Write down the open formulation of the supply chain model for the problem with four stages including suppliers, plants, warehouses and markets. This is supply chain question please do not change subject to do advanced math . I add on 4th picture openformulation example for understanding correctly . (This problem needs to be done in the form of open formulation as on page 4.Page 4 is just an example, it has nothing to do with the question.)

LOCATING PLANTS AND WAREHOUSES SIMULTANEOUSLY much more general form of the plant location model needs to be considered if the entire supply chain network from the supplier to the customer is to be designed. We consider a supply chain in which suppliers send material to factories that supply warehouses that supply markets as shown in Figure 5-13. Location and capacity allocation decisions have to be made for both factories and warehouses. Multiple warehouses may be used to satisfy demand at a market, and multiple factories may be used to replenish warehouses. It is also assumed that units have been appropriately adjusted such that one unit of input from a supply source produces one unit of the finished product. The model requires the following inputs: m = number of markets or demand points n = number of potential factory locations 1 = number of suppliers 1 = number of potential warehouse locations D; = annual demand from customer j K; = potential capacity of factory at site i Su = supply capacity at supplier h We = potential warehouse capacity at site e F; = fixed cost of locating a plant at site i fe = fixed cost of locating a warehouse at site e Chi = cost of shipping one unit from supply source h to factory i Cie = cost of producing and shipping one unit from factory i to warehouse e Cej = cost of shipping one unit from warehouse e to customer j Suppliers Plants Warehouses Markets 0 o The goal is to identify plant and warehouse locations as well as quantities shipped between var- ious points that minimize the total fixed and variable costs. Define the following decision variables: y = 1 if factory is located at site i, otherwise ye = 1 if warehouse is located at site e, otherwise Xej = quantity shipped from warehouse e to market j Xie = quantity shipped from factory at site i to warehouse e Xhi = quantity shipped from supplier h to factory at site i The problem is formulated as the following integer program: Min FM + lede + enew+ cierki + $ certis The objective function minimizes the total fixed and variable costs of the supply chain network subject to the following constraints: Exhi Sh for h=1,..., 1 (5.11) The constraint in Equation 5.11 specifies that the total amount shipped from a supplier cannot exceed the supplier's capacity. -. 2 0 for i=1,..., (5.12) The constraint in Equation 5.12 states that the amount shipped out of a factory cannot exceed the quantity of raw material received. Exie 5 Ky for i=1,..., n (5.13) The constraint in Equation 5.13 enforces that the amount produced in the factory cannot exceed its capacity. 27 Exej 20 for e = 1,..., 1 (5.14) j=1 The constraint in Equation 5.14 specifies that the amount shipped out of a warehouse cannot exceed the quantity received from the factories. Exej Wye for e=1,..., (5.15) j=1 The constraint in Equation 5.15 specifies that the amount shipped through a warehouse cannot exceed its capacity. xej=Dfor j=1,..., m (5.16) The constraint in Equation 5.16 specifies that the amount shipped to a customer must cover the demand. yo y E (0,1), Xejs Xie Xhi 2 0 (5.17) Open Formulation Example n=3, m=4 Minimize f1y1 + f2y2 + f3y3 + C11X11 + C12X12 + C13X13 + C14X14 + C21X21 + C22X22 + C23X23 + C24X24+ C31X31 + C32X32+ C33X33+ C34X34 st: X11 + x21 + X31 = D1 X 12 + X22 + X 32 = D2 X13 + X23 + X33 = -D3 X14 + X24 + X34 = D4 X11 + x12 + X13 + X14 = K1y1 X21 + X22 + X23+ X 24 = = K2Y2 X31 + X32 + X33+ X34 = K3Y3 yi = [0,1], for i = 1,2,3 xij >=0 for i = 1,2,3 j = 1,2,3,4