Reducing the mean supply delay of spare parts using lateral transshipments policies

Lateral transshipment has been studied lately as a promising policy for increasing the performances of multi-echelon spare parts inventory system. By lateral transshipment spare parts can be moved from one location with excess inventory to another location, at the same echelon, in shortage, with the aim of reducing supply delays of spare parts. This paper will examine the relative effectiveness of two lateral shipments approaches in reducing the mean supply delay (MSD) of a non-repairable item, with respect to a classical policy of no lateral shipments. A simulation model of a two echelon supply network has been implemented and an experiment has been performed by varying different parameters of the supply network, such as the number of warehouses (locations at the lower echelon), the supply lead time from the central depot, the spare parts demand uncertainty, and the size variability of the warehouses. Results show appreciable reductions of MSD when lateral shipments are allowed with respect to the classical policy, in almost every network configuration.     

A network approach to modeling the multi-echelon spare-part inventory system with backorders and interval-valued demand

A multi-echelon inventory system implies the existence of a hierarchy of stocking locations, and the dependence and interaction between them. We consider a multi-echelon, spare-part inventory management problem with outsourcing and backordering. The problem is characterized by deterministic repair time/cost, and supply and demand that lie within prescribed intervals and that vary over time. The objective is to minimize the total inventory and transportation costs. We develop a network model for problem analysis and present a network flow algorithm for solving the problem. We prove that the Wagner-Whitin property, known for the lot-sizing problem, can be extended to the spare-part inventory management problem under study.     

Modified critical fractile approach for a class of partial postponement problems

This paper studies a single period partial postponement problem, which is motivated by an inventory planning problem encountered in Reebok NFL replica jersey supply chain. We consider a group of regular products each facing a random demand. There are two stocking options. One is to procure the regular products. The other is to stock a common component which can be customized later to any one of the regular products, after demand realization.We obtain an insightful interpretation of the optimality conditions for this class of problems, and use it to obtain rules of thumb that practitioners can incorporate into their inventory models to determine the stocking levels to minimize the supply chain cost. Instead of proposing a numerical procedure to obtain the optimal solution, we propose an adaptation of the classical critical fractile approach for this class of partial postponement problem. The closed-form formula obtained are surprisingly effective. Our numerical results suggest that this simple approach to inventory planning often comes close to the performance of the optimal solution obtained from numerical method.     

The effects of emission trading on production and inventories in the Arrow–Karlin model

The paper deals with the effect of introduction of tradable permits on the production–inventory strategy of a firm. It is assumed that the firm will minimize its costs. The cost function consists of linear holding and convex production costs. After introducing emission trading, the cost function will contain a linear emission procurement/selling cost. We will compare the optimal production–inventory strategy before tradable permits and thereafter. The mathematical investigation is based on the well-known dynamic Arrow–Karlin model.     

Optimal production–inventory strategies for a HMMS-type reverse logistics system

The aim of the paper is to find optimal inventory policies in a reverse logistics system with special structure. It is assumed that demand is a known continuous function in a given planning horizon and return rate of used items is a given function. There is a constant delay between the using and return process. We investigate two stores. The demand is satisfied from the first store, where the manufactured and remanufactured items are stored. The returned products are collected in the second store and then remanufactured or disposed. The costs of this system consist of the quadratic holding costs for these two stores and the quadratic manufacturing, remanufacturing and disposal costs.The model is represented as an optimal control problem with two state variables (inventory status in the first and second store) and with three control variables (rate of manufacturing, remanufacturing and disposal). The objective is to minimize the sum of the quadratic deviation from described inventory levels in stores and from described manufacturing, remanufacturing and disposal rates. In this form, the model can be considered as a generalization of the well-known Holt et al. (Planning Production, Inventories, and Work Forces, Prentice-Hall, Englewood Cliffs, NJ, 1960) model with two warehouses. After solving the problem, we give some numerical examples to represent the optimal path in dependence of the demand rates.     

Coordinating a one-warehouse N-retailer distribution system under retailer-reporting

We consider a distribution system consisting of a System Administrator (SA) and N retailers managed under dynamic allocation and static routing policies. We study the system under two scenarios: (a) the up-to-date information scenario, under which the SA has access to the inventory levels at the retailers in real time and makes the replenishment and allocation decisions based on these information, aiming to minimize total supply chain cost; (b) the retailer-reporting scenario, under which the SA makes the replenishment and allocation decisions based on the information reported by the retailers. Under the retailer-reporting scenario, the retailers compete against each other by reporting their inventory levels falsely to get the desired allocations, which minimize the retailers’ expected cost. For N=2 retailers, we show that, in general, reporting truthfully does not minimize either retailer's expected cost/cycle over their respective replenishment/allocation cycles, and that the sum of the retailers' expected cost/cycle is strictly greater than in the up-to-date information scenario. We then show that by including a particular transfer-payment between the two retailers, truth-telling is a Bayesian equilibrium, and that the same system expected cost/period as in up-to-date information scenario can be achieved.     

Evaluation of two simple extreme transshipment strategies

We consider an organization that has more than one outlet (retailer or regional warehouse) where stock is held to meet customer demands. In such a situation, transshipments can be used to improve customer service and/or reduce the aggregate stock required. Unfortunately, the determination of an optimal transshipment policy (i.e. when to transship and how much) is a complex mathematical problem. However, in earlier research the authors observed that choosing the better of two extreme policies leads to performance that is nearly as good as a more complex analysis that takes account of the future impact of a transshipment on the cost at the location sending the shipment. These extreme policies are (i) never transship and (ii) always transship when there is a shortage at one location and stock available at another. In this paper, for the case of two stocking points, we develop an analytical approach for approximately estimating the total expected costs (carrying, replenishment, transshipments and lost sales) of these two policies. This provides a mechanism for choosing between the two policies for any given set of problem characteristics. The results of a numerical experiment are shown.     

Integer-ratio policies for distribution/inventory systems

We study a multistage distribution/inventory system with a central warehouse and N retailers. Customer demand arrives at each retailer at a constant rate. The retailers replenish their inventories from the warehouse, which in turn orders from an outside supplier. It is assumed that shortages are not allowed and lead times are negligible. The goal is to determine policies which minimize the overall cost in the system, that is, the sum of the costs at each facility consisting of a fixed charge per order and a holding unit cost. We propose a heuristic procedure to compute near-optimal policies. Computational results on several randomly generated problems are reported.     

Coordinated supply chain scheduling

A mixed integer programming approach is proposed for a long-term, integrated scheduling of material manufacturing, material supply and product assembly in a customer driven supply chain. The supply chain consists of three distinct stages: manufacturer/supplier of product-specific materials (parts), producer where finished products are assembled according to customer orders and a set of customers who generate final demand for the products. The manufacturing stage consists of identical production lines in parallel and the producer stage is a flexible assembly line. The overall problem is how to coordinate manufacturing and supply of parts and assembly of products such that the total supply chain inventory holding cost and the production line start-up and parts shipping costs are minimized. A monolithic approach, where the manufacturing, supply and assembly schedules are determined simultaneously, is compared with a hierarchical approach. Numerical examples modeled after a real-world integrated scheduling in a customer driven supply chain in the electronics industry are presented and some computational results are reported.     

A serial mixed produce-to-order and produce-in-advance inventory model with multiple retailers

We formulate a general mixed produce-to-order and produce-in-advance inventory model having multiple stocking echelons and multiple retailers. We show that the problem to find an optimal inventory policy for such a model with a uniform or a normal demand distribution can be reduced to a general constrained optimization problem.     

Economic lot-sizing and dynamic quantity competition

We study a problem of dynamic quantity competition in continuous time with two competing retailers facing different replenishment cost structures. Retailer 1 faces fixed ordering costs and variable procurement costs and all inventory kept in stock is subject to holding costs. Retailer 2 only faces variable procurement costs. Both retailers are allowed to change their sales quantities dynamically over time. Following the structure of the economic order quantity (EOQ) model, retailer 1 places replenishment orders in batches and retailer 2 follows a just-in-time (JIT) policy. The objective of both retailers is to maximize their individual average profit anticipating the competitor's replenishment and output decisions. The problem is solved by a two-stage hierarchical optimization approach using backwards induction. The second-stage model is a differential game in output quantities between the two retailers for a given cycle length. At the first stage, the replenishment policy is determined. We prove the existence of a unique optimal solution and derive an open-loop Nash equilibrium. We show that both retailers follow contrary output strategies over the order cycle. The EOQ retailer, driven by inventory holding costs, decreases his market share whereas the output of the JIT retailer increases. Moreover, depending on the cost structure, the EOQ retailer might partially be a monopolist. At the first stage, the EOQ retailer determines the cycle length, anticipating the optimal output trajectories at the second stage.     

Simultaneous control of production, repair/replacement and preventive maintenance of deteriorating manufacturing systems

This paper presents a method to find the optimal production, repair/replacement and preventive maintenance policies for a degraded manufacturing system. The system is subject to random machine failures and repairs. The status of the system is deemed to degrade with repair activities. When a failure occurs, the machine is either repaired or replaced, and a replacement action renews the machine, while a repair action brings it to a degraded operational state, with the next repair time increasing as the number of repairs increases as well. A preventive maintenance action is considered in order to improve the reliability of the machine, thereby reducing the amount of disruptions caused by machine failures. The decision variables are the production rate, the preventive maintenance rate and the repair/replacement switching policy upon machine failure. The objective of the study is to find the decision variables that minimize the overall cost, including repair, replacement, preventive maintenance, inventory holding and backlog costs over an infinite planning horizon. The proposed model is based on a semi-Markov decision process, and the stochastic dynamic programming method is used to obtain the optimality conditions. A numerical example is given to illustrate the proposed model, and a sensitivity analysis is considered in order to confirm the structure of the control policy and to illustrate the usefulness of the proposed approach.     

Inventory control in a two-echelon dual-channel supply chain with setup of production and delivery

This paper considers a two-echelon dual-channel supply chain model with setup of production and delivery and develops a new inventory control policy for the supply chain. Previously, a two-echelon supply chain model without setup of production and delivery is considered and a one-for-one inventory control policy is applied to the supply chain. In the inventory control policy, production is stopped when the warehouse inventory reaches the upper limit and is started again immediately after the inventory drops below the limit. Moreover, delivery to the retailer is stopped when the store inventory reaches the upper limit and is started again immediately after the inventory drops below the limit. The total cost that consists of inventory holding costs and lost sales cost is considered, and setup costs are not considered in the total cost. Once setup costs are introduced, the one-for-one inventory control policy is no longer appropriate. Then, this paper develops a new control policy for the two-echelon dual-channel supply chain with setup of production and delivery. As performance measure, the total cost that consists of inventory holding costs, lost sales cost, and production and delivery setup costs is considered, and the total cost calculated on the basis of Markov analysis demonstrates the effectiveness of the proposed control policy.     

Optimizing service-level and relevant cost for a stochastic multi-item cyclic production system

A multi-item make-to-order production system in a stochastic environment is analyzed. Assuming a common cycle production approach, the impact of safety stock, cycle time, demand, processing time and setup time on service-level and total relevant cost (holding, setup and backorder cost) is determined. To illustrate this relationship a trajectory for the service-level with respect to the relevant cost (holding and setup) is presented. Furthermore algorithms to calculate the cycle time which leads to maximum service-level at constant safety stock and to calculate the pair cycle time and safety stock which minimize total relevant cost are introduced.     

电力企业备品备件储备管理模式的新思考

针对电力企业当前的备品备件管理模式下存在管理难、利用率不高和资金占用大等问题,提出备品备件的联合储备、供应商管理库存储备和联合虚拟储备等新型模式,介绍了具体的储备方式,并展望了在电力企业的应用前景。     

A simple recovery strategy for economic lot scheduling problem: A two-product case

We examine strategies for recovering from machine breakdown or other forms of interruption in the Economic Lot Scheduling Problem and propose simple decision rules for recovery. Instead of considering inventory being held after production, we consider the scenario when work-in-progress or raw material arrives at a constant rate and the objective is to minimize the holding and set-up cost at the production facilities. This is mainly motivated by the use of third party logistic provider for storage and distribution of finished products in which the backorder and the associated cost may no longer be an important consideration. We first present the basic model under consideration. A probabilistic characterization of a general condition in which recovery to the original schedule is feasible is then presented. A special case of this result is given and discussed in the context of machine availability and utilization. We then focus on a two-product case and derive the optimal decision rules. It is shown that the resultant rules are independent of the duration and frequency of breakdown. Finally, a numerical analysis demonstrating the effectiveness of the proposed rules is presented.     

A heuristic algorithm for a multi-product dynamic lot-sizing and shipping problem

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) placed in a period is immediately shipped by some containers in the period and the total freight cost is proportional to the number of containers used. It is also assumed that backlogging is not allowed. The objective of this study is to simultaneously determine the lot-sizes and the transportation policy that minimizes the total costs, which consist of production cost, inventory holding cost, and freight cost. Because this problem is NP-hard, a heuristic algorithm with an adjustment mechanism is proposed based on the optimal solution properties. The computational results from a set of simulation experiment are also presented.     

Production capacity planning for multiple products under uncertain demand conditions

This study chiefly deliberates issues regarding capacity allocation for multiple products. When producing multiple products, a manufacturer needs to allocate a favorable production quantity to each product under conditions of uncertain demand since the excess or shortage of a product will in turn cause the loss of profit. The proposed model and the corresponding algorithm in this study are used to find out the optimal capacity allocation under the given probability density function of specific demands and to effectively allocate limited capacity to multiple products with an aim to maximize profit. Finally, the numerical example suggests that the marginal profit, the inventory holding cost, the shortage cost, the loss of excess production, and market demands should be considered in an effort to discover an optimal capacity allocation with regard to multiple products.     

Production planning and inventory allocation of a single-product assemble-to-order system with failure-prone machines

We consider the optimal production and inventory allocation of a single-product assemble-to-order system with multiple demand classes and lost sales. Each component is replenished by a dedicated machine that is subjected to unpredictable breakdowns. We find that the machine state not only influences the production and allocation decisions on its own component but also influences the decisions on the other components. Specifically, the optimal component production policy is a base-stock policy with the base-stock level non-decreasing in the inventory levels of the other components and the states of the other machines. The optimal component allocation policy is a rationing policy with the rationing level non-increasing in the inventory levels of the other components, the states of the other machines, and its own machine state. We use an exponential distribution to approximate the distribution of the total processing times and propose two heuristic policies to address the production and allocation decisions. The importance of taking machine failures into consideration is revealed through computational experiments.     

Channel coordination with the newsvendor model using asymmetric information

In this paper, after surveying short-term two-echelon supply channel coordination methods, we present an extended version of the newsvendor model in which the supplier has to fulfil all demand of the customer, even if this calls for an additional setup of production. Given uncertain demand forecast, the solution is an optimal production quantity that minimises the expected total cost including setup, inventory holding and obsolete inventory costs. Then, the model is studied in a decentralised setting where the customer has private information about the demand forecast, while the supplier knows the various cost factors. We suggest such a coordination protocol and payment scheme that provides both partners the right incentive for minimising the total cost: the customer is interested in sharing her unbiased demand forecast and uncertainty, while the supplier's rational decision concurs with the overall optimum. Hence, local decisions based on asymmetric information coordinate the channel in the global sense. The results are also demonstrated by taking some real-life test cases from an industrial study that motivated our work.