Laureano F. Escudero

On practical resource allocation for production planning and scheduling with period overlapping setups

Abstract Capacity requirements planning is normally based on long-term demand forecasts and part type mix estimates. In the execution of a production plan, it must often be recognized that the capacity assumptions previously made are no longer valid. This is because the part type mix, the operator or machine availability, or the existence of additional resources has changed. This may lead to underload as well as to overload situations for particular time periods. This paper presents a mixed 0–1 model and outlines a practical algorithm to schedule the production quantities. Our aproach takes into account all information available on the shop-floor level, such as: machine availability over the planning horizon, unit processing times for the part types, minor setup times (i.e., machine setups required when changing part types that belong to the same family), major setup times (i.e., machine setups required when changing part types that belong to different families), storable and non-storable resource availability and consumption, part type demand over the planning horizon, and bounds on production rate and backlogging. Furthermore, the model accounts correctly for costs corresponding to period overlapping setups. Also, the application of the model in some case studies is reported.

An inexact algorithm for the sequential ordering problem

Abstract Given the directed G = ( N , A ) and the penalty matrix C , the Sequential Ordering Problem (hereafter, SOP) consists of finding the permutation of the nodes from the set N , such that it minimizes a C -based function and does not violate the precedence relationships given by the set A . Strong sufficient conditions for the infeasibility of a SOPs instance are embedded in a procedure for the SOPs pre-processing. Note that it is one of the key steps in any algorithm that attempts to solve SOP. By dropping the constraints related to the precedence relationships, SOP can be converted in the classical Asymmetric Traveling Salesman Problem (hereafter, ASTP). The algorithm obtains (hopefully) satisfactory solutions by modifying the optimal solution to the related Assignment Problem (hereafter, AP) if it is not a Feasible Sequential Ordering (hereafter, FSO). The new solution ‘patches’ the subtours (if any) giving preference to the patches with zero reduced cost in the linking arcs. The AP-based lower bound on the optimal solution to ATSP is tightened by using some of the procedures given in [1]. In any case, a local search for improving the initial FSO is performed; it uses 3- and 4-changed based procedures. Computational results on a broad set of cases are reported.

Efficient reformulation for 0-1 programs: methods and computational results

Abstract We introduce two general methods for 0–1 program reformulation. Our first method generalizes coefficient reduction, our second method generalizes lifting. Together they provide a unifying interpretation of many previously described automatic reformulation methods. The particular model structures that we consider are individual knapsack constraints, pairs of knapsack constraints, clique and cover induced inequalities, variable upper bounding constraints and capacity expansion constraints. We describe several easy applications of our reformulation procedures. Some computational experience is reported, including the currently best known results on a well-known 147 × 2655 benchmark problem.

On maintenance scheduling of production units

Abstract A typical maintenance scheduling problem is presented as a large-scale mixed integer nonlinear programming case. Several relaxations of the conditions of variables and constraints are discussed. The optimal solution of the models based on these relaxations is viewed as the lower bound of the optimal solution in the original problem. A combined implicit enumeration and branch-and-bound algorithm is used. Typical dimension of the problems for which computational experience is reported is 25 production units in the system. 19 of these are to be maintained and a planning horizon of 52 weeks with 5 types of hours per week. The corresponding dimensions of the model are about 5700 constraints, 700 binary variables and 6500 nonlinear separable variables.

S3 sets, an extension of the Beale-Tomlin special ordered sets

In this work an extension of the Beale-Tomlin special ordered sets is introduced that has proved to be efficient for solving certain types of open shop scheduling problems. Besides their usual characteristics, exclusivity constraints in the jobs are allowed, more general than tree-like precedence structures are considered, and semi-active schedules that cannot be labeled as non-optimal solutions may occur. The problem is formulated as a large-scale 0–1 model. Computational experience on some real-life problems is reported.

Performance evaluation of independent superbasic sets on nonlinear replicated networks

Abstract In this paper we describe a new type of network flow problems that basically consists of the classical transshipment problem with the following extensions: (1) The replication of a network by producing subnetworks with identical structure, being linked by so-called linking arcs; (2) the objective function terms related to the linking arcs are non-differentiable nonlinear functions. By using a networks-specialized implementation of a linearly constrained nonlinear programming algorithm described elsewhere, we report the computational performance of the new concept of independent superbasic sets that allows to obtain in parallel independent pieces of the solution at each iteration.

On Solving a Large-Scale Resource Allocation Problem in Production Planning

Various production planning problems can be described and solved with Linear Programming (LP) models. In manufacturing applications setup often plays an important role. To solve a setup problem 0–1 variables must be introduced in the model, which leads to an increase in the model size and computational effort. This paper discusses several models to consider setup times in production planning. A decomposition methodology that does not consider the integrality of all 0–1 variables at once, but successively, is outlined. Results for an application in the modeling of the IBM Sindelfingen Multi-layer-ceramics (MLC) Punching area, are discussed.

On tightening cover induced inequalities

Abstract Here we describe computationally efficient procedures for tightening cover induced inequalities by using 0–1 knapsack constraints and, if available, cliques whose variables are included in the cover. An interesting application is the case where the cover is implied by the knapsack constraint. The tightening is achieved by increasing the coefficients of the cover inequality. The new constraint is 0–1 equivalent to and LP tighter than the original one. The computational complexity of the procedures is O(n log n), where n is the number of variables in the cover.

On diagonally preconditioning the truncated Newton method for super-scale linearly constrained nonlinear programming

Abstract We present an algorithm for super-scale linearly constrained nonlinear programming (LCNP) based on Newtons method. In large-scale programming solving the Newton equation at each iteration can be expensive and may not be justified when far from a local solution. For super-scale problems, the truncated Newton method (where an inaccurate solution is computed by using the conjugate-gradient method) is recommended; a diagonal BFGS preconditioning of the gradient is used, so that the number of iterations to solve the equation is reduced. The procedure for updating that preconditioning is described for LCNP when the set of active constraints or the partition of basic, superbasic and nonbasic (structural) variables have been changed.

New Procedures For Preprocessing 0–1 Models With Knapsack-Like Constraints And Conjunctive And/Or Disjunctive Variable Upper Bounds

AbstractWe present some preprocessing techniques for 0–1 models by taking advantage of the special structure provided by conjunctive and disjunctive variahle upper bounds, which are often used to express logical constraints. These new procedures include variable fixing, generation of clique and coverinduced inequalities, and coefficient reduction and related constraint generation procedures. By considering the information provided by the variable upper bound constraints, the procedures can be applied when the conditions required by the standard methods are not satisfied. Although some of our procedures require the solution of 0–1 problems arising from the original model, the subproblems (mainly, subset sum and set covering models) are usually small. In any case, our methodology can also be applied by using easily computed upper bounds on the optimal values of the subproblems.