Effect of coordinated replenishment policies on quality

Coordinated replenishment is a supply chain policy that affects many operational performance measures, including cost, lead time, and quality. In this paper, we develop a mathematical model of a simplified supply chain in which conformance quality is one of the supplier's decision variables and both the supplier and its customer are trying to minimize expected annual cost. Our expected cost model includes the important quality costs (appraisal, prevention, internal failure, and external failure) as well as holding, set-up, and ordering costs. Our results indicate that coordination leads to a decline in total cost but that coordination does not necessarily lead to an improvement in quality. In other words, buyers who are using coordinated replenishment may be trading higher quality for lower cost.     

Stock Rationing in a Continuous Review Two-Echelon Inventory Model

In this paper we consider a 1-warehouse, N-retailer inventory system where demand occurs at all locations. We introduce an inventory model which allows us to set different service levels for retailers and direct customer demand at the warehouse. For each retailer a critical level is defined, such that a retailer replenishment order is delivered from warehouse stock if and only if the stock level exceeds this critical level. It is assumed that retailer replenishment orders, which are not satisfied from warehouse stock, are delivered directly from the outside supplier, instead of being backlogged. We present an analytical upper bound on the total cost of the system, and develop a heuristic method to optimize the policy parameters. Numerical experiments indicate that our technique provides a very close approximation of the exact cost. Also, we show that differentiating among the retailers and direct customer demand can yield significant cost reductions.     

退货成本不同承担方式下供应链最优服务水平的确定

讨论了销售剩余成本分担情况下,供应链最优周期服务水平和订货策略的优化问题;对多周期补货策略提出了"变周期向前改进"的动态优化法.分析表明:销售剩余的处理方式和剩余成本的分配因子,对于最优服务水平有重要的影响;基于成本分担的多周期补货策略在销售季节的大部分时期维持了较高而稳定的服务水平和订货量.     

Robust distribution planning for supplier-managed inventory agreements when demand rates and travel times are stationary

Supplier-managed inventory (SMI) is a partnering agreement between a supplier and his customers. Under this SMI agreement, inventory monitoring and ordering responsibilities are entirely transferred to the supplier. Subsequently, the supplier decides both the quantity and timing of his customer deliveries. The inventory routing problem is an underlying optimization model for SMI partnerships to cost-effectively coordinate and manage customer inventories and related replenishments logistics. This paper discusses the case where customer demand rates and travel times are stochastic but stationary, and proposes a version of the inventory routing optimization model that generates optimal robust distribution plans. The approach proposed to obtain and deploy these robust plans combines optimization and Monte Carlo simulation. Optimization is used to determine the robust distribution plan and simulation is used to fine-tune the plan's critical parameters such as replenishment cycle times and safety stock levels. Results of a simplified real-life case implementing the proposed optimization-simulation approach are shown and discussed in detail.     

Optimal retailer's ordering policies in the EOQ model under trade credit financing

The main purpose of this note is to modify the assumption of the trade credit policy in previously published results to reflect the real-life situations. All previously published models implicitly assumed that the supplier would offer the retailer a delay period, but the retailer would not offer the trade credit period to his/her customer. In most business transactions, this assumption is debatable. In this note, we assume that the retailer also adopts the trade credit policy to stimulate his/her customer demand to develop the retailer's replenishment model. Furthermore, we assume that the retailer's trade credit period offered by supplier M is not shorter than the customer's trade credit period offered by retailer N(M?N). Under these conditions, we model the retailer's inventory system as a cost minimization problem to determine the retailer's optimal ordering policies. Then a theorem is developed to determine efficiently the optimal ordering policies for the retailer. We deduce some previously published results of other researchers as special cases. Finally, numerical examples are given to illustrate the theorem obtained in this note.     

An EOQ model for deteriorating items under trade credits

In the classical inventory economic order quantity (or EOQ) model, it was assumed that the supplier is paid for the items immediately after the items are received. However, in practices, the supplier may simultaneously offer the customer: (1) a permissible delay in payments to attract new customers and increase sales, and (2) a cash discount to motivate faster payment and reduce credit expenses. In this paper, we provide the optimal policy for the customer to obtain its minimum cost when the supplier offers not only a permissible delay but also a cash discount. We first establish a proper model, and then characterize the optimal solution and provide an easy-to-use algorithm to find the optimal order quantity and replenishment time. Furthermore, we also compare the optimal order quantity under supplier credits to the classical economic order quantity. Finally, several numerical examples are given to illustrate the theoretical results.     

Retailer��s optimal sourcing strategy by using one major supplier and one emergent supplier

Fast-changing market demand, short product life cycle, and unpredictable events have been enforcing companies in a supply chain to respond to customers’ needs as quickly as possible. While many firms are still seeking a better inventory management within the general business environment, this paper develops an ordering decision support model within a business environment with more unpredictable events. To reduce the uncertainty, a retailer adopts a double sourcing policy with one major supplier and one emergent supplier. Through a two-period dynamic programming model formulation and the simulations based on design of experiments, we analyzed the effects of factors such as penalty cost, backup ratio, purchasing cost ratio, and demand correlation coefficient on retailer’s ordering policy and expected profit. Detailed sensitivity analysis is further conducted based on combinations of penalty cost and backup ratio. Results show that the use of an emergent supplier help increase the retailer’s expected profits. It not only increases the retailer’s upstream sourcing flexibility, but also increases the retailer’s service level with a lower inventory level. As penalty cost or backup ratio increases, the contribution of emergent supplier increases.     

A semi-Markov model with holdout transshipment policy and phase-type exponential lead time

In this paper, a semi-Markov decision model of a two-location inventory system with holdout transshipment policy is reviewed under the assumption of phase-type exponential replenishment lead time rather than exponential lead time. The phase-type exponential lead time more closely approximates fixed lead time as the number of phases increases. Unlike past research in this area which has concentrated on the simple transshipment policies of complete pooling or no pooling, the research presented in this paper endeavors to develop an understanding of a more general class of transshipment policy. In addition, we propose an effective method to approximate the dynamic holdout transshipment policy.     

Optimal ordering policies with convertible lead times

A firm receives orders that will be required at an uncertain time given by an Erlang distribution, and over time observes the associated independent exponential events. The firm, in turn, places orders at a linear cost from a supplier with fixed lead time l and has the option of converting (expediting) each order, at a cost, over a certain time interval after the order is originally placed. A converted order arrives l_e < l units of time after it is converted. We show that a threshold policy is optimal. Under such a policy the firm places an order after a certain number of exponential events have been observed. An order is converted the first time, if any, when the residual lead time exceeds a time threshold related to the number of exponential events realized since the order was placed.     

An Iterative Algorithm for a Multiple Finite-source Queueing Model with Dynamic Priority Scheduling

A multiple finite source queueing model with a single server and dynamic, non-preemptive priority service discipline is studied in this paper. The times the customers spend at the corresponding sources are exponentially distributed. The service times of the customers can follow exponential, Erlang or hyperexponential probability density function. By using results published earlier and an extension of mean value analysis, an iterative algorithm was developed to obtain approximate values of the mean waiting times in queues for the priority classes. The mean number of waiting customers and the server utilization of each class are obtained using the result of this algorithm and Little's formula. The algorithm is preferable to the earlier method, because it does not increase in complexity as the number of customer classes increases.     

On Optimality of a Class of Dynamic Myopic Policies for Continuous-Time Replenishment with Periodic Updates

This paper is motivated by inventory problems arising in supply chains characterized by continuous replenishment programs based on information exchanged (reviewed) only intermittently between a manufacturing system (supplier) and a customer (retailer). When the replenishment is once-per-period, rather than at any point of time, a well-known result is the optimality of the so-called myopic base-stock policy. We generalize the notion of the base-stock policy and study the optimality of the corresponding class of dynamic myopic policies. We identify a myopic policy and prove that although the replenishment rule is dynamic, this policy is optimal when the demands are stationary and the number of review periods tends to infinity.     

On the Bullwhip Avoidance Phase: The Synchronised Supply Chain

The aim of this paper is to analyse the operational response of a Synchronised Supply Chain (SSC). To do so, first a new mathematical model of a SSC is presented. An exhaustive Latin Square design of experiments is adopted in order to perform a boundary variation analysis of the main three parameters of the periodic review smoothing (S, R) order-up-to policy: i.e., lead time, demand smoothing forecasting factor, and proportional controller of the replenishment rule. The model is then evaluated under a variety of performance measures based on internal process benefits and customer benefits. The main results of the analysis are: (I) SSC responds to violent changes in demand by resolving bullwhip effect and by creating stability in inventories under different parameter settings and (II) in a SSC, long production–distribution lead times could significantly affect customer service level. Both results have important consequences for the design and operation of supply chains.     

On the value of customer information for an independent supplier in a continuous review inventory system

We consider the inventory control problem of an independent supplier in a continuous review system. The supplier faces demand from a single customer who in turn faces Poisson demand and follows a continuous review (R, Q) policy. If no information about the inventory levels at the customer is available, reviews and ordering are usually carried out by the supplier only at points in time when a customer demand occurs. It is common to apply an installation stock reorder point policy. However, as the demand faced by the supplier is not Markovian, this policy can be improved by allowing placement of orders at any point in time. We develop a time delay policy for the supplier, wherein the supplier waits until time t after occurrence of the customer demand to place his next order. If the next customer demand occurs before this time delay, then the supplier places an order immediately. We develop an algorithm to determine the optimal time delay policy. We then evaluate the value of information about the customer’s inventory level. Our numerical study shows that if the supplier were to use the optimal time delay policy instead of the installation stock policy then the value of the customer’s inventory information is not very significant.     

Service differentiation in spare parts inventory management

The contemporary after-sales market is of increasing importance. One of the features required by the market is to provide differentiated service levels to different groups of customers. We use critical levels as a means to offer differentiation. Critical level policies aim to exploit the differences in target service levels by inventory rationing. In our multi-item single-location spare parts inventory model, we aim to minimize the spare parts provisioning cost, that is inventory holding and transportation cost, under the condition that aggregate mean waiting time constraints for all customer groups are met. In a computational experiment and a case study with data from a company in the semiconductor supplier industry, we show that significant cost reductions can be obtained when critical level policies are used instead of base stock policies (ie policies without critical levels).     

Two-echelon inventory model for deteriorating items with credit period dependent demand including shortages under trade credit

In real life situation, it is observed that demand of an item depends on the length of the credit period offered by the retailer to his customers which has a positive impact on demand of an item. But the impact of credit period on demand has received a very little attention by researchers. Furthermore, by allowing shortages as backlogging, the impact on the cost from the decay of the products can be balanced out. A profitable decision policy between a supplier and the retailers can be characterized by an agreement on the permissible delay in payments. Recently, Jaggi et al. (Eur J Oper Res 190:130–135, 2008) have investigated the impact of credit linked demand on the retailer’s optimal replenishment policy. The objective of this study is to extend Jaggi et al. (Eur J Oper Res 190:130–135, 2008) model by incorporating deterioration and backlogging. That is, we formulate a two-echelon inventory model for deteriorating items with credit period dependent demand including shortages under two-level trade credit financing and determine the retailer’s optimal replenishment policy when both the supplier as well as the retailer offers the credit period to stimulate customer demand. Furthermore, we establish some useful theorems to characterize the optimal solution and provide an easy and useful computational algorithm with the help of computer code using the software Matlab 7.0 to determine the optimal shortage point, cycle length, ordering quantity and credit period. A numerical example is included to illustrate the solution procedure for the mathematical model developed. Finally, we implement sensitivity analysis of the optimal solution with respect to the major parameters of the system and obtain some important managerial insights.     

Modeling and analysis for determining optimal suppliers under stochastic lead times

The policy of simultaneously splitting replenishment orders among several suppliers has received considerable attention in the last few years and continues to attract the attention of researchers. In this paper, we develop a mathematical model which considers multiple-supplier single-item inventory systems. The item acquisition lead times of suppliers are random variables. Backorder is allowed and shortage cost is charged based on not only per unit in shortage but also per time unit. Continuous review (s,Q)$(s\text{,}Q)$ policy has been assumed. When the inventory level depletes to a reorder level, the total order is split among n suppliers. Since the suppliers have different characteristics, the quantity ordered to different suppliers may be different. The problem is to determine the reorder level and quantity ordered to each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost, and shortage cost, is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared with the models in the literature. According to our extensive experiments, the model developed in this paper is the best model in the literature which considers order splitting for n-supplier inventory systems since it is the nearest model to the real inventory system.     

Analysis of optimal opportunistic replenishment policies for inventory systems by using a (s,S) model with a maximum issue quantity restriction

The analysis of optimal inventory replenishment policies for items having lumpy demand patterns is difficult, and has not been studied extensively although these items constitute an appreciable portion of inventory populations in parts and supplies types of stockholdings. This paper studies the control of an inventory item when the demand is lumpy. A continuous review (s,S) policy with a maximum issue quantity restriction and with the possibility of opportunistic replenishment is proposed to avoid the stock of these items being depleted unduly when all the customer orders are satisfied from the available inventory and to reduce ordering cost by coordinating inventory replenishments. The nature of the customer demands is approximated by a compound Poisson distribution. When a customer order arrives, if the order size is greater than the maximum issue quantity w, the order is satisfied by placing a special replenishment order rather than from the available stock directly. In addition, if the current inventory position is equal to or below a critical level A when such an order arrives, an opportunistic replenishment order which combines the special replenishment order and the regular replenishment order will be placed, in order to satisfy the customer's demand and to bring the inventory position to S. In this paper, the properties of the cost function of such an inventory system with respect to the control parameters s, S and A are analysed in detail. An algorithm is developed to determine the global optimal values of the control parameters. Indeed, the incorporation of the maximum issue quantity and opportunistic replenishment into the (s,S) policy reduces the total operating cost of the inventory system.