Joint Replenishment Policies Research Articles

A joint replenishment production-inventory model as an MMAP[K]/PH[K]/1 queue

In this paper we analyze a continuous review finite capacity production-inventory system with two products in inventory. With stochastic order quantities and time between orders, the model reflects a supply chain that operates in an environment with high levels of volatility. The inventory is replenished using an independent order-up-to (s, S) policy or a can-order (s, c, S) joint replenishment policy in which the endogenously determined lead times drive the parameters of the replenishment policy. The production facility is modeled as a multi-type MMAP[K]/PH[K]/1 queue in which there are K possible inventory positions when the order is placed and the age process of the busy queue has matrix-exponential distribution. We characterize the system and determine the steady state distribution using matrix analytic methods. Using numerical methods we obtain the inventory parameters that minimize the total ordering and inventory related costs. We present numerical comparisons of independent and joint replenishment policies with varying lead times, order quantities, and cost reductions. We further demonstrate the interplay between the two products in terms of lead times, order quantities and costs.

The joint replenishment problem: Optimal policy and exact evaluation method

We propose a new method to evaluate any stationary joint replenishment policy under compound Poisson demand. The method makes use of an embedded Markov chain that only considers the state of the system after an order is placed. The resulting state space reduction allows exact analysis of instances that until now could only be evaluated using approximation procedures. In addition, the size of the state space is not affected if we include nonzero lead times, backlog, and lost sales. We characterize the optimal joint replenishment policy, and use these characteristics to develop a greedy-optimal algorithm that generalizes the can-order policy, a well-known family in the class of joint replenishment policies. We numerically show that this generalized can-order policy only marginally improves the best conventional can-order policy. For sizeable systems with multiple items, the latter can now be found using our exact embedded Markov-chain method. Finally, we use our method to improve and extend the well-known decomposition approach.

Optimal replenishment policy for multi-item probabilistic inventory model with all-units discount

In this paper, we develop a multi item inventory model for the retailer by considering all-units discount offered by the supplier. Demands in this model are assumed to be probabilistic following a Gamma distribution with certain values of shape and scale parameters. The aim of the model is to determine the optimal replenishment policy that minimize the total inventory cost. The total inventory cost was composed from the purchasing, ordering, handling or storing and shortage costs. All shortages are handled by backorder. We compare the individual and joint replenishment policies for the model and develop an algorithm to find the optimal replenishment policy. Numerical examples are given to give a better understanding of the model in comparing the individual and joint replenishment policies. We also perform sensitivity analysis by changing values of shape and scale parameters of the demand distribution to analyse the effects on the optimal solution.

Dual Sourcing and Joint Replenishment of Hospital Supplies

In response to increasing supply chain costs, hospitals are investing in new technology to improve inventory visibility and control at the point of use. This poses new inventory optimization opportunities and challenges for hospital management. The technology-enabled increased inventory visibility allows hospitals to implement more sophisticated inventory policies to reduce costs and improve availability. One such policy, implemented at a large Midwest hospital, is a dual-source hybrid inventory system that combines periodic and continuous order-placement epochs under a single-item setting, in which different items are treated independently. In this paper, we extend the dual-source hybrid policy to a two-item setting. We propose different joint replenishment policies that take advantage of increased inventory visibility to coordinate periodic and continuous replenishments across items. We develop a simulation-based search engine and test the benefits of these different policies under different parameter settings. We find that more benefits can be obtained using simple joint replenishment policies than are obtained using just the hybrid policy without coordinated replenishments.

Joint replenishment and credit policies under two levels of trade credit financing when demand and bad-debt loss depends upon credit period

In practice, a firm usually receives trade credit financing from its supplier on the purchase of inventory. Similarly, in order to meet competition and generate credit sales over and above cash sales, the firm also gives credit period to their customers. However, the decision of granting credit period may have a disintegrating effect on cash sales apart from generating new credit sales because some of the cash customers may switch to credit purchase. In addition, despite of the best credit granting policies and collection practices, the firm may incurs some amount of bad debt losses because a certain fraction of buyers will undoubtedly be unable to pay off their debt obligations and become bad debt loss to the firm. In this paper, using discounted cash flow (DCF) approach, a mathematical model is developed to jointly determine optimal inventory and credit policies under two levels of trade credit financing when demand and bad-debt losses are dependent on credit period. The objective of the model is to maximize the present value of firm?s net profit per unit time by jointly optimizing the replenishment interval and date-terms credit period. Numerical examples and sensitivity analysis are presented to illustrate the effectiveness of the proposed model, and the results are discussed.

Optimal Joint Replenishment and Transshipment Policies in a Multi-Period Inventory System with Lost Sales

Mismatch between supply and demand when the uncertainty of the demand is high and the supply lead time is relatively long, such as seasonal good markets, can result in high overstocking and understocking costs. In this paper we propose transshipment as a powerful mechanism to mitigate the mismatch between the supply and demand. We consider a finite horizon multi-period inventory system where in each period two retailers have the option to replenish their inventory from a supplier (if there is any supply) or via transshipment from the other retailer. Each retailer observes nonnegative stochastic demand with general distribution in each period and incurs overstocking/understocking costs as well as costs for replenishment and transshipment that may be time dependent. We study a stochastic control problem where the objective is to determine the optimal joint replenishment and transshipment policies so as to minimize the total expected cost over the season. We characterize the structure of the optimal policy and show that unlike the known order-up-to level inventory policy, the optimal ordering policy in each period is determined based on two switching curves. Similarly, the optimal transshipment policy is also identified by two switching curves. These four curves together partition the optimal joint ordering and transshipment polices to eight regions where in each region the optimal policy is an order-up-to-curve policy. We demonstrate that the structure of the optimal policy holds for any known sequence and combination of ordering and transshipment over time.

Optimal Joint Replenishment and Transshipment Policies in a Multi-Period Inventory System With Lost Sales

Mismatch between supply and demand when the uncertainty of the demand is high and the supply lead time is relatively long such as seasonal good markets can result in high overstocking and understocking costs. In this paper we propose proactive transshipment as a powerful mechanism to mitigate the mismatch between the supply and demand. We consider a finite horizon multi-period inventory system where in each period two retailers have the options to replenish their inventory from a supplier (if there is any supply) or via proactive transshipment from the other retailer. Each retailer observes non-negative stochastic demand with general distribution during the season and incurs overstocking/understocking costs as well as costs for replenishment and transshipment which may be time dependent. We study a stochastic control problem where the objective is to determine the optimal joint replenishment and proactive transshipment policies so as to minimize the total expected cost over the season. We characterize the structure of the optimal policy, and show that, unlike the known order-up-to level inventory policy, the optimal ordering policy in each period is determined based on two switching curves. Similarly, the optimal transshipment policy is also identified by two switching curves. These four curves together partitions the optimal joint ordering and transshipment polices to eight regions where in each region the optimal policy is an order-up-to-curve policy. We demonstrate that the structure of the optimal policy holds for any known sequence and combination of ordering and proactive transshipment over time. We also show that in the optimal policy retailers try to share the risk of the overstocking and understocking costs.

Coordinated inventory replenishment and outsourced transportation operations

We consider a one-warehouse N retailers supply chain with stochastic demand. Inventory is managed in-house whereas transportation is outsourced to a 3PL provider. We develop analytical expressions for the operating characteristics under both periodic and continuous joint replenishment policies. We identify the settings where a periodic review policy is comparable to a continuous review one. In our numerical test-bed, the periodic policy performed best in larger supply chains operating with larger trucks. We also observed that if the excess utilization charge is less than 25%, outsourcing becomes beneficial even if outsourcing cost is 25% more than the in-house fleet costs.

Optimal joint replenishment, delivery and inventory management policies for perishable products

In this paper we analyze the optimal joint decisions of when, how and how much to replenish customers with products of varying ages. We discuss the main features of the problem arising in the joint replenishment and delivery of perishable products, and we model them under general assumptions. We then solve the problem by means of an exact branch-and-cut algorithm, and we test its performance on a set of randomly generated instances. Our algorithm is capable of computing optimal solutions for instances with up to 30 customers, three periods, and a maximum age of two periods for the perishable product. For the unsolved instances the optimality gap is always small, less than 1.5% on average for instances with up to 50 customers. We also implement and compare two suboptimal selling priority policies with an optimized policy: always sell the oldest available items first to avoid spoilage, and always sell the fresher items first to increase revenue.

Joint pricing and replenishment policies for group-buying auction

Group-buying auction has become a popular marketing strategy in the last decade. In this paper, a stochastic model is developed for an inventory system subjects to price-sensitive demand from group-buying auctions. The model discussed here takes into account the costs of inventory, transportation, dispatching and re-order as well as the penalty cost of non-successful auctions. Since a new cycle begins whenever there is a replenishment of products, the long-run average profit can be obtained by using the renewal theory. Closed form solution of the optimal replenishment quantity is derived and an optimal unit selling price is then obtained.

Fixed-interval joint-replenishment policies for distribution systems with multiple retailers and stochastic demand

We consider a distribution system consisting of a central warehouse and a group of retailers facing independent stochastic demand. The retailers replenish from the warehouse, and the warehouse from an outside supplier with ample supply. Time is continuous. Most previous studies on inventory control policies for this system have considered stock-based batch-ordering policies. We develop a time-based joint-replenishment policy in this study. Let the warehouse set up a basic replenishment interval. The retailers are replenished through the warehouse in intervals that are integer multiples of the basic replenishment interval. No inventory is carried at the warehouse. We provide an exact evaluation of the long-term average system costs under the assumption that stock can be balanced among the retailers. The structural properties of the inventory system are characterized. We show that, although it is well known that stock-based inventory control policies dominate time-based inventory control policies at a single facility, this dominance does not hold for distribution systems with multiple retailers and stochastic demand. This is because the latter can provide a more efficient mechanism to streamline inventory flow and pool retailer demand, even though the former may be able to use more updated stock information to optimize system performance. The findings of the study provide insights about the key factors that drive the performance of a multiechelon inventory control system. (c) 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 637-651, 2013 (Less)

A three-echelon supply chain coordination with quantity discounts for multiple items

This study derives an integrated model for three-echelon supply chain (i.e. single-supplier, single-vendor and multi-retailer) to minimise the joint costs of all participants associated with holding costs, ordering costs, and purchasing costs. We particularly emphasise that quantity discounts and joint replenishment policies can be utilised as coordination mechanisms among all parties. In addition, a linearisation approach and mixed integer method are developed not only to obtain an executable integer solution for a finite planning horizon problem but also to simplify the conventional multiple-step procedure used in the quantity discount. The result indicates that the coordination and consolidation of orders can lead to the total cost reduction. Finally, a numerical example is given to illustrate the benefits of orders coordination and consolidation.

Reducing system nervousness in multi-product inventory systems

In many paractical multi-product systems a joint setup cost is incurred when at least one product is ordered and an individual setup cost for each product is ordered. In those cases joint replenishment policies will lead to lower cost compared to independent replenishment of each product. We consider periodic review multi-product systems with independent stochastic demand. The objective is to find a replenishment policy which minimizes the long-run average setup and holding cost per unit time subject to a service level constraint. We examine the behaviour of the system under a rolling-horizon approach. Solving a deterministic problem gives a replenishment schedule for next N periods. The decision for the first period in the deterministic problem is implemented in the stochastic system. Due to the stochastic demand the actual sizes and timing will be different, referred to as system nervousness. We propose a procedure to adjust this decision in order to reduce the system nervousness. Simulation experiments show cost reductions between 2% and 8% and cost performance comparable with can-order strategies.

Separate vs. joint replenishment policies with maximum storage requirement costs

Multi-item inventory problems give rise to the possibility of time-phasing the replenishments of different items over the inventory cycle. Such a policy reduces the peak storage requirement, compared to a policy of simultaneous replenishment. This, in turn, increases the amount of warehouse space which is permanently available for leasing throughout the cycle. However, where cost savings may be achieved through combining setups of different items, as in the well known joint replenishment problem, such a time-phasing policy may increase total setup costs. This paper considers the two item joint replenishment problem, where a cost (equivalent to the opportunity cost of warehouse space) attaches to the peak storage requirement which occurs within the inventory cycle. Existing joint replenishment models do not consider such costs, but their consideration suggests that joint replenishment is not always optimal. We analyze possible policies under both joint and separate replenishment, and provide optimal closed form solutions. A numerical example to illustrate the tradeoff between joint and separate replenishment is provided.