Determination of an order-up-to policy in the stochastic economic lot scheduling model

We consider a production–inventory problem with compound renewal item demand. The model consists of stockpoints, one for each item, controlled according to (R,S)-policies and one machine which replenishes them. The replenishment orders are produced with a fixed rate on the machine with significant setup times and costs, which are stochastic and sequence dependent. The time between the release and the production of the replenishment order is called the waiting time. We develop analytical approximations for the first two moments of this waiting time, the order-up-to levels and the average physical inventory levels for all stockpoints, given the target fill rates. These analytical approximations allows for a quick evaluation of the waiting time which is important when optimization of the system is considered.     

An integrated production–distribution model for the dynamic location and allocation problem with safety stock optimization

The design and management of a multi-stage production–distribution system is one of the most critical problems in logistics and in facility management. Companies need to be able to evaluate and design different configurations for their logistic networks as quickly as possible. This means coordinating the entire supply chain effectively in order to minimize costs and simultaneously optimize facilities location, the allocation of customer demand to production/distribution centers, the inbound and outbound transportation activities, the product flows between production and/or warehousing facilities, the reverse logistics activities, etc.Full optimization of supply chain is achieved by integrating strategic, tactical, and operational decision-making in terms of the design, management, and control of activities. The cost-based and mixed-integer programming model presented in this study has been developed to support management in making the following decisions: the number of facilities (e.g. warehousing systems, distribution centers), the choice of their locations and the assignment of customer demand to them, and also incorporate tactical decisions regarding inventory control, production rates, and service-level determination in a stochastic environment. This paper presents an original model for the dynamic location–allocation problem with control of customer service level and safety stock optimization. An experimental analysis identifies the most critical factors affecting the logistics cost, and to finish, an industrial application is illustrated demonstrating the effectiveness of the proposed optimization approach.     

Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand

This paper studies alternative methods for reducing lead time and their impact on the safety stock and the expected total costs of a (Q,s) continuous review inventory control system. We focus on a single-vendor-single-buyer integrated inventory model with stochastic demand and variable, lot size-dependent lead time and assume that lead time consists of production and setup and transportation time. As a consequence, lead time may be reduced by crashing setup and transportation time, by increasing the production rate, or by reducing the lot size. We illustrate the benefits of reducing lead time in numerical examples and show that lead time reduction is especially beneficial in case of high demand uncertainty. Further, our studies indicate that a mixture of setup time and production time reduction is appropriate to lower expected total costs.     

Inventory control with a modified Croston procedure and Erlang distribution

This paper considers an inventory control system, primarily for a finished goods inventory. The purpose is to create a procedure that can handle both fast-moving items with regular demand and slow-moving items. The suggested procedure should be easy to implement in a modern computerized ERP-system. Essentially, the system is a periodic review system built around a Croston forecasting procedure. An Erlang distribution is fitted to the observed data using the mean and variance of the forecasted demand rate. According to probabilities for stock shortages, derived from the probability distribution, the system decides if it is time to place a new order or not. The Croston forecasting method is theoretically more accurate than ordinary exponential smoothing for slow-moving items. However, it is not evident that a Croston forecasting procedure (with assumed Erlang distribution) outperforms ordinary exponential smoothing (with assumed normal distribution) applied in a “practical” inventory control system with varying demand, automatically generated replenishment, etc. Our simulation study shows that the system in focus will present fewer shortages at lower inventory levels than a system based on exponential smoothing and the normal distribution.     

The performance of two popular service measures on management effectiveness in inventory control

Service is one of the inventory managers' concerns and is frequently incorporated into the ordering decisions. Since there are multiple measures of service available for evaluating the efficiency of an inventory system, a comparative study is necessary and has not been addressed in the literature. This paper evaluates two popular service measures, which are the probability of no stockout during lead time and the fill rate, in the context of continuous inventory systems. The performance of the two measures is examined by evaluating the tradeoff among the cost, the level of service, and the inventory turnover ratio.     

Variance amplification and the golden ratio in production and inventory control

A discrete linear control theory model of a generic model of a replenishment rule is presented. The replenishment rule, which we term a “Deziel Eilon—automatic pipeline, inventory and order-based production control system”, is guaranteed to be stable. From a z-transform model of the policy, an analytical expression for bullwhip is derived that is directly equivalent to the common statistical measure often used in simulation, statistical and empirical studies to quantify the bullwhip effect. This analytical expression clearly shows that we can reduce bullwhip by taking a fraction of the error between the target and actual inventory and pipeline (or work in progress (WIP) or “orders placed but not yet received”) positions. This is in contrast to the common situation where ordering policies account for all of the error every time an order is placed. Furthermore, increasing the average age of the forecast reduces bullwhip, as does reducing the production/distribution lead-time. We then derive an analytical expression for inventory variance using the same procedure to identify the closed form bullwhip expression.We assume that a suitable objective function is linearly related to the bullwhip and inventory variance amplification ratios and then optimise the PIC system for different weightings of order rate and inventory level variance. We highlight two forms of the objective function, one where “the golden ratio” can be used to determine the optimal gain in the inventory and WIP feedback loop and another that allows the complete range of possible solutions to be visualised. It is interesting that the golden ratio, which commonly describes the optimum behaviour in the natural world, also describes the optimal feedback gain in a production and inventory control system.     

The uniform distribution as a first practical approach to new product inventory management

It is common sense that the premises usually considered in inventory models have little applicability to new product inventory management. This paper develops a first practical approach to deal with this issue: the solution to the (Q, r) inventory model for uniform demand forecasts and lead-times. Based on the fact that the uniform distribution is defined by two parameters that are easy to estimate—maximum and minimum—this paper shows that such a premise may comprise a helpful and accurate decision support tool for managers until they begin to learn about the distribution characteristics of the demand during the lead-time.     

An extended production/recycling model with stationary demand and return rates

A production–recycling system is investigated. A constant demand can be satisfied with production and recycling. The used items are bought back and then recycled. The non-recycled products are disposed of. Two types of models will be analyzed. The first model examines the EOQ-related costs and minimizes the relevant costs. The second model generalizes the first model with the introduction of the cost function with linear waste disposal, recycling, production and buyback costs. It is asked whether the pure (either production or recycling) or mixed strategies are optimal and it will be shown that under these circumstances the mixed strategies are dominated by the pure strategies. The paper generalizes a former model proposed by the authors for the case of one recycling and one production batch to the case of arbitrary batch numbers.     

A discounted cash flow approach to the base stock inventory model

A widespread approach to inventory modelling is to associate costs with measures of system performance and determine the control policy which minimises the long run average cost per unit time. This type of approach ignores the impact of a control policy on the timing of the cash flows associated with payments to suppliers and revenue streams from customers. The approach in this paper is to concentrate on cash flows and determine the control policy which maximises the expected net present value of the cash flows associated with a demand, valued at the time when that demand occurs. There is a Poisson demand process, a fixed lead time, unsatisfied demand is backordered and the system is controlled using a base stock policy. A solution procedure is given and a comparison is made with an equivalent simple interest model and with the standard cost model with linear holding and shortage costs.     

The relationship between UK manufacturers’ inventory levels and supply,internal and market factors

A major survey of UK manufacturing plants was carried out to explore the relationships between certain factors and inventory levels. These factors include procurement lead time, customer delivery lead time, manufacturing lead time and levels of predictability of raw materials availability and customer demand levels. The sample for the study comprises UK manufacturing plants in different industrial sectors including engineering, process, electronics, household products and food sectors. The results of a correlation analysis show that supply chain management issues such as the procurement lead time and the frequency of raw materials delivery are significantly linked with the inventory level of manufacturing plants. Also, manufacturing lead times were found to be associated with inventory levels but there was no significant relationship between customer delivery lead times and inventory levels.     

A perishable inventory model with Markovian renewal demands

In the inventory model, people usually assume that the inter-demand time is independently identical distributed which may not be true in reality. Here we study an (s,S) continuous review model for items with an exponential random lifetime and a general Markovian renewal demand process. By constructing Markovian renewal equations, we derive the mean and the variance of the reorder cycle time and lead to a simple expression for the total expected long run cost rate. The numerical results illustrate the system behavior and lead to managerial insights into controlling such inventory systems.     

Integrated inventory models with controllable lead time and backorder discount considerations

Many companies use time as a means of differentiating themselves in the marketplace. In many literatures, the controllable lead time is regarded as a decision variable and decomposed into several components, each having a crashing cost function for the respective reduced lead time. When an item is out of stock, the loyal, patient and captive customers will wait until the outstanding orders arrive and are served from them. To compensate for the inconvenience of backordering and to secure orders, the supplier may offer a price discount on the stockout item. In this paper, an integrated inventory system in which shortage is allowed and both lead time and backordering are negotiable is investigated. The lead time crashing cost is represented as a function of reduced lead time and the quantities in the orders. There are two inventory models proposed in the paper, one with normally distributed demand, and another with generally distributed demand.     

Agents’ incentives under buy-back contracts in a two-stage supply chain

This paper investigates how the behavior of individual decision makers can affect the performance of a supply chain. We study a two-stage supplier–retailer system, using a buy-back contract. Each firm's actions are executed by an agent. The retailer's purchasing agent and the supplier's sales agent are compensated based on certain performance measures, and they act accordingly. We study the impacts of their behavior in both the supplier-as-leader and retailer-as-leader settings. We find that, unless their incentives are carefully constructed, the agents can strongly distort the system's behavior. Specifically, “channel stuffing” (packing the distribution channel with excess inventory) can occur in both settings. Only when the agents are compensated based on net profit do they act in accord with their firms’ objectives. These results may help explain some recent scandals.     

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.     

Order and inventory variance amplification: The equivalence of discrete and continuous time analyses

The well-known “Bullwhip Effect” concerns the increasing variance of orders as they proceed through the supply chain. In the continuous time representation we solve the delay-differential equation for the inventory balance, which is coupled to the ordering policy. The time domain evolution of the system emerges. We calculate the Bullwhip Effect and compare it to known results for the discrete time representation. The discrete and continuous Bullwhip Effect expressions have similar structures. We show that the two domains are managerially equivalent so that in practice either domain can be used to study a supply chain.     

Considering stochastic lead times in a manufacturing/remanufacturing system with deterministic demands and returns

In this paper we study a manufacturing/remanufacturing system with stochastic lead times and a constant demand. We base our approach on previous research in which we have developed models to describe an inventory system with stochastic lead times. In this paper, we first adopt this method to manufacturing/remanufacturing situations, where there are essentially two supply sources for replenishing serviceable inventory. We then provide a solution procedure when a cycle ordering policy is used. Secondly, we investigate the possibility to use a dual sourcing ordering policy in which each order is split between a manufacturing and a remanufacturing process. Finally, we compare the two ordering policies and illustrate how the lead-time patterns influence the economic consequences.     

供应链管理环境下的库存控制研究

研究供应链管理环境下企业库存控制方法,对于节约供应链成本、提高供应链整体效率有重要意义。本文从分析供应链管理环境下库存控制在实践中所出现的各种问题入手,阐述了供应链环境下库存控制的新特点,有针对性地提出解决问题的策略和方法。     

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 new methodology linking concentration dynamics to current and steady-state profits:Examining Korean industrial policy during take-off

We model the dynamics of industrial structure and market power using Korean manufacturing data during the take-off period (1978–82). Structure–Conduct–Performance [SCP] methodologies have been criticized for using accounting data and because a few superior firms may have greater shares and greater profits. Both are argued to present possible spurious correlations between concentration and profits. This paper follows earlier work which shows that market structure responds to observed accounting profits as if these were accurate indices of real profits, and not as if leading firms are perceived to have unmatchable advantages. The methodological contribution of this model is a new latent variable for steady-state profits derived from the speed of structural adjustment. Long run profits are identified by the hypothesis that structural adjustment will be more rapid when industries are farther from steady-state levels. We analyze the long run profits latent variable, finding strong support for this hypothesis. The speed of adjustment is greater for positive and negative deviations from steady-state structure. We show that the profits and structural adjustment relationship is non-monotone. The SCP criticisms above are based on spurious correlations which are monotone in profits and structure. Positing spurious correlations which are at the same time monotone in structure and non-monotone in structural adjustment seems less plausible than accepting the SCP results which are consistent with both. Our analysis also is new in that it is the first direct econometric analysis of Korean industrial policy during its take-off years. We note that in Korea, unlike elsewhere, Industrial Policy was hypothesized to lead to concentration and market power in the popular press and by professional economists. Ours is the first direct econometric analysis of this hypothesis, and we find it supported.     

Optimal inventory control of empty containers in inland transportation system

In this paper, we deal with an inventory control problem of empty containers in an inland transportation system. In inland container transportation, freights (containers) are transported between terminal and the customer’s location by trucks, trains and barges. Empty containers are an important logistic resource and shipping companies try to operate and manage empty containers efficiently. Because of the trade imbalance between hub ports, empty containers should be periodically repositioned from surplus areas to shortage areas. However, it is not easy to exactly forecast the demand of empty containers, and we therefore need to build an efficient way to reposition the empty containers. In this paper, we consider a shortage area and propose an efficient inventory policy to control empty containers. We assume that demands per unit time are independent and identically distributed random variables. To satisfy the demand of empty containers, we reposition empty containers from other hubs based on the (s, S) inventory policy, and also consider the lease of empty containers with zero lead time. For the leased containers, we should return the number of empty containers leased to the leaser after the specified period. For a given policy, simulation is used to estimate the expected cost rate and we use the optimization tool, OptQuest^® in Arena to obtain the near optimal (s, S) policy in numerical examples.