Control parametrization and finite element method for controlling multi-species reactive transport in a circular pool
Heung Wing Joseph Lee Chi Kin Chan Karho Yau Kar Hung Wong Colin Myburgh
In this paper, we consider an optimal control problem for a cleaning program involving effluent discharge of several species in a circular pool. A computational scheme combining control parametrization and finite element method is used to develop a cleaning program to meet the environmental health requirements. A numerical example is solved to illustrate the efficiency of our method.
keywords: Galerkin Scheme Species concentration control parametrization circular pool non-negativity requirement of state variables. optimal control
Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels
Kar Hung Wong Yu Chung Eugene Lee Heung Wing Joseph Lee Chi Kin Chan

This paper considers an optimal production scheduling problem in a single-supplier-multi-manufacturer supply chain involving production and delivery time-delays, where the time-delays for the supplier and the manufacturers can have different values. The objective of both levels is to find an optimal production schedule so that their production rates and their inventory levels are close to the ideal values as much as possible in the whole planning horizon. Each manufacturer's problem, which involves one time-delayed argument, can be solved analytically by using the necessary condition of optimality. To tackle the supplier's problem involving $n+1$ different time-delayed arguments (where $n$ is the number of manufacturers) by the above approach, we need to introduce a model transformation technique which converts the original system of combined algebraic/differential equations with $n+1$ time-delayed arguments into a sum of $n$ sub-systems, each of which consists of only two time-delayed arguments. Thus, the supplier's problem can also be solved analytically. Numerical examples consisting of a single supplier and four manufacturers are solved to provide insight of the optimal strategies of both levels.

keywords: Optimal control supply chain problem single-supplier multimanufacturer time delays in the production process multiple time delays
Auction and contracting mechanisms for channel coordination with consideration of participants' risk attitudes
Cheng Ma Y. C. E. Lee Chi Kin Chan Yan Wei

This paper considers a two-supplier one-retailer coordinated supply chain system with auction and contracting mechanism incorporating participants' risk attitudes. The risk attitude is quantified using the value-at-risk (VaR) measure and the retailer faces a stochastic linear price-dependent demand function. In the supply chain, the suppliers (providing identical products) compete with each other in order to win the ordering contract of the retailer. Several auction and contracting mechanisms are developed and compared. It can be analytically shown that the retail price of the risk-averse system is higher than that of the risk-neutral system, but the order quantity is lower than that of the risk-neutral system.

keywords: Supply chain coordination auction mechanism contracting mechanism wholesale price value-at-risk
A fractional programming model for international facility location
Guowei Hua Shouyang Wang Chi Kin Chan S. H. Hou
This paper presents a new mixed integer non-linear fractional programming model for multi-commodity, multi-period, budget constrained and capacitated global supply chain design problem. Our model simultaneously optimizes the facility location, capacity acquisition, and production-distribution decisions so as to maximize the profitability of the total investment over a planning horizon. The model is also compared with the profit-maximization model and the cost-minimization model. A branch-and-bound method and a rounding heuristic algorithm are developed to tackle the problem at hand. The computational results of solving 30 instances generated randomly show that our proposed model differs fundamentally from the other models and the rounding heuristic algorithm provides an efficient solution.
keywords: facility location branch-and-bound rounding heuristic algorithm. Supply chain design fractional programming
A mixed simulated annealing-genetic algorithm approach to the multi-buyer multi-item joint replenishment problem: advantages of meta-heuristics
T. W. Leung Chi Kin Chan Marvin D. Troutt
The Joint Replenishment Problem (JRP) is a multi-item inventory problem. The objective is to develop inventory policies that minimize total cost (comprised of holding and setup costs) over the planning horizon. In this paper we consider the extension of this problem to the multi-buyer, multi-item version of the JRP. We propose and test a mixed simulated annealing-genetic algorithm (SAGA) for the extended problem. Tests are conducted on problems from a leading bank in Hong Kong. Results are also compared to a pure GA approach and several interesting observations are made on the value of such meta-heuristics.
keywords: Meta-Heuristics. Genetic Algorithm Joint Replenishment Inventory Problems Multi-Buyer Extension Simulated Annealing
Optimal feedback production for a single-echelon supply chain
K.H. Wong Chi Kin Chan H. W.J. Lee
The dynamics of a supply chain have been modelled by several authors, yet no attempt has ever been made for finding the vendor's optimal production policy when facing such dynamics. In this paper, we model the dynamics of a supply chain as an infinite-horizon time-delayed optimal control problem. By approximating the time interval $[ 0,\infty )$ by $0,T_f$, we obtain an approximated problem $P(T_f)$ which can be easily solved by the control parametrization method. Moreover, we can show that the objective function of the approximated problem converges to that of the original problem as $T_f \to \infty $. Lastly, we also extend our method to solving a stochastic problem where the demand is a stochastic process with white noise input. Several examples for both the deterministic and the stochastic problems are solved to illustrate the efficiency of our method. In these examples, some important results relating the production rate to the demand are developed.
keywords: Optimal feedback synthesis Mathematical modeling Feedback control. Dynamical system in optimization and economics

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