Dantzig-Wolfe Decomposition and Lagrangean Relaxation-Based Heuristics for an Integrated Production and Maintenance Planning with Time Windows

In this chapter, two approaches are developed to solve the integrated production planning and maintenance problem. Moreover, Some Propositions and mathematical properties were suggested and applied in the proposed heuristics to solve the problem. The first heuristic developed is based on Dantzig-Wolfe decomposition. The Dantzig-Wolfe Decomposition principle reformulates the original model and Column generation is then used to deal with the huge number of variables of the reformulated model. A simple rounding heuristic and a smoothing procedure are finally carried out in order to obtain integer solutions. The second heuristic is based on Lagrangean relaxation of the capacity constraints and sub-gradient optimization. At every step of sub-gradient method, feasibility and improvement procedures are applied to the solution of the Lagrangean problem. Computational experiments are carried out to show the results obtained by our approaches and compared to those of commercial solver.

Achieving Fair Spectrum Allocation and Reduced Spectrum Handoff in Wireless Sensor Networks: Modeling via Biobjective Optimization

This paper considers the problem of centralized spectrum allocations in wireless sensor networks towards the following goals: (1) maximizing fairness, (2) reflecting the priority among sensor data, and (3) avoiding unnecessary spectrum handoff. We cast this problem into a multiobjective mixed integer nonconvex nonlinear programming that is definitely difficult to solve at least globally without any aid of conversion or approximation. To tackle this intractability, we first convexify the original problem using arithmetic-geometric mean approximation and logarithmic change of the decision variables and then deploy weighted Chebyshev norm-based scalarization method in order to collapse the multiobjective problem into a single objective one. Finally, we apply simple rounding method in order to obtain approximate integer solutions. The results obtained from the numerical experiments show that, by adjusting the weight on each objective function, the proposed algorithm allocates spectrum bands fairly with well observing each sensor’s priority and reduced spectrum handoffs.

THE ETIOLOGIC AGENTS OF VARICELLA AND HERPES ZOSTER

Fourteen strains of virus derived from the cutaneous lesions of cases of varicella and eight from patients with herpes zoster were propagated serially in primary explant cultures of human preputial or embryonic skin-muscle tissue. Infectious material could not be demonstrated in the fluid phase of infected cultures and inocula for passage therefore consisted of suspensions of infected tissue. Such tissue suspensions when stored in the frozen state did not regularly retain infectivity. The cytopathic process was focal and appeared to develop as the result of transfer of infectious material from cell to contiguous cell. Optimum development of the focal lesions in vitro related directly to conditions favoring optimum tissue growth and was further influenced by the spatial relationship of the tissue outgrowth. A variety of types of cells of human origin and several of monkey origin were susceptible to infection and responded with the formation of intranuclear inclusion bodies. The cellular response otherwise was variable, ranging from simple rounding with little change in size to the formation of large multinucleated cytoplasmic syncytia. Strains of virus recovered from patients with varicella and from patients with herpes zoster could not be distinguished on the basis of their cultural attributes.