José M. Gutiérrez

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.

Policies for a single-vendor multi-buyer system with finite production rate

We deal with a multi-echelon inventory system in which one vendor supplies an item to multiple buyers. The vendor produces the item at a finite rate and customer demand occurs at each buyer at a constant rate. There is a holding cost per unit stored per unit time at the vendor and at each buyer. Each time a production is carried out the vendor incurs a setup cost. Moreover, placing an order at a buyer entails a fixed ordering cost. Shortages are not allowed. The goal is to determine the order quantities at the buyers and the production and shipment schedule at the vendor in order to minimize the average total cost per unit time. We formulate the problem in terms of integer-ratio policies and we develop a heuristic procedure. We also show how the problem should be addressed in case of independence among the vendor and the buyers. Both solution procedures are illustrated with a numerical example. Finally, we present the results of a numerical study which illustrates the performance of the heuristic for computing integer-ratio policies. Additionally, we compare the integer-ratio policies with the decentralized policies, and a sensitivity analysis of parameters is also reported.

Note on “An efficient approach for solving the lot-sizing problem with time-varying storage capacities”

In a recent paper Gutierrez et al. (2008) show that the lot-sizing problem with inventory bounds can be solved in O(T log T) time. In this note we show that their algorithm does not lead to an optimal solution in general.

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.

Bicriteria trade-off analysis in a two-echelon inventory/distribution system

We would like to comment on the paper by Bookbinder and Chen, in which they developed algorithms to obtain the Pareto-optimal solution set for a two-echelon inventory= distribution system. We have only focused our attention on the deterministic demand case. In such a situation, these authors proposed a solution method based on a theorem (see p 710 in Bookbinder and Chen), which determines the non-dominated solutions. Moreover, in their paper, two numerical examples representative of the two cases considered in such theorem are provided. Unfortunately, the procedure proposed by Bookbinder and Chen does not determine the Pareto-optimal set properly. Besides, the numerical examples solved in their paper can be used to show this assertion.

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.

Determining the Pareto set in a bicriteria two-echelon inventory/distribution system

This article concerns two-echelon inventory/distribution system, consisting of a warehouse and a retailer. We assume that the demand is deterministic and stockouts are not permitted. Two criteria are considered: to minimize the annual inventory cost and the annual total number of damaged items by improper shipment handling. The problem consists of determining the non-dominated inventory policies in such a way that the trade-off between both criteria is achieved. We present the characterization of the non-dominated optimal solution set and we use this result to correct the solution method previously proposed by other authors for a problem with identical cost structure. An efficient algorithm to calculate the non-dominated solution set is introduced. Computational results on several randomly generated problems are reported.

Integration of a Heuristic Method into an ERP Software: A Successful Experience for a Dynamic Multi-item Lot Sizing Problem

This chapter focuses on the successful collaboration between a research team at the Universidad de La Laguna (Tenerife, Spain) and the firm ITOP Management Consulting, which is a SAP partner mainly interested in developing solutions for SMEs. Company representatives came to our group to propose us both the design of an efficient algorithm to reduce inventory costs in companies, and its eventual integration as an add-on in SAP Business One platform. The problem arises in those firms with storage capacity that should schedule the replenishment orders for several items along a finite planning horizon. After 2 years, the algorithm was finally implemented in C# and .NET. A comprehensive computational experiment was carried out considering a wide range of random instances. The experimental results revealed that heuristic solutions were on average 5 % above the best solution provided by CPLEX optimizer.