Journal of Industrial & Management Optimization
January 2007 , Volume 3 , Issue 1
Special Issue on Supply Chain Optimization and Four Regular Papers
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The problems inherent in designing and operating supply chains provide a rich practical context for the development and application of optimization models. From large scale (nonlinear) network design and flow problems to operational execution under uncertainty, the various problems faced in practice by supply chain managers often lead to interesting and complex optimization problems. The primary objective of the Journal of Industrial and Management Optimization is to ''promote collaboration between optimization specialists, industrial practitioners and management scientists so that important practical industrial and management problems can be addressed by the use of appropriate, recent advanced optimization techniques.'' This journal, therefore, provides an excellent fit for the analysis of difficult supply chain design, planning, and operations problems for which optimization models can significantly impact performance.
Optimization models, especially nonlinear optimization models, have been widely used to solve integrated supply chain design problems. In integrated supply chain design, the decision maker needs to take into consideration inventory costs and distribution costs when the number and locations of the facilities are determined. The objective is to minimize the total cost that includes location costs and inventory costs at the facilities, and distribution costs in the supply chain. We provide a survey of recent developments in this research area.
This paper presents an approach to take into account market opportunities when designing production-distribution networks. Three types of sub-markets found in several industrial contexts are analyzed: spot markets, contracts and Vendor Managed Inventory (VMI) agreements. For contracts and VMI agreements, customer preferences with respect to different logistics policies are considered. A price-supply function is proposed to model the spot market behavior. The production-distribution network design problem is formulated as a two-stage stochastic program with fixed recourse. Finally, a sample average approximation method (SAA), based on Monte Carlo sampling techniques, is used to solve the model.
An important service provided by third-party logistics (3PL) firms is to manage the inbound logistics of raw materials and components from multiple suppliers to several manufacturing plants. A key challenge for these 3PL firms is to determine how to coordinate and consolidate the transportation flow, so as to get the best overall logistics performance. One tactic is to establish consolidation hubs that collect shipments from several suppliers, consolidate these shipments, and direct the consolidated shipments to the appropriate manufacturing plant. We consider the network design problem to implement this tactic, namely deciding the number, location and operation of consolidation hubs so as to minimize the total logistics costs for the network. To solve this network design problem, we define candidate shipping options for each potential hub, for which we can pre-compute the shipping quantities required from each supplier, and the incurred shipping costs and inventory holding costs. We formulate the problem as an integer linear optimization model and illustrate how to solve large instances using Lagrangian relaxation and a subgradient optimization algorithm. Our results indicate that the bounds obtained are fairly tight and are superior to the bounds obtained from the solution of the LP relaxation.
We present a continuous relaxation technique for the Concave Piecewise Linear Network Flow Problem (CPLNFP), which has a bilinear objective function and network constraints. We show that a global optimum of the resulting problem is a solution of CPLNFP. The theoretical results are generalized for a concave minimization problem with a separable objective function. An efficient and effective Dynamic Cost Updating Procedure (DCUP) is considered to find a local minimum of the relaxation problem, which converges in a finite number of iterations. We show that the CPLNFP is equivalent to a Network Flow Problem with Flow Dependent Cost Functions (NFPwFDCF), and we prove that the solution of the Dynamic Slope Scaling Procedure (DSSP) is an equilibrium solution of the NFPwFDCF. The numerical experiments show that the proposed algorithm can provide a better solution than DSSP using less amount of CPU time and iterations.
The requirements problem with pricing flexibility generalizes the standard economic lot-sizing problem by recognizing that the demand for a good can often be influenced by adjusting its price level. This naturally leads to a profit maximization model that integrates price setting as well as production and inventory management. In this paper, we consider the NP-hard problem that arises in the presence of general cost functions as well as time-varying production capacities. We study a reformulation of the problem as an economic lot-sizing problem and use this reformulation to derive running times for dynamic programming and approximation algorithms for the requirements planning problem.
Transfer prices are an effective strategy for improving the after-tax profits of global supply chains with differential tax rates. Rigorous evidence of their effectiveness has been established by many researchers for deterministic settings. To the best of our knowledge, there has been no research studying the impact of transfer prices in stochastic supply chain settings. We attempt to fill this void by studying a two-stage supply chain in which the end-customer demand is random. This forces the retailer to behave like a newsvendor and balance overage costs with underage costs. Using a combination of analytical and computational techniques, we show that randomness in a supply chain magnifies the impact of transfer prices. We analyze possible reasons behind this behavior and also summarize the impact of various supply chain parameters (customer base, price elasticity, overage and underage costs, etc.) on the magnitude of profit improvement.
In this paper a general integro-differential equations on Banach space are considered. Existence of $\alpha $-mild solutions is proved. Existence of optimal controls of systems governed by general integro-differential equations is also presented.
Motivated by instability analysis of unstable (excited state) solutions in computational physics/chemistry, in this paper, the minimax method for solving an optimal control problem with partially uncontrollable variables is embedded into a more general min-equilibrium problem. Results in saddle critical point analysis and computation are modified to provide more information on the minimized objective values and their corresponding riskiness for one to choose in decision making. A numerical algorithm to compute such minimized objective values and their corresponding riskiness is devised. Some convergence results of the algorithm are also established.
An inventory problem in which the stochastic demand rate in each period is considered. A model is presented to compute optimal order quantities and optimal delivery points in the planning period. This model can also account for any anticipated price change that may occur from time to time. In addition the model can be used to compute volume discounts in accordance to the size of the order. A stochastic global optimization algorithm is used to obtain the numerical results.
The adaptive regulation is considered for a class of nonlinear systems including the Hammerstein systems and Wiener systems as special cases. The observations are corrupted by noise. By using the intrinsic stability of the system a direct adaptive regulation control is designed with the help of the stochastic approximation (SA) method, and its optimality is proved. A numerical example is provided.
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