Distribution
Problem: Consider a buyer facing a uniform deterministic demand of 10000 units annually. The ordering cost being 100 every order and the inventory holding cost is $2 per unit per year. These are the only two relevant costs. The buyer acts rationally and will order according to EOQ given by [pic 1] where D is the annual demand, CO is the ordering cost and h is the inventory carrying cost. Once the buyer orders according to his EOQ, the overall cost is given as:[pic 2] In addition, suppose the buyer places the order with a manufacturer who incurs a set up cost of $300 per set up. If the manufacturer follows a lot for lot policy, the total cost incurred by the manufacturer is [pic 3]where CS is the set up cost. At this ordered quantity, the manufacturer’s overall cost=3000. The total supply chain cost is 2000+3000=5000. This was the case when buyer assumes the role of a dominant player.
When the supplier is the dominant player, his optimal policy will be to set up only once in the planning horizon and not to keep any inventory. He will be keener to ship the entire demand to the buyer in one shipment. The supplier’s cost in this scenario will be $300 while for the buyer the cost= 10000/2*2+100=10100 and the total supply chain cost= $10400.Joint Economic Lot SizingIn JELS model, the supplier and the buyer will try to optimize for the entire chain. As a result of the same, the total cost function for the supply chain is given as[pic 4]and the optimal solution yields [pic 5]. At this point we have the optimal ordering quantity is given as 2000 units. The resulting buyer and the supplier’s cost are given as $2500 and $1500 respectively. The total supply chain cost is 4000. It is evident from the above example that coordination through JELS model provides better solution in terms of cost savings but the dominant player is always made worse off in the coordinated case as compared to the original case. Because of the same reason, we need to focus on decentralized mechanisms of SC coordination like Quantity discount and reverse discount. In quantity discount, supplier will provide incentive to the buyer and in reverse discount; the buyer will provide incentive to the supplier so that in either of the cases and agreement regarding the optimal solution is reached. The incentive from either of the partners will compensate the other partner. In quantity discount, if the buyer is to be made a part of the JELS like model, a compensation of $500 is to be transferred to him. The resulting quantity discount be 500/10000=0.05 per unit. While in the case of reverse discount, benefits needed to be passed to the supplier through reverse discounts and the value is 1200/10000=0.12.