A note on the convexity of service-level measures of the (r,q) system
Article Abstract:
A proof is presented for the reorder-point/order-quantity (r,q) system wherein the mean outstanding backorders and stockouts as a function of unit time are jointly convex in the r and q control variables. Two random variables, D and I, characterized inventory position and lead time demand to characterize the average outstanding backorders as B(q,r) = E(sub D,I)(max(D-I,O)), where E is the expectation operator. I was also expressed as a random variable that was uniformly distributed on the interval, (r,r+q). Moreover, a nondecreasing stochastic process with stationary increments and continuous sample paths was used to characterize cumulative demand. This led to the formation of the equation B(q,r) = E(sub D,U)(b(q,r,D,U)), where I was replaced by r+qU and U was uniform on (O,1).
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1998
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DEA on relaxed convexity assumptions
Article Abstract:
Data Envelopment Analysis (DEA) is a mathematical programming strategy that is used to measure production frontiers and the relative efficiency of Decision Making Units. DEA methods have traditionally assumed the convexity of the underlying set of suitable input-output combinations. Petersen (1990) attempted to relax this assumption by relying only on the assumption of convex isoquants. However, the Petersen approach has proven to be inconsistent with the relaxed set of assumptions considered. One of its major flaws is that the input-output measures of efficiency it proposed invoked different assumptions. An attempt is made to identify the assumptions actually involved and to re-relax them to achieve consistency for the input-out measures.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1996
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Piecewise-linear approximation methods for nonseparable convex optimization
Article Abstract:
An algorithm is detailed to solve non-separable, convex optimization difficulties. This technique employs iterative, piecewise-linear approximation of the non-separable objective element, but needs function values only along a set of translated axes, in this way avoiding the problem of dimensionality often associated with grid techniques for multi-dimensional problems. A global convergence proof is offered under the notion that the objective function is 'Lipschitz continuous' and can be differentiated, and that the feasible set is compact and convex.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1988
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