Transportation model with quantity discounts

Abhilash Bhat (PGP/18/121)Puroo Soni (PGP/18/158)Sanjit Sahoo (PGP/18/164)Shachi Tayal (PGP/18/165)Transportation Problem with Quantity DiscountsTransportation Problem??? Transportation problem is a distribution problem wherein the goods held at various supply nodes are to be distributed to various locations based on their demand. The solution helps a manager decide the quantities to be shipped on various routes to minimize the cost of transportation. Solved using LP method Simple transportation assumes the cost of transportation to be fixed for the routes. But in reality, cost of transportation per unit decreases as the number of units increases.2 types of discount schemes:* All Quantity Discount Scheme* Increasing Quantity Discount SchemeALL Quantity Discount SchemeIn Normal practice as the no. of units ordered increases , a discount is offered. This is known as quantity discount. There are two types of quantity discounts:-1212C111C112C113C212SUPPLYDEMANDS1S2D1D2C213C222C223C221C123C122C121C211

Rs.950/bottle

Rs.900/bottle

Demand

Supply(0)Mm

LP model with quantity discountsVariable Description

(i,j) signifies the source and destination pair

K(i,j) signifies number of distinct transportation cost slabs for the source and destination pair (i,j)

Thus, Xijk denotes the amount transported from ith supply node to jth demand node

Cijk denotes the corresponding shipping cost for kth slabQuantity shipped, per unit shipping cost, and breakpointsValue of QUnit TaskIntervalXij1Cij10 Q Qij1Xij2Cij2Qij1+1 Q Qij2.........XijK(i,j)CijK(i,j)Qij[K(i,j)-1]+1 QObjective functionThe objective function to minimize is:Z =i =1mj =1nk =1k (i,j)cijXijkZ= The total cost of transportationConstraintsj =1nk =1K (i,j)Xijk ai if i =1 ai >mj =1 bjni =1mk =1K (i,j)Xijk= ai otherwise bj if i =1 ai =01220=01230=000X223C2234Z223Q222+1301Q2234002210>=02110=02120=02130