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Volume 1, 2005

Journal of Industrial & Management Optimization

July 2005 , Volume 1 , Issue 3

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Supply contract model with service level constraint
Jun Wu, Shouyang Wang and Wuyi Yue
2005, 1(3): 275-287 doi: 10.3934/jimo.2005.1.275 +[Abstract](758) +[PDF](211.8KB)
Abstract:
This paper addresses a new topic of supply chain management: service level constraint for a supply contract model in a buyer's perspective. The concept of order fill rate is introduced in the supply contract model as a measurement of customer service level. The buyer's optimal ordering decisions in both stages are derived by using the dynamic programming approach. The impact of the service level on the making of optimal decisions is analyzed. The main results include that: (1) the optimal ordering quantity with service level constraint is larger than or equal to that without constraint; (2) the optimal service level setting of the buyer is determined by the system parameters. The results presented in this paper provide insights for managers looking to find a tradeoff between profit maximization and customer service level.
Optimal execution strategy with an endogenously determined sales period
Guibin Lu, Qiying Hu, Youying Zhou and Wuyi Yue
2005, 1(3): 289-304 doi: 10.3934/jimo.2005.1.289 +[Abstract](713) +[PDF](235.3KB)
Abstract:
We discuss the problem of the optimal liquidation of a financial product in which both the market risk of the asset and the market impact of the investor's own dealings are considered, and where the asset is liquidated over several sales periods with a constant sales interval. The investor chooses the sales volume in each period as well as the volume over the entire sales period in order to minimize the expected execution costs under a certain level of risk. We obtain an explicit solution for the optimal execution strategies and present four numerical examples to show that the proportion between market risk and liquidity risk exerts a major influence over the optimal execution strategy. We also show that to obtain the optimal result the investor should liquidate his holdings over a short sales period.
Decision making of transportation plan, a bilevel transportation problem approach
G.S. Liu and J.Z. Zhang
2005, 1(3): 305-314 doi: 10.3934/jimo.2005.1.305 +[Abstract](492) +[PDF](160.3KB)
Abstract:
As we know, the transportation plan plays a very important role in reducing cost and time of shipping products. In this paper, we propose a bilevel transportation model to help decision makers to work more efficiently. We propose an exact penalty method for the bilevel transportation model, then test it by using both randomly generated test problems and problems with practical data which are collected in a very large company in China. These results of numerical tests show that the exact penalty method is very efficient in solving both kinds of problems.
Some new results on multi-dimension Knapsack problem
Yuzhong Zhang, Fan Zhang and Maocheng Cai
2005, 1(3): 315-321 doi: 10.3934/jimo.2005.1.315 +[Abstract](514) +[PDF](185.3KB)
Abstract:
We claim a conclusion on Multi-Dimensional Knapsack Problem (MKP), which extends an important proposition by Dantzig firstly, then address to a special case of this problem, and constitute a polynomial algorithm, extending Zukerman et al's work.
A-shaped bin packing: Worst case analysis via simulation
Wenxun Xing and Feng Chen
2005, 1(3): 323-335 doi: 10.3934/jimo.2005.1.323 +[Abstract](603) +[PDF](228.3KB)
Abstract:
An A-shaped bin packing problem, where the items are cylinders and they must be packed into an A-shaped tower in each bin is considered in this paper. It is a variant of the classical one dimensional bin packing problem. For the off-line version of the problem, it is the same to the classical bin packing problem. For the on-line version of the problem, directly extended and radius-classified heuristics from the classical bin packing are analyzed and compared with the worst case analysis and simulation methods. The worst case analysis shows that the asymptotic competitive ratios of heuristics extended from the next fit, the worst fit, the best fit, the almost worst fit, the harmonics are all infinity except of the first fit with asymptotic competitive ratio 2. The radius-classified heuristics perform as well as in classical bin packing in view of the worst case analysis. Simulation results show that the best fit is the best among the directly extended heuristics and give the equilibrium point of choosing directly extended or radius-classified heuristics for an instance.
Algorithms by layer-decomposition for the subgraph recognition problem with attributes
Yifan Xu
2005, 1(3): 337-343 doi: 10.3934/jimo.2005.1.337 +[Abstract](565) +[PDF](205.0KB)
Abstract:
Given two planar graphs $G$ and $H$, the subgraph recognition problem (SRP) is concerned with finding all isomorphic subgraphs of $H$ in $G$. Using the idea of layer-decomposition, we develop algorithms for SRP that have computational complexity $O(n(\Delta-1)^{k-1})$, where $\Delta$ is the degree of $G$ and $n, k$ are the orders of $G, H$ respectively.
Optimal preemptive online scheduling to minimize lp norm on two processors
Donglei Du, Xiaoyue Jiang and Guochuan Zhang
2005, 1(3): 345-351 doi: 10.3934/jimo.2005.1.345 +[Abstract](682) +[PDF](199.5KB)
Abstract:
We consider an on-line scheduling problem, where jobs arrive one by one to be scheduled on two identical parallel processors with preemption. The objective is to minimize the machine completion time vector with respect to the $l_p$ norm. We present a best possible deterministic on-line scheduling algorithm along with a matching lower bound.
A PTAS for the p-batch scheduling with pj = p to minimize total weighted completion time
Jinjiang Yuan and Weiping Shang
2005, 1(3): 353-358 doi: 10.3934/jimo.2005.1.353 +[Abstract](538) +[PDF](173.1KB)
Abstract:
We consider the single machine parallel-batching scheduling problem with precedence relations, release dates and identical processing times to minimize total weighted completion time. We give a polynomial-time approximation scheme (PTAS) for the problem.
Theoretical analysis and a search procedure for the joint replenishment problem with deteriorating products
Ming-Jong Yao and Yu-Chun Wang
2005, 1(3): 359-375 doi: 10.3934/jimo.2005.1.359 +[Abstract](554) +[PDF](352.6KB)
Abstract:
We investigate the Joint Replenishment Problem (JRP) with deteriorating products in this paper. Many researchers have been devoting their efforts to solve the JRP for some thirty years. Though, there exists no JRP model that considers deterioration cost incurred from obsolescence, damage, spoilage, evaporation, and decay that often happens in the real world. Our focus in this study is to conduct theoretical analysis on the mathematical model for the JRP with deteriorating products by exploring the optimality structure and deriving several interesting properties on the optimal objective curve. By utilizing our theoretical results, we propose a search procedure that can efficiently solve the optimal solution. Based on our numerical experiments, we show that the proposed algorithm provides significantly better replenishment strategy than the case in which the decision maker ignores the deteriorating factor.
Nonlinear dynamical systems of bio-dissimilation of glycerol to 1,3-propanediol and their optimal controls
Caixia Gao, Enmin Feng, Zongtao Wang and Zhilong Xiu
2005, 1(3): 377-388 doi: 10.3934/jimo.2005.1.377 +[Abstract](626) +[PDF](211.1KB)
Abstract:
In this study simplified mathematical models of the nonlinear dynamic systems of dissimilation of glycerol to 1,3-propanediol by {\it Klebsiella pneumoniae} in continuous, batch and fed-batch cultures are investigated. Considering big errors between the experimental results and computational values in the existing models, the parameter identification models for these systems are established. The properties of the solutions for the nonlinear dynamic systems are discussed and the identifiability of the parameters is proved. In view of the sudden increase of the glycerol and alkali in fed-batch culture, this paper proposes a nonlinear impulsive system of fed-batch culture. The existence, uniqueness and regularity properties of piecewise solution for the system are proved. Based on the nonlinear impulsive system, the paper constructs an optimal control model in view of the controllability of volumes of glycerol added to the reactor instantaneously, and the existence of the optimal control is obtained.
A new recurrent neural network adaptive approach for host-gate way rate control protocol within intranets using ATM ABR service
Lixin Xu and Wanquan Liu
2005, 1(3): 389-404 doi: 10.3934/jimo.2005.1.389 +[Abstract](669) +[PDF](249.9KB)
Abstract:
In this paper, a new neural network adaptive control strategy based on Host Gate Way Rate Control Protocol (HGRCP) is proposed for intranet congestion management. The control algorithm is based on the Elman recurrent neural network via using the ABR service of an ATM backbone network. Simulations confirm that the proposed algorithm will produce lower queue level variance at the gateway. Meanwhile, the learning capability can be improved significantly.
The model of heat transfer of the arctic snow-ice layer in summer and numerical simulation
Yila Bai, Haiqing Zhao, Xu Zhang, Enmin Feng and Zhijun Li
2005, 1(3): 405-414 doi: 10.3934/jimo.2005.1.405 +[Abstract](715) +[PDF](211.9KB)
Abstract:
For the Arctic ice layer with high temperature in summer, the concepts of enthalpy degree, specific enthalpy and enthalpy conduction coefficient etc. are introduced in terms of the concept of enthalpy in calorifics. Heat conduction equation of enthalpy is constructed in the process of phase transformation of the Arctic ice. The condition of determinant solution and the identification model of diffusion coefficient of enthalpy are presented. Half implicit difference scheme and Schwartz alternating direction iteration are applied to solve the enthalpy conduction equation and sensitivity equation. Furthermore the Newton-Raphson algorithm is used for identification. The numerical results illustrate that the mathematic model and optimization algorithm are precise and feasible by the data(2003.8)of the Second Chinese Arctic Research Expedition in situ.

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