Mail Order Mart (MOM)20 will ship qj pounds of small-order novelty goods over the next week to regions j = 1,

c, 27 of the United States. MOM’s distribution facility is located in New England region 1. Orders can be directly shipped from the distribution center by small parcel carriers at cost p1, j per pound. An often cheaper alternative is to drop-ship (i.e., group)

the week’s orders for a region j into a bulk quantity that can be sent by common carrier freight to an intermediate point in region i for ci per pound 1c1 ! 02, and then be directly shipped from i on to j at small-parcel cost pi,j per pound.

However, common carriers require a minimum of 1000 pounds per shipment. MOM wants to identify the least total cost way to meet this week’s shipping needs. Formulate an ILP model of this shipping problem using the decision variables

(i, j = 1,

c, 27)

xi,j ! c 1 if goods bound for region j are drop are drop shipped via region i 0 otherwise 1x1, j = 1 implies direct shipping to j.2