of buyers. The first one is based upon profit sharing. The second one resembles the classical all unit quantity discount schedule. We have thus provided for the supplier a procedure for setting all unit quantity discount schedules.