Marcos Colebrook

A new characterization for the dynamic lot size problem with bounded inventory

In this paper, we address the dynamic lot size problem with storage capacity. As in the unconstrained dynamic lot size problem, this problem admits a reduction of the state space. New properties to obtain optimal policies are introduced. Based on these properties a new dynamic programming algorithm is devised. Superiority of the new algorithm to the existing procedure is demonstrated. Furthermore, the new algorithm runs in O(T) expected time when demands vary between zero and the storage capacity. Computational results are reported for randomly generated problems.

Undesirable facility location problems on multicriteria networks

This paper is devoted to the location of undesirable facilities on multicriteria networks. Firstly, we analyze the undesirable center and median models establishing new properties to characterize the efficient solutions and rules to remove inefficient edges. Then, by means of a convex combination of these two latter functions, we address the λ-anti-cent-dian problem providing an effective rule to remove inefficient edges as well as a polynomial algorithm that solves the problem. Finally, we also comment on how this model can be slightly modified to generalize other models presented in the literature.

A polynomial algorithm for the production/ordering planning problem with limited storage

This paper concerns the dynamic lot size problem where the storage capacity is limited and shortages are allowed. The planning horizon is divided into T periods and, for each period, concave functions to define the holding/stockout and production costs are considered. It is proved that the results derived in a previous work for the dynamic lot size problem assuming time-varying storage capacities remain valid for the case with backlogging.

A polynomial algorithm for the multicriteria cent-dian location problem

Given a network with several weights per node and several lengths per edge, we address the problem of locating a facility on the network such that the convex combinations of the center and median objective functions are minimized. Since we consider several weights and several lengths, various objective functions should be minimized, and hence we have to solve a multicriteria cent-dian location problem. A polynomial algorithm to characterize the efficient location point set on the network is developed. Furthermore, this model can generalize other problems such as the multicriteria center problem and the multicriteria median problem. Computing time results on random planar networks considering different combinations of weights and lengths are reported, which strengthen the polynomial complexity of the procedure.

A new bound and an O( mn ) algorithm for the undesirable 1-median problem (maxian) on networks

The problem of locating an undesirable facility on a network with n nodes and m edges so as to maximize its total weighted distance to all nodes is addressed. We propose a new upper bound to the problem. Likewise, we develop a new algorithm in O(mn) time which dynamically updates this new upper bound. Computational results on low and high dense networks, as well as planar networks, are presented.

Effective replenishment policies for the multi-item dynamic lot-sizing problem with storage capacities

We address the dynamic lot-sizing problem considering multiple items and storage capacity. Despite we can easily characterize a subset of optimal solutions just extending the properties of the single-item case, these results are not helpful to design an efficient algorithm. Accordingly, heuristics are appropriate approaches to obtain near-optimal solutions for this NP-hard problem. Thus, we propose a heuristic procedure based on the smoothing technique, which is tested on a large set of randomly generated instances. The computational results show that the method is able to build policies that are both easily implemented and very effective, since they are on average 5% above the best solution reported by CPLEX. Moreover, an additional computational experiment is carried out to show that the performance of this new heuristic is on average better and more robust than other methods previously proposed for this problem.

A new algorithm for the undesirable 1-center problem on networks

Recent papers have developed efficient algorithms for the location of an undesirable (obnoxious) 1-center on general networks with n nodes and m edges. Even though the theoretical complexity of these algorithms is fine, the computational time required to get the solution can be diminished using a different model formulation and slightly improving the upper bounds. Thus, we present a new O(mn) algorithm, which is more straightforward and computationally faster than the previous ones. Computing time results comparing the former approaches with the proposed algorithm are supplied.

Centralized and decentralized inventory policies for a single-vendor two-buyer system with permissible delay in payments

In todays business transactions, vendors usually offer their buyers a delay period in payment. This strategy has benefits to the vendor since it attracts new buyers who consider the delay period as a type of price reduction. In addition, permissible delay in payments also is advantageous for the buyers since they do not have to pay the vendor immediately after they receive the items. In contrast, the buyers can delay the payment until the end of the allowed period and during the credit period they can earn interest on the accumulated revenues. However, if the payment is not settled by the end of the credit period, a higher interest is charged. Under this scenario, an inventory model consisting of a single vendor which supplies an item to two different buyers is analyzed. First, we address the problem assuming that buyers and vendor are willing to cooperate and the integrated model is derived in terms of single-cycle policies. Next, we analyze a decentralized model where the buyers and the vendor make decisions independently. A numerical example is solved to illustrate both strategies. We carry out a computational study to compare integrated and decentralized policies. A sensitivity analysis is also performed to examine the effects of each parameter on both total costs. According to the computational results and the statistical analysis, in most scenarios the integrated policies outperform the decentralized strategies. HighlightsThe one-vendor two-buyer inventory system with permissible delay in payments is addressed.The problem is analyzed under both a cooperative and a non-cooperative environment.A numerical example is solved to illustrate the solutions approaches.Both solution procedures have been implemented and the computational results reveal that in most cases the integrated policies outperform the decentralized strategies.

An O(mn) algorithm for the anti-cent-dian problem

The problem of locating an undesirable facility on a network under the anti-cent-dian criterion is addressed. Such criterion represents the convex combination of the undesirable center (maximize the minimum distance) and the undesirable median (maximize the sum of distances). To determine the optimal location point, we propose an efficient algorithm in O(mn) which improves a former approach proposed by other authors in O(mnlogn) time. This new algorithm is based on a new upper bound and on some specific properties of the anti-cent-dian problem.

Locating a facility on a network with multiple median‐type objectives

We consider the problem of locating a single facility on a network in the presence of r >= 2median‐type objectives, represented by r sets of edge weights (or lengths)corresponding toeach of the objectives. When r = 1, then one gets the classical 1‐median problem whereonly the vertices need to be considered for determining the optimal location (Hakimi [1]).The paper examines the case when r >= 2 and provides a method to determine the non‐dominatedset of points for locating the facility.