Luxembourg Centre for Logistics and Supply Chain Management

We consider the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster emergency' supply source. Unsatisfied demand is backordered and ordering decisions are made periodically. The optimal control policy for this system is known to be complex. For this reason we study a type of base-stock policy known as the dual-index policy (DIP) as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their corresponding order-up-to-levels. Previous work on this policy assumes deterministic lead times and uses simulation to find the optimal order-up-to levels. We provide an alternate proof for the result that separates the optimization of the DIP in two one-dimensional problems. An insight from this proof allows us to generalize the model to accommodate stochastic regular lead times and provide an approximate evaluation method based on limiting results so that optimization can be done without simulation. An extensive numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead times.

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 use 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 show that it is useful to decrease upstream stock levels. In cases with high demand uncertainty, high backlogging cost or long lead times, we conclude that dual-sourcing can lead to significant savings.

We consider the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster 'emergency' supply source. Unsatisfied demand is backordered and ordering decisions are made periodically. The optimal control policy for this type of system is known to be complex. For this reason we study a type of base-stock policy known as the Dual-Index policy as control mechanism for this inventory system. under this policy ordering decisions are based on a regular and an emergency inventory position and their order-up-to-levels. In each period first an order is placed with the emergency supplier so that the emergency inventory position (onhand stock + outstanding orders arriving within the emergency lead time - backorders) meets its order-up-to-level. Next a regular order is placed to raise the regular inventory position (on-hand stock + all outstanding orders - backorders) to its order-up-to-level. Previous work on this type of policy assumes deterministic lead times and uses simulation to find the optimal order up to levels. We extend the policy to accommodate stochastic regular lead times and provide an approximate evaluation method so that optimization can be done without simulation. A numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead-times. We also give managerial insights into the use of the model with deterministic lead-time, when in fact lead times are stochastic.

This article considers the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster “emergency” supply source. Unsatisfied demand is backordered and ordering decisions are made periodically. The optimal control policy for this system is known to be complex. For this reason a type of base-stock policy known as the Dual-Index Policy (DIP) is used as the as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their corresponding order-up-to levels. Previous work on this policy assumes deterministic lead times and uses simulation to find the optimal order-up-to levels. This article provides an alternate proof for the result that separates the optimization of the DIP in two one-dimensional problems. An insight from this proof allows the model to be generalized to accommodate stochastic regular lead times and provide an approximate evaluation method based on limiting results so that optimization can be done without simulation. An extensive numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead times.

We consider a single inventory location where multiple types of repairable spare parts are kept to service several different fleets of assets. Demand for each part is modeled by a Markov modulated Poisson process (MMPP). Each fleet has a target for the maximum expected mean number of assets down for lack of a spare part. The inventory manager can meet this target by stocking repairables and by expediting the repair of parts. Expedited repairs have a shorter lead time. There are multiple  repair shops (or departments) that handle the repair of parts and the mean number of expedited repairs that can be requested per time unit is constrained per repair shop. A dual-index policy makes stocking and expediting decisions that depend on demand fluctuations for each spare part type. We formulate the above problem as a non-linear non-convex integer programming problem and provide an algorithm based on column generation to compute feasible solutions and tight lower bounds. We show how to use the MMPP to model demand fluctuations in this and other settings, including a moment fitting algorithm. We quantify the value of lead time
flexibility and show that effective use of this flexibility can yield cost reductions of around 25%.

We consider the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster 'emergency' supply source. Unsatised demand is backordered and ordering decisions are made periodically. The optimal control policy for this system is known to be complex. For this reason we study a type of base-stock policy known as the dual-index policy (DIP) as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their corresponding order-up-to-levels. Previous work on this policy assumes deterministic lead times and uses simulation to nd the optimal order-up-to levels. We provide an alternate proof for the result that separates the optimization of the DIP in two one-dimensional problems. An insight from this proof allows us to generalize the model to accommodate stochastic regular lead times and provide...