Allocating Fibers in Cable Manufacturing

Abstract

We study the problem of allocating stocked fibers to made-to-order cables with the goals of satisfying due dates and reducing the costs of scrap, setup, and fiber circulation. These goals are achieved by generating remnant fibers either long enough to satisfy future orders or short enough to scrap with little waste. They are also achieved by manufacturing concatenations, in which multiple cable orders are satisfied by the production of a single cable that is afterwards cut into the constituent cables ordered. We use a function that values fibers according to length, and which can be viewed as an approximation to the optimal value function of an underlying dynamic programming problem. The daily policy that arises under this approximation is an integer program with a simple linear objective function that uses changes in fiber value to take into account the multi-period consequences of decisions. We describe our successful implementation of this integer program in the factory, summarizing our computational experience as well as realized operational improvements.Cable Manufacturing, Resource Pricing and Allocation, Remnant Inventory System, Discrete Optimization, Dynamic Programming Approximations

Effective management policies for remnant inventory supply chains

“…There is no guarantee that an arbitrary dual vector will satisfy properties that are intuitively appealing with the interpretation of the dual price for a remnant as its inherent value. Adelman and Nemhauser (1999) present several such properties in their work on the single-location problem with no cutting costs and no scrap values. Letting n ++ denote the set of vectors in n with strictly positive elements, we generalize the well known concepts of monotonicity and superadditivity as follows.…”

“…The interested reader is referred to Adelman and Nemhauser (1999) for a further discussion of these types of properties when δ = 0 for a single-facility problem. It suffices to say that such properties should be satisfied by the value function if we plan to use them for a stochastic policy, but picking an arbitrary optimal dual vector for our problem does not guarantee this.…”

“…One early paper that discusses how to incorporate remnant values into the cutting stock problem is the one by Scheithauer (1991); however, it does not provide details on how to compute the remnant values. The work most closely related to ours addresses a problem in the fiber optic industry where shorter lengths of fiber optic cable are to be cut from standard lengths and/or feasible remnants on a continuing basis Adelman and Nemhauser, 1999). In these papers, the authors consider a single supply and a single demand location and build a linear programming model that allows standard 438 Rajgopal et al duality results to place a "value" on remnants of any size; this in turn leads to a cutting policy adapted to a stochastic demand environment wherein one chooses the size of the piece to be cut based upon the reduction in its value when it is cut to a remnant of smaller size.…”

“…The first one requires the development of a new perturbation procedure to develop inherent values; as we demonstrate in Section 4, using the same approach as the one in Adelman and Nemhauser (1999) for this problem results in costs that on average are about 5-7% higher, and in the worst case could be almost 30% higher. With the second and third generalizations, desirable properties of the inherent values have to be suitably redefined and the resulting characteristics of the optimum are shown to depend on the relative magnitudes of scrap values and cutting costs.…”

“…These subnetworks are then connected to the various demand locations as part of a larger distribution network; thus the overall network is one comprising of several smaller subnetworks. Each of the subnetworks is represented using a model similar to that proposed in Adelman and Nemhauser (1999) for their single-supplier/single-user problem. In this model, nodes in each subnetwork represent the various sizes that could be present at the facility at any time as standard (raw) stock, finished product, remnants or scrap, where node m represents size m. The flow along an arc from node m to node n (where n < m) represents the number of units of size m that are cut down to remnants of size n (while producing that many pieces of size m − n in the process); Fig.…”