Computing (R, S) policies with correlated demand

This paper considers the single-item single-stocking non-stationary stochastic lot-sizing problem under correlated demand. By operating under a nonstationary (R, S) policy, in which R denote the reorder period and S the associated order-up-to-level, we introduce a mixed integer linear programming (MILP) model which can be easily implemented by using off-theshelf optimisation software. Our modelling strategy can tackle a wide range of time-seriesbased demand processes, such as autoregressive (AR), moving average(MA), autoregressive moving average(ARMA), and autoregressive with autoregressive conditional heteroskedasticity process(AR-ARCH). In an extensive computational study, we compare the performance of our model against the optimal policy obtained via stochastic dynamic programming. Our results demonstrate that the optimality gap of our approach averages 2.28% and that computational performance is good

Generalizing backdoors

Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.

Generalized Solutions for the joint replenishment problem with correction factor

In this paper we give a complete analysis of the joint replenishment problem (JRP) under constant demands and continuous time. We present a solution method for the JRP when a correction is made for empty replenishments, and we test the solution procedures with real data. We show that the solutions obtained differ from the standard JRP when no correction is made in the cost function. We further show that the JRP with correction outperforms independent ordering. Additional numerical experiments are presented.inventory;joint replenishment;correction factor

Two notes on the joint replenishment problem under constant demand

Inventory Control;Inventory Models;management science

An efficient optimal solution method for the joint replenishment problem

During the last two decades, many heuristic procedures for the joint replenishment problem have appeared in the literature. The only available optimal solution procedure was based on an enumerative approach and was computationally prohibitive. In this paper we present an alternative optimal approach based on global optimisation theory. By applying Lipschitz optimisation one can find a solution with an arbitrarily small deviation from an optimal value. An efficient procedure is presented which uses a dynamic Lipschitz constant and generates a solution in little time. The running time of this procedure grows only linearly in the number of items

The Can-Order Policy for One-Warehouse N-Retailer Inventory System: A Heuristic Approach

We study an application of the can-order policy in one-warehouse n-retailer inventory system, and propose a heuristic approach for setting the appropriate inventory policy. On the can-order policy, an order is triggered when a retailer's inventory position reaches its must-order level. Then other retailers are examined whether their inventory reaches their can-order level, and if so they are filled by this order as well. Warehouse fulfills all involved retailers' inventory to their order-up-to levels. The can-order policy is not only able to save the total system-wide cost from joint replenishment, but it is also simple to use. Computer simulation is utilized to preliminarily study and to determine the best-known solution. We propose a heuristic approach utilizing decomposition technique, iterative procedure, and golden section search to obtain the satisfying total system-wide cost. This can save our computational time to find the appropriate inventory policy setting. We found that the proposed heuristic approach performs very well with the average cost gap less than 2% comparing to the best-known solution. It also provides satisfactory computational time from the reduced search space. Thus, the can-order policy can be very useful for such system

Generalized Solutions for the joint replenishment problem with correction factor

In this paper we give a complete analysis of the joint replenishment problem (JRP) under constant demands and continuous time. We present a solution method for the JRP when a correction is made for empty replenishments, and we test the solution procedures with real data. We show that the solutions obtained differ from the standard JRP when no correction is made in the cost function. We further show that the JRP with correction outperforms independent ordering. Additional numerical experiments are presented

Sustainability analysis in integrated inventory control and transportation systems

Due to the importance of costs as well as environmental effects of logistical activities throughout supply chains, such as inventory holding, freight transportation, and warehousing activities, this dissertation models and analyzes four integrated inventory control and transportation problems that account for economic and environmental aspects of a supply chain agents related decisions. The first model presents an integrated inventory control and transportation problem in a single item deterministic demand setting. A supply chain agents inventory control and transportation mode selection problem is solved under carbon cap, carbon cap and trade, carbon cap and offset, and carbon tax regulations. The second model focuses on an integrated inventory control and transportation problem in a single item stochastic demand setting integrating environmental objectives into a continuous review inventory control system with considerations of two different transportation modes. The third model studies an integrated inventory control and transportation problem in a multi-item deterministic demand setting, in which, a decision making method is developed considering the economic and environmental objectives. In the fourth model, a multi-item stochastic demand consolidation policy is analyzed with the consideration of heterogeneous freight trucks for transportation. It is shown that the consolidation policy suggested can result in substantial economic as well as environmental benefits for the supply chain agents --Abstract, page iii

On the inventory routing problem with stationary stochastic demand rate

One of the most significant paradigm shifts of present business management is that individual businesses no longer participate as solely independent entities, but rather as supply chains (Lambert and Cooper, 2000). Therefore, the management of multiple relationships across the supply chain such as flow of materials, information, and finances is being referred to as supply chain management (SCM). SCM involves coordinating and integrating these multiple relationships within and among companies, so that it can improve the global performance of the supply chain. In this dissertation, we discuss the issue of integrating the two processes in the supply chain related, respectively, to inventory management and routing policies. The challenging problem of coordinating the inventory management and transportation planning decisions in the same time, is known as the inventory routing problem (IRP). The IRP is one of the challenging optimization problems in logis-tics and supply chain management. It aims at optimally integrating inventory control and vehicle routing operations in a supply network. In general, IRP arises as an underlying optimization problem in situations involving simultaneous optimization of inventory and distribution decisions. Its main goal is to determine an optimal distribution policy, consisting of a set of vehicle routes, delivery quantities and delivery times that minimizes the total inventory holding and transportation costs. This is a typical logistical optimization problem that arises in supply chains implementing a vendor managed inventory (VMI) policy. VMI is an agreement between a supplier and his regular retailers according to which retailers agree to the alternative that the supplier decides the timing and size of the deliveries. This agreement grants the supplier the full authority to manage inventories at his retailers'. This allows the supplier to act proactively and take responsibility for the inventory management of his regular retailers, instead of reacting to the orders placed by these retailers. In practice, implementing policies such as VMI has proven to considerably improve the overall performance of the supply network, see for example Lee and Seungjin (2008), Andersson et al. (2010) and Coelho et al. (2014). This dissertation focuses mainly on the single-warehouse, multiple-retailer (SWMR) system, in which a supplier serves a set of retailers from a single warehouse. In the first situation, we assume that all retailers face a deterministic, constant demand rate and in the second condition, we assume that all retailers consume the product at a stochastic stationary rate. The primary objective is to decide when and how many units to be delivered from the supplier to the warehouse and from the warehouse to retailers so as to minimize total transportation and inventory holding costs over the finite horizon without any shortages