Supply chain networks,electronic commerce,and supply side and demand side risk

In this paper, we develop a supply chain network model in which both physical and electronic transactions are allowed and in which supply side risk as well as demand side risk are included in the formulation. The model consists of three tiers of decision-makers: the manufacturers, the distributors, and the retailers, with the demands associated with the retail outlets being random. We model the optimizing behavior of the various decision-makers, with the manufacturers and the distributors being multicriteria decision-makers and concerned with both profit maximization and risk minimization. We derive the equilibrium conditions and establish the finite-dimensional variational inequality formulation. We provide qualitative properties of the equilibrium pattern in terms of existence and uniqueness results and also establish conditions under which the proposed computational procedure is guaranteed to converge. We illustrate the supply chain network model through several numerical examples for which the equilibrium prices and product shipments are computed. This is the first multitiered supply chain network equilibrium model with electronic commerce and with supply side and demand side risk for which modeling, qualitative analysis, and computational results have been obtained.     

Combining variable neighborhood search and estimation of distribution algorithms in the protein side chain placement problem

The aim of this work is to introduce several proposals for combining two metaheuristics: variable neighborhood search (VNS) and estimation of distribution algorithms (EDAs). Although each of these metaheuristics has been previously hybridized in several ways, this paper constitutes the first attempt to combine both optimization methods. The different ways of combining VNS and EDAs will be classified into three groups. In the first group, we will consider combinations where the philosophy underlying VNS is embedded in EDAs. Considering different neighborhood spaces (points, populations or probability distributions), we will obtain instantiations for the approaches in this group. The second group of algorithms is obtained when probabilistic models (or any other machine learning paradigm) are used in order to exploit the good and bad shakes of the randomly generated solutions in a reduced variable neighborhood search. The last group of algorithms contains the results of alternating VNS and EDAs. An application of the first approach is presented in the protein side chain placement problem. The results obtained show the superiority of the hybrid algorithm in comparison with EDAs and VNS.     

Cyanoethylation of methyl and ethyl ethers of dimethylphenols

The C-cyanoethylation of the methyl and ethyl ethers of dimethylphenols has been carried out with acrylonitrile in the presence of anhydrous AlCl₃ to furnish propionitrile derivatives. The latter on hydrolysis to the corresponding propionic acids followed by cyclization with PPA afforded the appropriate indanones, whose structures have been established on the basis of spectral data and by the formation of 2, 4-DNP derivatives.     

Optimization of Batch Reactions in Series with Uncertainty

Certain types of chemical reactions, such as the global deprotection of a polypeptide, are extremely complex. As a result, it may be very difficult or expensive to develop accurate models of these chemical reactions. Without a satisfactory kinetic model for the reaction, it is difficult to develop an optimum operating policy that will maximize the profit. Stochastic optimization is applied in this work to an example process step to obtain the optimum reaction temperature and reaction time. In the case of the “here and now” problem, the optimal conditions are a lower reaction temperature and a longer reaction time than obtained from the deterministic problem. The average reaction time for the “wait and see” problem is also longer than the deterministic case, but the average reaction temperature is very close to that of the deterministic problem. Both normally and uniformly – distributed uncertain parameters are considered.     

Differential inclusions with unbounded right-hand side and necessary optimality conditions

We study the properties of the trajectories of a differential inclusion with unbounded measurable–pseudo-Lipschitz right-hand side that takes values in a separable Banach space and consider the problem of minimizing a functional over the set of trajectories of such a differential inclusion on an interval. We obtain necessary optimality conditions in the form of Euler–Lagrange differential inclusions for a problem with free right end.     

Forcing with adequate sets of models as side conditions

We present a general framework for forcing on ω₂ with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on ω₂, adding a nonreflecting stationary subset of , and adding an ω₁‐Kurepa tree.     

Differential inclusions with unbounded right-hand side: Existence and relaxation theorems

For a conflict-controlled dynamical system whose motion is described by neutraltype functional differential equations in Hale’s form and for a quality index that evaluates the motion history realized up to the terminal instant of time, we consider a differential game in the class of control-with-guide strategies. We construct an approximating differential game in the class of pure positional strategies in which the motion of a conflict-controlled system is described by ordinary differential equations and the quality index is terminal. We show that the value of the approximating game gives the value of the original game in the limit, and that the optimal strategies in the original game can be constructed by using the optimal motions of the approximating game as guides.     

Transportation problem with nonlinear side constraints a branch and bound approach

In a container terminal management, we are often confronted with the following problem: how to assign a reasonable depositing position for an arriving container, so that the efficiency of searching for and loading of a container later can be increased. In this paper, the problem is modeled as a transportation problem with nonlinear side constraints (TPNSC). The reason of nonlinear side constraints arising is that some kinds of containers cannot be stacked in the same row (the space of storage yard is properly divided into several rows). A branch and bound algorithm is designed to solve this problem. The algorithm is based on the idea of using disjunctive arcs (branches) for resolving conflicts that are created whenever some conflicting kinds of containers are deposited in the same row. During the branch and bound, the candidate problems are transformed into classical transportation problems, so that the efficient transportation algorithm can be applied, at the same time the reoptimization technique is employed during the branch and bound. Further, we design a heuristic to obtain a feasible initial solution for TPNSC in order to prune some candidates as early and/or as much as possible. We report computational results on randomly generated problems.     

The transportation problem with exclusionary side constraints and two branch-and-bound algorithms

The transportation problem with exclusionary side constraints, a practical distribution and logistics problem, is formulated as a 0–1 mixed integer programming model. Two branch-and-bound (B&B) algorithms are developed and implemented in this study to solve this problem. Both algorithms use the Driebeek penalties to strengthen the lower bounds so as to fathom some of the subproblems, to peg variables, and to guide the selection of separation variables. One algorithm also strongly exploits the problem structure in selecting separation variables in order to find feasible solutions sooner. To take advantage of the underlying network structure of the problem, the algorithms employ the primal network simplex method to solve network relaxations of the problem. A computational experiment was conducted to test the performance of the algorithms and to characterize the problem difficulty. The commercial mixed integer programming software CPLEX and an existing special purpose algorithm specifically designed for this problem were used as benchmarks to measure the performance of the algorithms. Computational results show that the new algorithms completely dominate the existing special purpose algorithm and run from two to three orders of magnitude faster than CPLEX.     

Systems of difference equations with localized effect of right side

Criteria are obtained which state that a system of difference equations with constant coefficients must possess Green matrices whose norms exponentially decrease with an increase in the node coordinates. The Green formula in any network region is obtained for systems satisfying these criteria.Translated from Matematicheskie Zametki, Vol. 6, No. 2, pp. 249–255, February, 1969.     

Coordinating a three-echelon supply chain under price and quality dependent demand with sub-supply chain and RFM strategies

The paper considers a three-echelon supply chain which consists of one supplier, one manufacturer and one retailer for trading a single product. The market demand at the retailer is influenced by the retail price and the quality of the product. The quality of the finished product at the manufacturer depends on the supplier’s raw material quality. We analyze the model for both deterministic and stochastic demand patterns. We first study the centralized and decentralized systems, and then the decentralized system with a sub-supply chain coordination strategy (where the manufacturer chooses to merge with either the supplier or the retailer and then acts as a single entity) and the two-level retail fixed mark-up (RFM) strategy. In the case of the two-level RFM strategy, the manufacturer and the retailer use fixed mark ups over the supplier’s wholesale price. The proposed models are demonstrated through numerical examples. It is observed from the numerical study that the two-level RFM strategy is superior to the sub-supply chain coordination strategy. Further, the two-level RFM strategy in the stochastic demand scenario is not as effective as in the deterministic demand scenario.     

Generalized equilibrium for conflict problems with side interests of participants

A generalized equilibrium for conflict problems with partially overlapping game sets of participants is proposed; this equilibrium turns out to be nonempty even in those cases where all known equilibria are empty.     

On solutions of hyperbolic differential inclusions with nonconvex right-hand side

The existence of a generalized solution with continuous derivativesu _x ,u _y is proved for the differential inclusionu _xy F(x, y, u) with a nonconvex right-hand side satisfying the Lipschitz conditioninx, y, andu.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 531–534, April, 1995.     

Invariant stabilization of pulse systems with a nonlinear right-hand side

The Lyapunov function of the quadratic form is used for the analytical synthesis of a robust stabilizing control for two classes of nonlinear pulse modulated systems described by functional differential equations with a lagging argument.