Many production problems involve facility setups that lead to integer variables, production decisions that are continuous, and demands that are likely to be random. While these problems can be quite ...difficult to solve, we propose a model and an efficient solution technique for this basic class of stochastic mixed-integer programs. We use a set of scenarios to reflect uncertainty. The resulting mathematical model is solved using Lagrangian relaxation. We show that the duality gap of our relaxation is bounded above by a constant that depends on the cost function and the number of branching points in the scenario tree. We apply our technique to the problem of generating electric power. Numerical results indicate significant savings when the stochastic model is used instead of a deterministic one.
Robust-optimization models belong to a special class of stochastic programs, where the traditional expected cost minimization objective is replaced by one that explicitly addresses cost variability. ...This paper explores robust optimization in the context of two-stage planning systems. We show that, under arbitrary measures for variability, the robust optimization approach might lead to suboptimal solutions to the second-stage planning problem. As a result, the variability of the second-stage costs may be underestimated, thereby defeating the intended purpose of the model. We propose sufficient conditions on the variability measure to remedy this problem. Under the proposed conditions, a robust optimization model can be efficiently solved using a variant of the L-shaped decomposition algorithm for traditional stochastic linear programs. We apply the proposed framework to standard stochastic-programming test problems and to an application that arises in auctioning excess electric power.
We present a methodology for managing outsourcing projects from the vendor's perspective, designed to maximize the value to both the vendor and its clients. The methodology is applicable across the ...outsourcing lifecycle, providing the capability to select and target new clients, manage the existing client portfolio and quantify the realized benefits to the client resulting from the outsourcing agreement. Specifically, we develop a statistical analysis framework to model client behavior at each stage of the outsourcing lifecycle, including: (1) a predictive model and tool for white space client targeting and selection—
opportunity identification (2) a model and tool for client risk assessment and project portfolio management—
client tracking, and (3) a systematic analysis of outsourcing results,
impact analysis, to gain insights into potential benefits of IT outsourcing as a part of a successful management strategy. Our analysis is formulated in a logistic regression framework, modified to allow for non-linear input–output relationships, auxiliary variables, and small sample sizes. We provide examples to illustrate how the methodology has been successfully implemented for targeting, tracking, and assessing outsourcing clients within IBM global services division.
Scope and purpose
The predominant literature on IT outsourcing often examines various aspects of vendor–client relationship, strategies for successful outsourcing from the client perspective, and key sources of risk to the client, generally ignoring the risk to the vendor. However, in the rapidly changing market, a significant share of risks and responsibilities falls on vendor, as outsourcing contracts are often renegotiated, providers replaced, or services brought back in house. With the transformation of outsourcing engagements, the risk on the vendor's side has increased substantially, driving the vendor's financial and business performance and eventually impacting the value delivery to the client. As a result, only well-ran vendor firms with robust processes and tools that allow identification and active management of risk at all stages of the outsourcing lifecycle are able to deliver value to the client. This paper presents a framework and methodology for managing a portfolio of outsourcing projects from the vendor's perspective, throughout the entire outsourcing lifecycle. We address three key stages of the outsourcing process: (1) opportunity identification and qualification (i.e. selection of the most likely new clients), (2) client portfolio risk management during engagement and delivery, and (3) quantification of benefits to the client throughout the life of the deal.
The authors develop a model and a solution technique for the problem of generating electric power when demands are not certain. They also provide techniques for improving the current methods used in ...solving the traditional unit commitment problem. The solution strategy can be run in parallel due to the separable nature of the relaxation used. Numerical results indicate significant savings in the cost of operating power generating systems when the stochastic model is used instead of the deterministic model.
The authors develop a technique for refining the unit commitment obtained from solving the Lagrangian. Their model is a computer program with nonlinear constraints. It can be solved to optimality ...using the branch-and-bound technique. Numerical results indicate a significant improvement in the quality of the solution obtained.
The electric power industry is going through deregulation. As a result, the load on the generating units of a utility is becoming increasingly unpredictable. Furthermore, electric utilities may need ...to buy power or sell their production to a power pool that serves as a spot market for electricity. These trading activities expose utilities to volatile electricity prices. In this paper, we present a stochastic model for the unit commitment that incorporates power trading into the picture. Our model also accounts for fuel constraints and prices that may vary with electricity prices and demand. The resulting model is a mixed-integer program that is solved using Lagrangian relaxation and Bender's decomposition. Using this solution approach, we solve problems with 729 demand scenarios on a single processor to within 0.1% of the optimal solution in less than 10 minutes. Our numerical results indicate that significant savings can be achieved when the spot market is entered into the problem and when stochastic policy is adopted instead of a deterministic one.
We consider a special class of non-convex programs that are encountered in dispatching the generating units of an electric company. The general form of these problems is
{
min
c
T
x:l
j⩽A
jx
j⩽u
j,x
...j⩾0,∑
j=1
mx
i,t
j=f
i(y
i,t),By=d,y⩾0}
, where
c⩾0, all entries in
A are non-negative, and
f
i
(
y
i,
t
)⩾0. We show that one can achieve global optimality in the case of
l
j
=0. For the special case in which
A
j
is a vector of ones, we suggest an alternative formulation in which the non-linearity is moved to the objective function. Numerical results indicate significant improvement in the number of iterations and computer time needed to solve the problem.
Many production problems involve facility setups that lead to integer variables, production decisions that are continuous, and demands that are likely to be random. While these problems can be quite ...difficult to solve, a model and an efficient solution technique are proposed for this basic class of stochastic mixed-integer programs. A set of scenarios are used to reflect uncertainty. The resulting mathematical model is solved using Lagrangian relaxation. It is shown that the duality gap of the relaxation is bounded above by a constant that depends on the cost function and the number of branching points in the scenario tree. The technique is applied to the problem of generating electric power. Numerical results indicate significant savings when the stochastic model is used instead of a deterministic one.
It is shown that the block principal pivot algorithm for the linear complementarity problem solves the problem for a special class of matrices in at most n block principal pivot steps. Cycling ...examples for the BPPA in which the matrix is positive definite or symmetric positive definite are provided. For LCP of order three, it is proved that strict column (row) diagonal dominance is a sufficient condition to avoid cycling.
