The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

THERMAL BEHAVIOR STUDY AND DECOMPOSITION KINETICS OF SALBUTAMOL UNDER ISOTHERMAL AND NON-ISOTHERMAL CONDITIONS

The thermal decomposition of salbutamol (beta(2) - selective adrenoreceptor) was studied using differential scanning calorimetry (DSC) and thermogravimetry/derivative thermogravimetry (TG/DTG). It was observed that the commercial sample showed a different thermal profile than the standard sample caused by the presence of excipients. These compounds increase the thermal stability of the drug. Moreover, higher activation energy was calculated for the pharmaceutical sample, which was estimated by isothermal and non-isothermal methods for the first stage of the thermal decomposition process. For isothermal experiments the average values were E(act) = 130 kJ mol(-1) (for standard sample) and E(act) = 252 kJ mol(-1) (for pharmaceutical sample) in a dynamic nitrogen atmosphere (50 mL min(-1)). For non-isothermal method, activation energy was obtained from the plot of log heating rates vs. 1/T in dynamic air atmosphere (50 mL min(-1)). The calculated values were E(act) = 134 kJ mol(-1) (for standard sample) and E(act) (=) 139 kJ mol(-1) (for pharmaceutical sample).