The Industry Secrets For Decitabine

fj is employed to represent the fixed cost of opening a facility at web-site j J, vj may be the support capacity of facility at website j, di is definitely the demand of consumer i I, and cij is the cost of serving a single unit of demand at consumer i from website j, in other word, the unit variable shipping different cost amongst client i from web page j. We reasonably presume that cij �� 0, fj �� 0, and vj �� 0 for all i I, for all j J. And two binary variables are set as:Xj={1if??a??facility??setup??on???site??i;0otherwise;Yij={1if??facility??j??serves??customer??i;0otherwise.(1)Then the general model of DFLP could be stated as the following linear mixed-integer program:min??��=��j=1mfjXj+��i=1n��j=1mdicijYij(2)Subject??to?��j=1mYij=1??i��I(3)��i=1ndiYij��vjXj??j��J(4)Yij?Xj��0??i��I,???j��J(5)Xj��0,1??j��J(6)Yij��0,1??i��I,???j��J.

(7)The objective function (2) is to minimize the total system cost, including the location cost and the shipment cost. Constraint (3) is the demand constraint, which makes the Decitabinedemand of each customer be met; (4) is the variable upper bound constraint; (5) is the capacity constraint of facility; (6) and (7) are standard binary integrality constraints.3. Simulated Annealing Algorithm for DFLPKirkpatrick et al. [23] introduced the concept of simulated annealing (SA) algorithmin 1983, which is a stochastic optimization technique. To be specific, SA is a probabilistic heuristic for the global optimization problems of finding a good approximation to the global optimum of a given objective function in the search space. It is often used when the solution space is discrete.

In the searching process, the SA accepts not only better but also worse neighboring solutions with a certain probability. This means that the SA has the ability to escape from the local minima. Therefore, it can find high-quality solutions that do not strongly depend upon the choice of the initial solution compared to other local search algorithms. And its another advantage over the other heuristic algorithms is the ease of implementation. So we adopted SA as the basic solution method to solve the DFLP. In last 30 years, SA has been studied widely and used extensively in many optimization problems [24�C29], which have proved that SA is an effective tool for approximating globally optimal solutions to many NP-hard optimization problems.

In order to describe the procedure of the SA, S, S��, S���, and S- are used to represent the different feasible solutions of the model; D(Ti) is the cooling function of temperature, in which Ti is the current temperature value. Tf is the stop temperature value. N is the maximum iteration number at each value. ��(S) is used to represent the objective function value of the solution S. According to Jayaraman and Ross [19], the SA for DFLP could be given as follows.Step 1 (initialization) �� Set iteration counter i = 1.