Demand constraints

Another illustration of operations research is the use of linear programming techniques (Section 5.14) to obtain optimal mixtures of gasoline ingredients that will produce a result suitable for different climatic conditions and subject to demand constraints on a long-range basis. 

The two following examples are different with respect to the demands, constraints, objective functions and the whole master data and transaction data. They were constructed as reference examples out of real life requirements and real life systems. 

C8 G10>=0 Number to ship must be greater than or equal toO. You can solve this problem faster by selecting the Assume linear model check box in the Solver Options dialog box before clicking Solve. A problem of this type has an optimum solution at which amounts to ship are integers, if all of the supply and demand constraints are integers. ... 

Reactor systems that can be described by a yield matrix are potential candidates for the application of linear programming. In these situations, each reactant is known to produce a certain distribution of products. When multiple reactants are employed, it is desirable to optimize the amounts of each reactant so that the products satisfy flow and demand constraints. Linear programming has become widely adopted in scheduling production in olefin units and catalytic crackers. In this example, we illustrate the use of linear programming to optimize the operation of a thermal cracker sketched in Figure E 14.1. 

The problem is to allocate optimally the crudes between the two processes, subject to the supply and demand constraints, so that profits per week are maximized. The objective function and all constraints are linear, yielding a linear programming problem (LP). To set up the LP you must (1) formulate the objective function and (2) formulate the constraints for the refinery operation. You can see from Figure El6.1 that nine variables are involved, namely, the flow rates of each of the crude oils and the four products. 

The total demand constraint The total number of employees days worked per week must be sufficient to meet the total weekly demand for shifts. Since each employee works exactly five days per week ... 

The maximum daily demand constraint The number of employees must be sufficient to meet the maximum demand on any day. 

Vehicles Allocate available vehicles to jobs and determine the number of trips to make, subject to vehicle size, availability, and demand constraints. 

Totsd demand constraint (scheduhng), 1748 Total-enclosure concept, 598 Total productive maintenance (TPM), 551-553, 1557, 1619-1620... 

Here, yi, yu, and ym denote the decisions to install technology I, II, or III, respectively. Symbol D denotes the electricity demand, and Pi, Pn, and Pm denote the power supplied by each technology. For simplicity we assume that Pi = Pn = Pm = 10, and we set D — 10. Note that the demand constraint [7.9e] implies that only one technology must be installed. AH the objectives (C, E, L) are normalized by their best and worst possible values (these can be obtained from Table 7.1) so as to lie in the range [0,1]. 

The supply constraints guarantee that the total amount shipped from any warehouse does not exceed its capacity. The demand constraints guarantee that the total amount shipped to a market meets the minimum demand at that market. 

Demand constraints for each retailer The total amount shipped to a retailer from the three warehouses should be equal to the retailer s demand. 

Demand constraint The demand of buyer) for product i has to be satisfied using a combination of the suppliers. Tire demand constraint is given by ... 

For objectives 2 and 3, you can use the total demand as the denominator for the weighted average expressions. The constraints in the model include capacity constraints of the supplier and the demand constraint of the buyers. 

Constraints (7.27) represent the capacity limits at each supplier. The total order placed with a supplier should be less than or equal to the capacity available at the supplier. Note that the binary variable is used to activate the constraint for a supplier k only if k is chosen in the model. Constraints (7.28) introduce the demand constraints. Demand for product i at buyer j must be satisfied. Constraint (7.29) limits the number of selected suppliers to N. Constraints (7.30) and (7.31) are used to linearize the original nonlinear cost function that arises due to price discounts. The sequence 0 = is the... 

The next step is to construct cells for the constraints in Equations 5.1 and 5.2 and the objective function. The constraint cells and objective function are shown in Figure 5-5. Cells B22 B26 contain the capacity constraints in Equation 5.2, and cells B28 F28 contain the demand constraints in Equation 5.1. The objective function is shown in cell B31 and measures the total fixed cost plus the variable cost of operating the network. 

B29 corresponds to the demand constraint for the market in Atlanta. The constraint in cell B22 corresponds to the capacity constraint for the factory in Baltimore. The capacity constraints require that the cell value be greater than or equal to (>) 0, whereas the demand constraints require the cell value be equal to 0. 

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