ISSN:
1547-5816
eISSN:
1553-166X
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Journal of Industrial & Management Optimization
July 2006 , Volume 2 , Issue 3
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2006, 2(3): 237-254
doi: 10.3934/jimo.2006.2.237
+[Abstract](2411)
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Abstract:
In this paper, we are concerned with the maximum flow problem in the distribution network, a new kind of network recently introduced by Fang and Qi. It differs from the traditional network by the presence of the $D$-node through which the commodities are to be distributed proportionally. Adding $ D $-nodes complicates the network structure. Particularly, flows in the distribution network are frequently increased through multiple cycles. To this end, we develop a type of depth-first-search algorithm which counts and finds all unsaturated subgraphs. The unsaturated subgraphs, however, could be invalid either topologically or numerically. The validity are then judged by computing the flow increment with a method we call the multi-labeling method. Finally, we also provide a phase-one procedure for finding an initial flow.
In this paper, we are concerned with the maximum flow problem in the distribution network, a new kind of network recently introduced by Fang and Qi. It differs from the traditional network by the presence of the $D$-node through which the commodities are to be distributed proportionally. Adding $ D $-nodes complicates the network structure. Particularly, flows in the distribution network are frequently increased through multiple cycles. To this end, we develop a type of depth-first-search algorithm which counts and finds all unsaturated subgraphs. The unsaturated subgraphs, however, could be invalid either topologically or numerically. The validity are then judged by computing the flow increment with a method we call the multi-labeling method. Finally, we also provide a phase-one procedure for finding an initial flow.
2006, 2(3): 255-268
doi: 10.3934/jimo.2006.2.255
+[Abstract](2409)
+[PDF](199.0KB)
Abstract:
We study in this paper the Quick Response (QR) policy in a two-echelon single-manufacturer single-retailer supply chain with a fashion product and dual information updating. To be specific, under Quick Response, a fashion retailer can collect market information towards the sales of a pre-seasonal product whose demand is closely related to the demand of the seasonal product. This information is then used to update both the unknown mean and unknown variance for the seasonal product's demand by Bayesian approach. We consider the situation that there are ordering and production costs uncertainty and differences. After deriving the analytical model, we show the conditions under which QR is beneficial to the supply chain. Measures that can be taken to create Pareto improvement scenario in the supply chain and the individual echelons are discussed. Managerial insights are developed.
We study in this paper the Quick Response (QR) policy in a two-echelon single-manufacturer single-retailer supply chain with a fashion product and dual information updating. To be specific, under Quick Response, a fashion retailer can collect market information towards the sales of a pre-seasonal product whose demand is closely related to the demand of the seasonal product. This information is then used to update both the unknown mean and unknown variance for the seasonal product's demand by Bayesian approach. We consider the situation that there are ordering and production costs uncertainty and differences. After deriving the analytical model, we show the conditions under which QR is beneficial to the supply chain. Measures that can be taken to create Pareto improvement scenario in the supply chain and the individual echelons are discussed. Managerial insights are developed.
2006, 2(3): 269-286
doi: 10.3934/jimo.2006.2.269
+[Abstract](1891)
+[PDF](224.0KB)
Abstract:
This paper addresses Henig efficiency of a multi-product network equilibrium model based on Wardrop's principle. We show that in both the single and multiple criteria cases, such proper efficiency can be recast as a vector variational inequality. In the multiple criteria case, we derive a sufficient and a necessary condition for Henig efficiency in terms of a vector variational inequality by using the Gerstewitz's function.
This paper addresses Henig efficiency of a multi-product network equilibrium model based on Wardrop's principle. We show that in both the single and multiple criteria cases, such proper efficiency can be recast as a vector variational inequality. In the multiple criteria case, we derive a sufficient and a necessary condition for Henig efficiency in terms of a vector variational inequality by using the Gerstewitz's function.
2006, 2(3): 287-296
doi: 10.3934/jimo.2006.2.287
+[Abstract](2147)
+[PDF](166.6KB)
Abstract:
In this note, a mathematical program with complementarity constraints (MPCC) is reformulated as a nonsmooth constrained mathematical program via the Fischer-Burmeister function. Quadratic penalty functions are used to treat this nonsmooth constrained program. We investigate necessary and sufficient conditions that guarantee the convergence of optimal values of unconstrained penalized problems to the optimal value of the original MPCC.
In this note, a mathematical program with complementarity constraints (MPCC) is reformulated as a nonsmooth constrained mathematical program via the Fischer-Burmeister function. Quadratic penalty functions are used to treat this nonsmooth constrained program. We investigate necessary and sufficient conditions that guarantee the convergence of optimal values of unconstrained penalized problems to the optimal value of the original MPCC.
2006, 2(3): 297-318
doi: 10.3934/jimo.2006.2.297
+[Abstract](2067)
+[PDF](1197.3KB)
Abstract:
While many firms and researchers have developed various supply chain solutions, there are many underlying reasons why these solutions have not been adopted in practice. Some key reasons, as articulated by Lee and Billington (1992), include organizational barriers, coordination challenges among marketing, manufacturing, and logistics, technical challenges in the area of information systems, as well as conflicting supply chain performance metrics. Other key reasons are due to alternative performance measures besides total expected relevant cost, which include sales target, product substitution, product clearance, sales per square foot, etc. In order to understand how these alternative performance measures affect the supply chain solution, we make an initial attempt to analyze how alternative measures would affect the simplest form of inventory policy, namely, the newsvendor solution. To identify various alternative measures and to explore how such order decisions are made, we conducted a simple experiment by giving a single-period inventory problem to 250 MBA students and 6 professional buyers who order fashion items. We observed that both groups select their order quantities less than the newsvendor solution and made their ordering decisions based on various specific performance metrics besides total expected cost. These observations have motivated us to analyze how these performance metrics would affect the ordering decision. Our analysis indicates that, under these performance metrics, it is rational for the decision maker to order less than the newsvendor solution.
While many firms and researchers have developed various supply chain solutions, there are many underlying reasons why these solutions have not been adopted in practice. Some key reasons, as articulated by Lee and Billington (1992), include organizational barriers, coordination challenges among marketing, manufacturing, and logistics, technical challenges in the area of information systems, as well as conflicting supply chain performance metrics. Other key reasons are due to alternative performance measures besides total expected relevant cost, which include sales target, product substitution, product clearance, sales per square foot, etc. In order to understand how these alternative performance measures affect the supply chain solution, we make an initial attempt to analyze how alternative measures would affect the simplest form of inventory policy, namely, the newsvendor solution. To identify various alternative measures and to explore how such order decisions are made, we conducted a simple experiment by giving a single-period inventory problem to 250 MBA students and 6 professional buyers who order fashion items. We observed that both groups select their order quantities less than the newsvendor solution and made their ordering decisions based on various specific performance metrics besides total expected cost. These observations have motivated us to analyze how these performance metrics would affect the ordering decision. Our analysis indicates that, under these performance metrics, it is rational for the decision maker to order less than the newsvendor solution.
2006, 2(3): 319-338
doi: 10.3934/jimo.2006.2.319
+[Abstract](2024)
+[PDF](253.6KB)
Abstract:
This paper develops a new derivative-free method for solving linearly constrained nonsmooth optimization problems. The objective functions in these problems are, in general, non-regular locally Lipschitz continuous function. The computation of generalized subgradients of such functions is difficult task. In this paper we suggest an algorithm for the computation of subgradients of a broad class of non-regular locally continuous Lipschitz functions. This algorithm is based on the notion of a discrete gradient. An algorithm for solving linearly constrained nonsmooth optimization problems based on discrete gradients is developed. We report preliminary results of numerical experiments. These results demonstrate that the proposed algorithm is efficient for solving linearly constrained nonsmooth optimization problems.
This paper develops a new derivative-free method for solving linearly constrained nonsmooth optimization problems. The objective functions in these problems are, in general, non-regular locally Lipschitz continuous function. The computation of generalized subgradients of such functions is difficult task. In this paper we suggest an algorithm for the computation of subgradients of a broad class of non-regular locally continuous Lipschitz functions. This algorithm is based on the notion of a discrete gradient. An algorithm for solving linearly constrained nonsmooth optimization problems based on discrete gradients is developed. We report preliminary results of numerical experiments. These results demonstrate that the proposed algorithm is efficient for solving linearly constrained nonsmooth optimization problems.
2006, 2(3): 339-349
doi: 10.3934/jimo.2006.2.339
+[Abstract](2424)
+[PDF](203.1KB)
Abstract:
We consider an integrated distribution network design problem in which all the retailers face uncertain demand. The risk-pooling benefit is achieved by allowing some of the retailers to operate as distribution centers (DCs) with commitment in service level. The target is to minimize the expected total cost resulted from the DC location, transportation, and inventory. We formulate it as a two-stage nonlinear discrete stochastic optimization problem. The first stage decides which retailers to be selected as DCs and the second stage deals with the costs of DC-retailer assignment, transportation, and inventory. In the literature, the similar models require the demands of all retailers in each scenario to have their variances identically proportional to their means. In this paper, we remove this restriction. We reformulate the problem as a set-covering model and solve it by a column generation approach. With a variable fixing technique, we are able to efficiently solve problems of moderate-size (up to one hundred retailers and nine scenarios).
We consider an integrated distribution network design problem in which all the retailers face uncertain demand. The risk-pooling benefit is achieved by allowing some of the retailers to operate as distribution centers (DCs) with commitment in service level. The target is to minimize the expected total cost resulted from the DC location, transportation, and inventory. We formulate it as a two-stage nonlinear discrete stochastic optimization problem. The first stage decides which retailers to be selected as DCs and the second stage deals with the costs of DC-retailer assignment, transportation, and inventory. In the literature, the similar models require the demands of all retailers in each scenario to have their variances identically proportional to their means. In this paper, we remove this restriction. We reformulate the problem as a set-covering model and solve it by a column generation approach. With a variable fixing technique, we are able to efficiently solve problems of moderate-size (up to one hundred retailers and nine scenarios).
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