A simulation optimization approach for a two-echelon inventory system with service level constraints

In this paper, we present a simulation optimization algorithm for solving the two-echelon constrained inventory problem. The goal is to determine the optimal setting of stocking levels to minimize the total inventory investment costs while satisfying the expected response time targets for each field depot. The proposed algorithm is more adaptive than ordinary optimization algorithms, and can be applied to any multi-item multi-echelon inventory system, where the cost structure and service level function resemble what we assume. Empirical studies are performed to compare the efficiency of the proposed algorithms with other existing simulation algorithms.     

A solution approach to the inventory routing problem in a three-level distribution system

We consider the infinite horizon inventory routing problem in a three-level distribution system with a vendor, a warehouse and multiple geographically dispersed retailers. In this problem, each retailer faces a demand at a deterministic, retailer-specific rate for a single product. The demand of each retailer is replenished either from the vendor through the warehouse or directly from the vendor. Inventories are kept at both the retailers and the warehouse. The objective is to determine a combined transportation (routing) and inventory strategy minimizing a long-run average system-wide cost while meeting the demand of each retailer without shortage. We present a decomposition solution approach based on a fixed partition policy where the retailers are partitioned into disjoint and collectively exhaustive sets and each set of retailers is served on a separate route. Given a fixed partition, the original problem is decomposed into three sub-problems. Efficient algorithms are developed for the sub-problems by exploring important properties of their optimal solutions. A genetic algorithm is proposed to find a near-optimal fixed partition for the problem. Computational results show the performance of the solution approach.     

Product allocation to different types of distribution center in retail logistics networks

We consider the problem of assigning stockkeeping units to distribution centers (DCs) belonging to different DC types of a retail network, e.g., central, regional, and local DCs. The problem is motivated by the real situation of a retail company and solved by an MIP solution approach. The MIP model reflects the interdependencies between inbound transportation, outbound transportation and instore logistics as well as capital tied up in inventories and differences in picking costs between the warehouses. A novel solution approach is developed and applied to a real-life case of a leading European grocery retail chain. The application of the new approach results in cost savings of 6% of total operational costs compared to the present assignment. These savings amount to several million euros per year. In-depth analyses of the results and sensitivity analyses provide insights into the solution structure and the major related issues.     

A normal approximation model for safety stock optimization in a two-echelon distribution system

This paper presents an approximation model for the retailer replenishment lead-times in a two-echelon distribution system, and discusses its implementation for safety stock optimization in a one-warehouse and N-identical retailers system. The model assumes normality of demand and nominal lead times. It takes into account not only the averages of these parameters but also their variances. This approximation model is first tested on a two-echelon, one-warehouse and N-identical retailers system using discrete event simulation. It is then applied to optimize the safety stock in a two-echelon distribution system of a European market leader in the production and distribution of air conditioning equipment. Results of this implementation are analysed and discussed in detail.     

An inventory system with two suppliers and default risk

This paper considers the problem of joint replenishment and pricing for a single product with two suppliers and supply disruption. Our objective is to maximize the total profit by choosing an appropriate replenishment and pricing policy. We not only obtain that the form of the optimal policy has a (s,S,p,σ,Σ)-type, but also analyze how supply disruption affects the profit function and the optimal policy.     

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.     

Interval availability analysis of a two-echelon,multi-item system

In this paper we analyze the interval availability of a two-echelon, multi-item spare part inventory system. We consider a scenario inspired by a situation that we encountered at Thales Netherlands, a manufacturer of naval sensors and naval command and control systems. Modeling the complete system as a Markov chain we analyze the interval availability and we compute in closed and exact form the expectation and the variance of the availability during a finite time interval [0, T]. We use these characteristics to approximate the survival function using a Beta distribution, together with the probability that the interval availability is equal to one. Comparison of our approximation with simulation shows excellent accuracy, especially for points of the distribution function below the mean value. The latter points are practically most relevant.     

Analysis of a two-echelon inventory system with two supply modes

In this paper, we consider a serial two-echelon periodic review inventory system with two supply modes at the most upstream stock point. As control policy for this system, we propose a natural extension of the dual-index policy, which has three base-stock levels. We consider the minimization of long run average inventory holding, backlogging, and both per unit and fixed emergency ordering costs. We provide nested newsboy characterizations for two of the three base-stock levels involved and show a separability result for the difference with the remaining base-stock level. We extend results for the single-echelon system to efficiently approximate the distributions of random variables involved in the newsboy equations and find an asymptotically correct approximation for both the per unit and fixed emergency ordering costs. Based on these results, we provide an algorithm for setting base-stock levels in a computationally efficient manner. In a numerical study, we investigate the value of dual-sourcing in supply chains and illustrate that dual-sourcing can lead to significant cost savings in cases with high demand uncertainty, high backlogging cost or long lead times.     

Inventory control as a discrete system control for the fixed-order quantity system

This paper shows how to model a problem to find optimal number of replenishments in the fixed-order quantity system as a basic problem of optimal control of the discrete system. The decision environment is deterministic and the time horizon is finite. A discrete system consists of the law of dynamics, control domain and performance criterion. It is primarily a simulation model of the inventory dynamics, but the performance criterion enables various order strategies to be compared. The dynamics of state variables depends on the inflow and outflow rates. This paper explicitly defines flow regulators for the four patterns of the inventory: discrete inflow – continuous/discrete outflow and continuous inflow – continuous/discrete outflow. It has been discussed how to use suggested model for variants of the fixed-order quantity system as the scenarios of the model. To find the optimal process, the simulation-based optimization is used.     

A continuous approximation procedure for determining inventory distribution schemas within supply chains

This paper presents an integrated inventory distribution optimization model that simultaneously incorporates the issues of location, production, inventory, and transportation within a supply chain. The objective is to determine the optimal number and size of shipments under varying but commonly practiced production and shipping scenarios. A continuous approximation procedure is proposed to determine the optimal number and size of shipments. Three production and shipping scenarios are investigated and closed form expressions for the optimal number of shipments for each scenario are obtained. A numerical example is presented to demonstrate the usefulness of the model.     

Uniform distribution of inventory positions in two-echelon periodic review systems with batch-ordering policies and interdependent demands

We consider a two-level inventory system in which there are one supplier and multiple retailers. The retailers face stochastic, interdependent customer demands. Each location employs a periodic-review (R,nQ), or lot-size reorder point, inventory policy. We show that each location's inventory positions are stationary and the stationary distribution is uniform and independent of any other's.     

Joint optimization of price and order quantity with shortages for a two-warehouse system

In developing the best strategy for real-world applications, the vendor must have some knowledge of the buyers’ behavior such as response to shortages and price increases. Using this knowledge, he can develop a policy that will ensure the largest net profit. Considering the fact, a two-warehousing inventory model has been developed where the demand is price-sensitive under the bulk release rule. Stockouts are allowed and are fully backlogged. Moreover, the transportation cost is taken to be dependent on the transported units. The model jointly optimizes the selling price and the order quantity by maximizing the system profit. Results have been validated with the help of a numerical example.      

Replenishment routing problems between a single supplier and multiple retailers with direct delivery

We consider the replenishment routing problems of one supplier who can replenish only one of multiple retailers per period, while different retailers need different periodical replenishment. For simple cases satisfying certain conditions, we obtain the simple routing by which the supplier can replenish each retailer periodically so that shortage will not occur. For complicated cases, using number theory, especially the Chinese remainder theorem, we present an algorithm to calculate a feasible routing so that the supplier can replenish the selected retailers on the selected periods without shortages.     

On two-echelon inventory systems with Poisson demand and lost sales

We consider a two-echelon, continuous review inventory system under Poisson demand and a one-for-one replenishment policy. Demand is lost if no items are available at the local warehouse, the central depot, or in the pipeline in between. We give a simple, fast and accurate approach to approximate the service levels in this system. In contrast to other methods, we do not need an iterative analysis scheme. Our method works very well for a broad set of cases, with deviations to simulation below 0.1% on average and below 0.36% for 95% of all test instances.     

Retail replenishment models with display-space elastic demand

We study a single store multi-product inventory problem in which product sales are a composite function of shelf space. Since sales tend to deplete the amount of product on display, the effective shelf space assigned to the product diminishes with time unless replenishment occurs. We consider the problem of optimal replenishment times under these conditions. We assume a linear dependence of sales rate to effective shelf space in all our analysis. We present exact and approximate solutions for the single product and multi-product cases. For the single product case, we study the effect of space elasticity, cross elasticity and empty space elasticity on the optimal replenishment period. For the multi-product case we present a computationally attractive method using matrix exponentials and develop error bounds for this method.     

Comparing improvement strategies for inventory inaccuracy in a two-echelon supply chain

Classical inventory theory often assumes no discrepancies between recorded inventory and actual inventory. However, inventory records are usually inaccurate due to many reasons in practice. For example, inventory shrinkage refers to the difference between booked inventory that a company should have as a result of its sales, purchasing, and manufacturing processes and actual inventory that it has on hand. This paper concerns the impact of inventory shrinkage to a supply chain and investigates different strategies to deal with inventory shrinkage. We consider a single-period two-echelon supply chain consisting of a Stackelberg manufacturer and a retailer whose inventory is subject to shrinkage errors. Our analysis is based on a single-period newsvendor model and considers the following cases of order decisions: (a) the retailer ignores the inventory errors; (b) the retailer estimates the errors; (c) the retailer shares the inventory error information with the manufacturer; and (d) RFID technology is used to reduce or eliminate the errors. The first case is the base strategy and a common practice for many supply chains, the other two represent certain non-technological strategies of the retailer when dealing with inventory inaccuracy, and the last one represents a technology improvement strategy by the manufacturer to reduce or eliminate inventory shrinkage errors. We compare these improvement strategies and derive critical tag price for RFID implementation as a technological remedy for the inventory inaccuracy problem. Conditions for the profitability of RFID adoption are discussed.     

A production-inventory model with probabilistic deterioration in two-echelon supply chain management

In this study, a production-inventory model is developed for a deteriorating item in a two-echelon supply chain management (SCM). An algebraical approach is applied to find the minimum cost related to this entire SCM. We consider three types of continuous probabilistic deterioration function to find the associated cost. The purpose of this study is to obtain the minimum cost with integer number of deliveries and optimum lotsize for the three different models. Some numerical examples, sensitivity analysis and graphical representation are given to illustrate the model. A numerical comparison between the three models is also given.     

Efficient computation of time-based customer service levels in a multi-item, multi-echelon supply chain: A practical approach for inventory optimization

Time-based item fill rates, or “channel” fill rates, are the building blocks needed to evaluate steady-state compliance with time-based customer service agreements. Exact computation of channel fill rates is both difficult and time-consuming, yet their accurate assessment is essential for system-wide inventory optimization. We describe and validate a practical method for computing channel fill rates in a multi-item, multi-echelon service parts distribution system. A simulation study is presented which shows that, in a three-echelon setting, our estimation errors are very small over a wide range of base stock level vectors. A more accurate, though less efficient, approximation method is also evaluated for comparison.     

An algorithm for repairable item inventory system with depot spares and general repair time distribution

We consider the problem of determining the initial spare inventory level for a multi-echelon repairable item inventory system. We extend the previous results to the system, which has an inventory at the central depot as well as at bases and with a general repair time distribution. We propose an algorithm which finds spare inventory level to minimize the total expected cost and simultaneously to satisfy a specified minimum service rate. Extensive computational experiments show that the algorithm is accurate and efficient.