Beatriz Abdul-Jalbar

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.

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.

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.

An O ( T log T ) Algorithm for the Dynamic Lot Size Problem with Limited Storage and Linear Costs

In this paper the dynamic lot size problem with time varying storage capacities and linear costs is addressed. Like in the uncapacitated version, this problem can be formulated as a network flow problem. Considering the properties of the underlying network, we devise an O(T log T) greedy algorithm to obtain optimal policies and we report computational results for randomly generated problems.

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.

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.