Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

Holding costs under push or pull conditions - The impact of the Anchor Point

Holding costs are traditionally determined from the investment in physical stock during a cycle. An alternative approach instead derives holding costs from Net Present Value (NPV) functions. It is known that applying both frameworks to the same system can lead to different holding cost valuations, but little explanation has been offered. By introducing the Anchor Point in a model, this paper shows, for four different systems, that traditional holding cost models (implicitly) assume pull conditions, while current NPV approaches model push conditions. This explains in part the differences between the methods. It is shown that the Anchor Point concept allows the construction of NPV models under pull conditions, giving results in better correspondence with traditional models. The traditional framework is restricted to pull conditions and important considerations could be easily overlooked, leading to wrong valuations of holding costs. NPV seems superior as such considerations are automatically incorporated. The application to multi-echelon inventory systems provides interesting insights on the roles of echelon stocks and lead-times, and offers potential for future research.     

Coordination mechanisms for inventory control in three-echelon serial and distribution systems

This paper is concerned with the coordination of inventory control in three-echelon serial and distribution systems under decentralized control. All installations in these supply chains track echelon inventories. Under decentralized control the installations will decide upon base stock levels that minimize their own inventory costs. In general these levels do not coincide with the optimal base stock levels in the global optimum of the chain under centralized control. Hence, the total cost under decentralized control is larger than under centralized control. To remove this cost inefficiency, two simple coordination mechanisms are presented: one for serial systems and one for distribution systems. Both mechanisms are initiated by the most downstream installation(s). The upstream installation increases its base stock level while the downstream installation compensates the upstream one for the increase of costs and provides it with a part of its gain from coordination. It is shown that both coordination mechanisms result in the global optimum of the chain being the unique Nash equilibrium of the corresponding strategic game. Furthermore, all installations agree upon the use of these mechanisms because they result in lower costs per installation. The practical implementation of these mechanisms is discussed.     

A two-echelon inventory model with lost sales

This paper considers a single-item, two-echelon, continuous-review inventory model. A number of retailers have their stock replenished from a central warehouse. The warehouse in turn replenishes stock from an external supplier. The demand processes on the retailers are independent Poisson. Demand not met at a retailer is lost. The order quantity from each retailer on the warehouse and from the warehouse on the supplier takes the same fixed value Q, an exogenous variable determined by packaging and handling constraints. Retailer i follows a (Q, R_i) control policy. The warehouse operates an (SQ, (S − 1)Q) policy, with non-negative integer S. If the warehouse is in stock then the lead time for retailer i is the fixed transportation time L_i from the warehouse to that retailer. Otherwise retailer orders are met, after a delay, on a first-come first-served basis. The lead time on a warehouse order is fixed. Two further assumptions are made: that each retailer may only have one order outstanding at any time and that the transportation time from the warehouse to a retailer is not less than the warehouse lead time. The performance measures of interest are the average total stock in the system and the fraction of demand met in the retailers. Procedures for determining these performance measures and optimising the behaviour of the system are developed.     

Joint-optimization of inventory policies on a multi-product multi-echelon pharmaceutical system with batching and ordering constraints

This paper presents a methodology to find near-optimal joint inventory control policies for the real case of a one-warehouse, n-retailer distribution system of infusion solutions at a University Medical Center in France. We consider stochastic demand, batching and order-up-to level policies as well as aspects particular to the healthcare setting such as emergency deliveries, required service level rates and a new constraint on the ordering policy that fits best the hospital’s interests instead of abstract ordering costs. The system is modeled as a Markov chain with an objective to minimize the stock-on-hand value for the overall system. We provide the analytical structure of the model to show that the optimal reorder point of the policy at both echelons is easily derived from a simple probability calculation. We also show that the optimal policy at the care units is to set the order-up-to level one unit higher than the reorder point. We further demonstrate that optimizing the care units in isolation is optimal for the joint multi-echelon, n-retailer problem. A heuristic algorithm is presented to find the near-optimal order-up-to level of the policy of each product at the central pharmacy; all other policy parameters are guaranteed optimal via the structure provided by the model. Comparison of our methodology versus that currently in place at the hospital showed a reduction of approximately 45% in the stock-on-hand value while still respecting the service level requirements.     

A model for heuristic coordination of real life distribution inventory systems with lumpy demand

This paper presents an approximation model for optimizing reorder points in one-warehouse N-retailer inventory systems subject to highly variable lumpy demand. The motivation for this work stems from close cooperation with a supply chain management software company, Syncron International, and one of their customers, a global spare parts provider. The model heuristically coordinates the inventory system using a near optimal induced backorder cost at the central warehouse. This induced backorder cost captures the impact that a reorder point decision at the warehouse has on the retailers’ costs, and decomposes the multi-echelon problem into solving N + 1 single-echelon problems. The decomposition framework renders a flexible model that is computationally and conceptually simple enough to be implemented in practice.     

Newsvendor equations for optimal reorder levels of serial inventory systems with fixed batch sizes

We consider a stochastic serial inventory system with a given fixed batch size per stage and linear inventory holding and penalty costs. For this system, echelon stock (R,nQ) policies are known to be optimal. On the basis of new average costs formulas, we obtain newsvendor equations for the optimal reorder levels.     

A multi-product multi-echelon inventory control model with joint replenishment strategy

On the basis of analyzing the shortages of present studies on multi-echelon inventory control, and considering some restrictions, this paper applies the joint replenishment strategy into the inventory system and builds a multi-product multi-echelon inventory control model. Then, an algorithm designed by Genetic Algorithm (GA) is used for solving the model. Finally, we respectively simulate the model under three different ordering strategies. The simulation result shows that the established model and the algorithm designed by GA have obvious superiority on reducing the total cost of the multi-product multi-echelon inventory system. Moreover, it illustrates the feasibility and the effectiveness of the model and the GA method.     

A new revenue sharing mechanism for coordinating multi-echelon supply chains

A new type of revenue sharing (RS) contract mechanism for multi-echelon supply chains between the most downstream entity and all upstream entities is proposed. The new RS contract is analyzed in the linear supply chain setting facing stochastic demand. Advantages over mechanisms with RS contracts between all pairs of adjacent entities are discussed and demonstrated.     

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.