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The considerable potential to increase operational efficiency and decrease costs has sparked a surge of interest in supply chain management research during the last decade. Closer collaboration with other parties and the integration of various decision processes can benefit each individual party in the supply chain.

The single-vendor, single-buyer dilemma is regarded as a fundamental component of every supply chain. For this problem, several shipping rules have been presented in the literature. With the assumption of an unlimited production rate, Goyal proposed a lot-for-lot policy. With the assumption of a finite production rate, Banarjee developed a lot-for-lot strategy. Goyal modified the lot-by-lot assumption by assuming that the seller supplies the lot in many equal-sized shipments. Goyal devised a scheme in which shipping sizes rise by a geometrically rising factor. Hill extended Goyal's model by include the geometric growth factor as a choice variable. Without making any assumptions about the shipment policy, Hill discovered the best solution to the challenge. Goyal and Nebebe proposed a scheme in which the initial cargo is tiny and the subsequent shipments are larger and equal in size.

The transportation cost is considered to be part of the ordering cost in all of the models above. This assumption is incorrect in most cases since transportation costs are influenced by route selections and cargo size. In their inventory model, Baumol and Vinod included freight costs. They suggested two methods for minimizing inventory costs and maximizing profits. In an order-sizing model, freight rates, speed, fluctuation in speed, and en-route losses are all included. They believe that the cost of shipping each unit is constant and unaffected by the quantity of the package. However, freight rate discounts based on cargo size became widespread practice when the shipping sector in the United States was deregulated in the early 1990s.

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Lee is one of the first studies to include the discounted freight cost in the EOQ model directly. He assumed that the cost of shipping is fixed and increases in a step function manner as the order size grows. A price reduction for large purchases is another form of discount. Burwell et al looked at a profit maximization model that included freight and price reductions. They anticipated a demand structure that was price sensitive. Tersine and Barman devised a model for the scenario of continuous demand and a price and freight discount.

Over a defined planning horizon, the manufacturer obtains raw materials from suppliers, transforms them to completed goods, and sends the items to each consumer at a predetermined interval of time. Buyers specify the demand for finished goods, and the shipping quantity for each buyer is predetermined. The goal is to minimize the system cost by determining the production start time, the initial and ending inventory, the cycle beginning and finishing time, the number of raw material orders in each cycle, and the number of cycles over a given planning horizon. DHL offers its users the best tracking service available.

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