Joaquín Sicilia

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.

The problem of the optimal biobjective spanning tree

This paper studies the problem of finding the set of optimal spanning trees of a connected graph, considering two cost functions defined on the set of edges. This problem is NP-hard and the solution is described through an algorithm that builds the family of efficient trees. This algorithm needs two procedures that solve the following uniobjective problems: the construction of all the spanning trees of a connected graph and the construction of the whole set of minimum cost spanning trees. The computational results obtained are shown in Section 5.

Policies for inventory/distribution systems: The effect of centralization vs. decentralization

Abstract This paper concerns with a multi-echelon inventory/distribution system considering one-warehouse and N-retailers. The retailers are replenished from the warehouse. We assume that the demand rate at each retailer is known. The problem consists of determining the optimal reorder policy which minimizes the overall cost, that is, the sum of the holding and replenishment costs. Shortages are not allowed and lead times are negligible. We study two situations: when the retailers make decisions independently and when the retailers are branches of the same firm. Solution methods to determine near-optimal policies in both cases are provided. Computational results on several randomly generated problems are reported.

Short Communication: The lot size-reorder level inventory system with customers impatience functions

In this paper, we study a continuous review inventory model with deterministic demand. The model allows shortages, which are partially backlogged. The backlogging is characterized using an approach in which customers are considered impatient. Total profit function is developed using three general costs: holding cost, order cost and shortage cost. Holding cost is based on average stocks and order cost is fixed per replenishment. In shortage cost, we include three significant costs: the unit backorder cost (depending on the shortage time), the goodwill cost (constant) and the opportunity cost. A general approach is presented to determine the economic lot size, the reorder level and the minimum total inventory cost. We consider two customers impatience functions to illustrate the application of the procedure. This paper extends several models studied by other authors.

The integrality of the lot size in the basic EOQ and EPQ models: Applications to other production-inventory models

In this paper we present a method to obtain the solution of the classic economic order quantity (EOQ) and economic production quantity (EPQ) models when the lot size must be an integer quantity. This approach is operatively very simple and allows obtaining a rule to discriminate between the situation in which the optimal solution is unique and when there are two optimal solutions. Also, this method is applicable to the resolution of other production-inventory models. We expose some of them and illustrate the use of the method with numerical examples.

AN INVENTORY SYSTEM WITH PARTIAL BACKLOGGING MODELED ACCORDING TO A LINEAR FUNCTION

In this paper, we study an inventory system with partial backlogging, in which the backlogging rate is a continuous and nonincreasing two piece function. The total shortage cost includes three significant costs: the unit backorder cost (depending on the backorder time), the opportunity cost, and the goodwill cost. This model generalizes several inventory systems studied by other authors. The optimal policy is characterized through several results, which depend on the values of the known input parameters. Illustrative examples and a sensitivity analysis, which help us understand the theoretical results, are also given.

A tabu search algorithm for the Open Shop problem

In this paper we consider the minimum makespan Open Shop problem without preemption. It is well-known that the case with only two machines can be optimally solved in linear time, whereas the problem with an arbitrary number of machines is NP-hard in the strong sense. We propose a tabu search algorithm for the solution of the problem which uses simple list scheduling algorithms to build the starting solutions. The algorithm is extensively tested on randomly generated instances.

A new heuristic to solve the one-warehouse N-retailer problem

We deal with a multi-echelon inventory system in which one warehouse supplies an item to multiple retailers. Customer demand arrives at each retailer at a constant rate. The retailers replenish their inventories from the warehouse that in turn orders from an outside supplier. It is assumed that shortages are not allowed and lead times are negligible. The goal is to determine replenishment policies that minimize the overall cost in the system. We develop a heuristic to compute efficient policies, which also can easily be used in a spreadsheet application. The main idea consists of finding a balance between the replenishment and the inventory holding costs at each installation. This new heuristic we compare with two other approaches proposed in the literature; the computational studies show that in most of the instances generated the new method provides lower costs.

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.

Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level

We study an EOQ inventory model with demand rate and holding cost rate per unit time, both potentially dependent on the stock level. The ordering cost, the holding cost and the gross profit from the sale of the item are considered. The objective is to maximize the average profit per unit time. We present the analytical formulation of the problem and demonstrate the existence and uniqueness of the optimal cycle time, giving a numerical algorithm to obtain it. Moreover, we provide two fundamental theoretical results: a rule to check when a given cycle time is the optimal policy, and a necessary and sufficient condition for the profitability of the system. Several EOQ models analyzed by other authors are particular cases of the one here studied. We present some numerical examples to illustrate the proposed algorithm and analyze the sensitivity of the optimal solution with respect to changes in various parameters of the system.