Recently, retailers who directly deal with poultry farmers increase in Japan. It therefore becomes necessary for the poultry farmers to deliver products to the retailers frequently in accordance with the retailers’ demand. The retailer purchases (raw) chicken meat from the poultry farmer. The stock of the poultry farmer increases due to growth, in contrast, the inventory level of the retailer i...

In this paper we analyze a supply contract for a single product that speci®es that the cumulative orders placed by a buyer, over a ®nite horizon, be at least as large as a (contracted upon) given quantity. We assume that the demand for the product is uncertain, and the buyer places orders periodically. We derive the optimal purchase policy for the buyer for a given total minimum quantity commit...

To attract and keep customers, companies, especially those in e-business, are increasingly offering free shipping to buyers whose order sizes exceed the free shipping quantity. In this paper, given the supplier offers free shipping and the retailer faces stochastic demand, we determine the retailer’s (i.e., the newsvendor’s) optimal order quantity and the optimal selling price simultaneously. W...

The classic Economic Order Quantity model assumes that the unit purchasing cost is not based on the order quantity. In practice, a supplier may offer purchasers an all-units discount. We develop a model and solution procedure for the EOQ with all-unit discounts and partial backordering at a constant rate. We show, and illustrate with a numerical example, how that model can be used to find the s...

It is only an order quantity which is decided for a spot selling time in the classical newsboy problem. Both the purchase timing and the time-variant variance of the demand are neglected. When the vendor gives a price discount for early purchase, the buyer purchases the quantities of price discount at the cost of forecast bias. The buyer has to forecast the demand early before purchase ahead of...