This article introduces a new Cost Management and Decision Support System (DSS) applicable to Order Management. This model is better fit and compatible with today's competitive, and constantly changing, business e...
详细信息
This article introduces a new Cost Management and Decision Support System (DSS) applicable to Order Management. This model is better fit and compatible with today's competitive, and constantly changing, business environment. The presented Profitable-To-Promise (PTP) approach is a novel modeling approach which integrates System Dynamics (SD) simulation with mixed-integer programming (MIP). This Order Management model incorporates Activity-Based Costing and Management (ABC/M) as a link to merge the two models. MIP and SD. This combination is introduced as a hybrid Decision Support System. Such a system can evaluate the profitability of each Order Fulfillment policy and generate valuable cost information. Unlike existing optimization-based DSS models, the presented hybrid modeling approach can perform on-time cost analysis. This will lead to better business decisions based on the updated information. (C) 2011 Elsevier B.V. All rights reserved.
This article is based on a real-life problem of a global aluminium supply chain network driven by an aluminium smelter. At each echelon of the aluminium supply chain network, several members are involved which are sca...
详细信息
This article is based on a real-life problem of a global aluminium supply chain network driven by an aluminium smelter. At each echelon of the aluminium supply chain network, several members are involved which are scattered around the world. Producing aluminium begins with bauxite mining. Next, aluminium oxide is made from bauxite and finally aluminium is produced from aluminium oxide. A novel type of mixed-integer decision-making model, including a time-continuous representation of the planning period, is presented. The model enables coordination of production quantities and times of all supply chain members in order to minimise production and transportation costs of the whole supply chain minus bonus payments for early deliveries which are stipulated between the supply chain network and its customers. Material flows can take place with or without temporary storage of intermediate products at supplying and/or receiving sites. Furthermore, relax-and-fix heuristics are presented. A number of randomly generated scenarios are presented to demonstrate that the heuristics can find nearly optimal solutions along with drastically reduced computation times. The relax-and-fix heuristic enables iterative planning between centralised and decentralised decision makers.
Recently there has been considerable research on simple mixed-integer sets, called mixing sets, and closely related sets arising in uncapacitated and constant capacity lot-sizing. This in turn has led to study of more...
详细信息
Recently there has been considerable research on simple mixed-integer sets, called mixing sets, and closely related sets arising in uncapacitated and constant capacity lot-sizing. This in turn has led to study of more general sets, called network-dual sets, for which it is possible to derive extended formulations whose projection gives the convex hull of the network-dual set. Unfortunately this formulation cannot be used (in general) to optimize in polynomial time. Furthermore the inequalities defining the convex hull of a network-dual set in the original space of variables are known only for some special cases. Here we study two new cases, in which the continuous variables of the network-dual set are linked by a bidirected path. In the first case, which is motivated by lot-sizing problems with (lost) sales, we provide a description of the convex hull as the intersection of the convex hulls of 2(n) mixing sets, where n is the number of continuous variables of the set. However optimization is polynomial as only n + 1 of the sets are required for any given objective function. In the second case, generalizing single arc flow sets, we describe again the convex hull as the intersection of an exponential number of mixing sets and also give a combinatorial polynomial-time separation algorithm.
The most widely used progress measure for branch-and-bound (B&B) algorithms when solving mixed-integer programs (MIPs) is the MIP gap. We introduce a new progress measure that is often much smoother than the MIP g...
详细信息
The most widely used progress measure for branch-and-bound (B&B) algorithms when solving mixed-integer programs (MIPs) is the MIP gap. We introduce a new progress measure that is often much smoother than the MIP gap. We propose a double exponential smoothing technique to predict the solution time of B&B algorithms and evaluate the prediction method using three MIP solvers. Our computational experiments show that accurate predictions of the solution time are possible, even in the early stages of B&B algorithms.
In this paper, we study the problem of technical transient gas network optimization, which can be considered a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the ...
详细信息
In this paper, we study the problem of technical transient gas network optimization, which can be considered a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the network arcs. Applying an implicit box scheme to the isothermal Euler equation, we derive a mixed-integer nonlinear program. This is solved by means of a combination of (i) a novel mixed-integer linear programming approach based on piecewise linearization and (ii) a classical sequential quadratic program applied for given combinatorial constraints. Numerical experiments show that better approximations to the optimal control problem can be obtained by using solutions of the sequential quadratic programming algorithm to improve the mixed-integer linear program. Moreover, iteratively applying these two techniques improves the results even further.
The mean-risk stochastic mixed-integer programs can better model complex decision problems under uncertainty than usual stochastic (integer) programming models. In order to derive theoretical results in a numerically ...
详细信息
The mean-risk stochastic mixed-integer programs can better model complex decision problems under uncertainty than usual stochastic (integer) programming models. In order to derive theoretical results in a numerically tractable way, the contamination technique is adopted in this paper for the postoptimality analysis of the mean-risk models with respect to changes in the scenario set, here the risk is measured by the lower partialmoment. We first study the continuity of the objective function and the differentiability, with respect to the parameter contained in the contaminated distribution, of the optimal value function of the mean-risk model when the recourse cost vector, the technology matrix and the right-hand side vector in the second stage problem are all random. The postoptimality conclusions of the model are then established. The obtained results are applied to two-stage stochastic mixed-integer programs with risk objectives where the objective function is nonlinear with respect to the probability distribution. The current postoptimality results for stochastic programs are improved.
In healthcare systems, the operating theatre is recognised as having an important role, notably in terms of generated income and cost. Its management, and in particular its scheduling, is thus a critical activity. A l...
详细信息
In healthcare systems, the operating theatre is recognised as having an important role, notably in terms of generated income and cost. Its management, and in particular its scheduling, is thus a critical activity. A less costly organisation of the operating rooms needs a more rational use of the resources, which requires optimising the surgical schedule. As we are concerned in the medical staff well-being, we integrate the surgeons' preferences when setting up such schedules. This planning process is usually decomposed in two sequential phases: a planning stage followed by a scheduling stage. Due to this decomposition the resulting solutions may turn out to be sub-optimal. This paper describes a mixed-integer programming that completely covers the planning and scheduling of the surgical operations. The pursued objective is twofold: minimising the operating cost and maximising the surgeons' welfare.
Deciding what question to branch on at each node is a key element of search algorithms. In this paper, we describe a collection of techniques for branching decisions that are motivated from an information-theoretic pe...
详细信息
Deciding what question to branch on at each node is a key element of search algorithms. In this paper, we describe a collection of techniques for branching decisions that are motivated from an information-theoretic perspective. The idea is to drive the search to reduce the uncertainty (entropy) in the current subproblem. We present four families of methods for branch question selection in mixedintegerprogramming that use this idea. In the first, a variable to branch on is selected based on lookahead. This method performs comparably to strong branching on MIPLIB, and better than strong branching on hard real-world procurement optimization instances on which CPLEX's default strong branching outperforms CPLEX's default branching strategy. The second family combines this idea with strong branching. The third family does not use lookahead, but instead exploits the tie between indicator variables and the variables they govern. This significantly outperforms the state-of-the-art branching strategies on both combinatorial procurement problems and facility location problems. The fourth family concerns branching using carefully constructed linear inequality constraints over sets of variables. (C) 2010 Elsevier B.V. All rights reserved.
Tailored for a complex application in the process industry, this article examines a multi-product production planning and scheduling problem with sequence-dependent setup cost and times. The manufacturing process is c...
详细信息
Tailored for a complex application in the process industry, this article examines a multi-product production planning and scheduling problem with sequence-dependent setup cost and times. The manufacturing process is characterised by a two-stage structure where the sequencing problem occurs on the first level and contribution margin, holding cost, penalty cost are accounted on the second level. We present a hybrid mixed-binary optimisation model based on the general lot-sizing and scheduling problem [Fleischmann, B. and Meyr, H. 1997. The general lotsizing and scheduling problem. OR Spectrum, 19 (1), 11-21], which combines discrete and continuous-time elements within a standard inventory and lot-size (IL) formulation. Since the IL formulation does not provide sharp linear programming-relaxation bounds, we present two alternative reformulations based on a transportation problem. In a numerical study inspired by real industry data, we show that on average, both reformulations yield significant improvements in computation time and integrality gap.
We show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut (which we defined in 2010). We extend this result to show that crooke...
详细信息
We show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut (which we defined in 2010). We extend this result to show that crooked cross cuts give the convex hull of mixed-integer sets with more integer variables if the coefficients of the integer variables form a matrix of rank 2. We also present an alternative characterization of the crooked cross cut closure of mixed-integer sets similar to the one on the equivalence of different definitions of split cuts presented in Cook et al. (1990) [4]. This characterization implies that crooked cross cuts dominate the 2-branch split cuts defined by Li and Richard (2008) [8]. Finally, we extend our results to mixed-integer sets that are defined as the set of points (with some components being integral) inside a closed, bounded and convex set. (C) 2011 Elsevier B.V. All rights reserved.
暂无评论