INVESTMENT IN SETUP COST,LEAD TIME,AND DEMAND PREDICTABILITY IMPROVEMENT IN THE EOQ MODEL

We study an economic order quantity/reorder point (EOQ/ROP) model with stochastic demand and backorders where options of investing in reducing setup cost, lead time, and variance of demand forecast errors are available. The model is quite comprehensive relative to previous models since it simultaneously addresses the strategic decisions associated with these three investment opportunities as well as the tactical decisions of determining both the lot size and the safety stock. We develop a simple search procedure to obtain the optimal values of setup cost, lead time, variance of demand forecast errors, order quantity, and safety stock multiplier. Computational studies are performed to determine the sensitivity of the optimal solution of the model to changes in the model's parameters.     

The Value of Supplier Information to Improve Management of a Retailer's Inventory

The distribution of lead time demand is essential for determining reorder points in inventory systems. Usually, the distribution of lead time demand is approximated directly. However, in some cases it may be worthwhile to take the demand per unit time and lead time into account, particularly when specific information is available. This paper deals with the situation where a supplier, who produces on order in fixed production cycles, provides information on the status of the coming production run. The retailer can use this information to gain insight into the lead-time process. A fixed order (s_vQ) strategy is presented, with a set of reorder points s_v depending on the time t until the first possible delivery, which is determined by the information of the supplier. A Markov model that analyzes a given (s_vQ) strategy is used to quantify the value of the information provided by the supplier. Some numerical examples show that the approach may lead to considerable cost savings compared to the traditional approach that uses only one single reorder point, based on a two-moments approximation. Using this numerical insight, the pros and cons of a more frequent exchange of information between retailers and suppliers can be balanced.     

A comparison of several approximations to the lead time demand distribution

Several distributions have been used for approximating the lead time demand distribution in inventory systems. We compare five distributions, the normal, the logistic, the lognormal, the gamma and the Weibull for obtaining the expected number of back orders, the reorder levels to have a given protection and the optimal order quantity, reorder levels in continuous review models of (Q, r) type. The normal and the logistic distributions are inadequate to represent the situations where the coefficient of variation (the ratio of the standard deviation to the mean) of the lead time demand distribution is large. The lognormal, the gamma and the Weibull distributions are versatile and adequate; however the lognormal seems to be a viable candidate because of its computational simplicity.     

Inventory Rationing in a Make‐to‐Stock System with Batch Production and Lost Sales

We address an inventory rationing problem in a lost sales make‐to‐stock (MTS) production system with batch ordering and multiple demand classes. Each production order contains a single batch of a fixed lot size and the processing time of each batch is random. Assuming that there is at most one order outstanding at any point in time, we first address the case with the general production time distribution. We show that the optimal order policy is characterized by a reorder point and the optimal rationing policy is characterized by time‐dependent rationing levels. We then approximate the production time distribution with a phase‐type distribution and show that the optimal policy can be characterized by a reorder point and state‐dependent rationing levels. Using the Erlang production time distribution, we generalize the model to a tandem MTS system in which there may be multiple outstanding orders. We introduce a state‐transformation approach to perform the structural analysis and show that both the reorder point and rationing levels are state dependent. We show the monotonicity of the optimal reorder point and rationing levels for the outstanding orders, and generate new theoretical and managerial insights from the research findings.     

Sizing Inventory When Lead Time and Demand are Correlated

Determining appropriate inventory levels has been a subject of interest for both researchers and practitioners. Standard practice is to treat lead time demand as a random sum of random numbers and rely on established probability theory to calculate both reorder point and safety stock levels. A key assumption in these calculations, however, is that lead time and demand are not correlated. In this paper, we first explore situations where this assumption is untrue and then develop equations to determine the reorder point and the safety stock when lead time and demand are correlated. More specifically, we (1) derive formulas for the average and variance of the demand in a lead time, which can then be used to calculate the reorder point and the safety stock, (2) apply these formulas to two distributions for which there is a closed‐form solution: normal and Poisson, and (3) examine the effect of correlation on safety stock requirements under the normal distribution.     

A mixed inventory model with variable lead time and random supplier capacity

In this paper, we have studied analytically the implication of a controllable lead-time and a random supplier capacity on the continuous review inventory policy, in which the order quantity, reorder point and lead-time are decision variables. Two models are considered: the normal lead-time demand and lead-time demand is distributed free. For both cases, after formulating the general model, some properties of the optimal ordering policy have been developed. Particularly, we have shown that the expected annual total cost is a unimodal function and quasi-convex in the order quantity. When the variable capacity distribution is exponential, we develop effective procedures for finding the optimal solutions. Furthermore, the effects of parameters are also performed.     

AN ALTERNATE MODEL FOR LEAD-TIME DEMAND: CONTINUOUS-REVIEW INVENTORY SYSTEMS

The calculation of reorder points when the distribution of lead-time demand is normal is quite complex, primarily because of having to bound it away from negative demand values. A number of researchers have sought feasible alternative forms of lead-time demand which can be calculated without undue difficulty. It is proposed here to assume a Poisson (daily) demand and an exponential lead time (days). If they are assumed independent their convolution is geometric, which is itself asymptotically exponential. This has a number of advantages: (1) The exponential lead time is appropriate where the lead time is often short (i.e., local source), occasionally longer (when the local sources stock out), and, infrequently, quite long. (2) The geometric lead-time demand is independent of changes of time scale. (3) Reorder points and lot sizes appear in simple closed form. (4) The exponential asymptote is sufficiently close that this further simplification is usually warranted.     

Setups and effective capacity: the impact of lot sizing techniques in an MRP environment

This study investigates how lot sizing techniques influence the profit performance, inventory level, and order lardiness of an assembly job shop controlled by MRP. Four single-level lot sizing techniques are compared by simulation analysis under two levels of master schedule instability and two levels of end item demand. A second analysis investigates the influence of a multilevel lot sizing technique, the generalized constrained-K (GCK) cost modification, on the four single-level techniques at low demand and low nervousness. The analyses reveal a previously unreported phenomenon. Given the same inventory costs, the single-level lot sizing techniques generate substantially different average batch sizes. The lot sizing techniques maintain the following order of increasing average batch size (and decreasing total setup time):

economic order quantity (EOQ)

period order quantity (POQ)

least total cost (LTC)

Silver-Meal heuristic (SML)

The causes for different average batch sizes among the lot sizing techniques are analysed and explained. Demand lumpiness, inherent in multilevel manufacturing systems controlled by MRP, is found to be a major factor. The number of setups each lot sizing technique generates is the primary determinant of profit performance, inventory level, and order tardiness. EOQ, a fixed order quantity technique, is less sensitive to nervousness than the discrete lot sizing techniques. EOQ_, however, generates the smallest average batch size, and, therefore, the most setups. Since setups consume capacity, EOQ, is more sensitive to higher demand. SML generates the largest average batch sizes, and is, therefore, less sensitive to increased demand. At low demand, the other lot sizing techniques perform better on all criteria. They generate smaller batches and, therefore, shorter actual lead times. The GCK cost modification increases the average batch size generated by each lot sizing technique. GCK improves the profit and customer service level of EOQ the lot sizing technique with the smallest batches. GCK causes the other lot sizing techniques to generate excessively large batches and, therefore, excessively long actual lead times.     

A decision support system for a third-party coordinator managing supply chain with demand uncertainty

Global supply chains reduce cost but increase lead times, complexities and uncertainties. Retailers in consumer products industry are getting shorter lead time to respond to market demand. To meet this challenge, many rely on third party supply chain managers (SCMs) for economically supplying required quantities of finished products quickly. However, due to shorter ‘time to market’, the SCM has to procure raw materials and start production process based on expected demand. Since SCM absorbs financial penalties associated with under- and over-estimation of demand from retailer, finding an optimal production lot size and product customisation strategy are essential to an SCM's operation. We develop a profit maximisation model and provide a close-form solution that allows an SCM to calculate optimal production lot size. The model is used to examine profitability of postponing product customisation. Finally, the effect of demand variation on SCM's profitability is explored.     

Dual Sourcing Under Random Supply Capacities: The Role of the Slow Supplier

Sourcing from multiple suppliers with different characteristics is common in practice for various reasons. This paper studies a dynamic procurement planning problem in which the firm can replenish inventory from a fast and a slow supplier, both with uncertain capacities. The optimal policy is characterized by two reorder points, one for each supplier. Whenever the pre‐order inventory level is below the reorder point, a replenishment order is issued to the corresponding supplier. Interestingly, the reorder point for the slow supplier can be higher than that of the fast even if the former has a higher cost, lower reliability, and smaller capacity than the latter, suggesting the possibility of ordering exclusively from an inferior slow supplier in the short term. Moreover, the firm may allocate a larger portion of the long‐term total order quantity to the slow supplier than to the fast, even if the former does not possess any cost or reliability advantage over the latter. Such phenomena, different from the observations made in previous studies, happen when the demand is uncertain and the supply is limited or unreliable. Our observations highlight the importance of incorporating both demand uncertainty and supplier characteristics (i.e., cost, lead time, capacity and uncertainty) in a unified framework when formulating supplier selection and order allocation strategies.     

The disassembly line: balancing and modeling,by S.M. McGovern and S.M. Gupta

This note addresses a problem faced by an actual firm. The problem is to decide on the optimal level of product quality. In performing the economic analysis to determine product quality level, the firm considers revenue, production costs, and research and development costs. However, this note shows that ignoring inventory costs in the analysis will lead to suboptimal product quality levels. Also, including inventory costs in the analysis will lead to reduced production lot sizes. Numerical examples are used to illustrate the results of the model.     

运输成本对批量敏感时的供应链批量协调策略比较研究

以一个多周期、随机客户需求和单位产品运输成本对批量敏感的供应链为研究对象,建立了由生产商负责产品运输时,供应链分散决策情形下的最佳批量模型,并提出了基于批量折扣和改由批发商负责产品运输的供应链批量协调策略.研究结果表明:当由生产商负责产品运输时,单位产品运输成本对批量越不敏感,生产商的最佳生产批量越小,与批发商要求的短周期、小批量订货越接近;如果改由批发商负责产品运输,批发商的最佳订货批量更接近于生产商的最佳生产批量.最后,通过数例分析发现,对生产商来讲,当单位产品运输成本对批量不太敏感时,批量折扣政策优于改由批发商负责产品运输的策略,但当单位产品运输成本对批量较敏感时,后者优于前者.     

The Effect of Lead Time Uncertainty on Safety Stocks

The pressure to reduce inventory investments in supply chains has increased as competition expands and product variety grows. Managers are looking for areas they can improve to reduce inventories without hurting the level of service provided. Two areas that managers focus on are the reduction of the replenishment lead time from suppliers and the variability of this lead time. The normal approximation of lead time demand distribution indicates that both actions reduce inventories for cycle service levels above 50%. The normal approximation also indicates that reducing lead time variability tends to have a greater impact than reducing lead times, especially when lead time variability is large. We build on the work of Eppen and Martin (1988) to show that the conclusions from the normal approximation are flawed, especially in the range of service levels where most companies operate. We show the existence of a service‐level threshold greater than 50% below which reorder points increase with a decrease in lead time variability. Thus, for a firm operating just below this threshold, reducing lead times decreases reorder points, whereas reducing lead time variability increases reorder points. For firms operating at these service levels, decreasing lead time is the right lever if they want to cut inventories, not reducing lead time variability.     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

The effects of the warranty cost on the imperfect EMQ model with general discrete shift distribution

In this paper, we investigate the effect of the warranty cost on optimization of the economic manufacturing quality (EMQ). This is done for a deteriorating process where the production process shifts from the in-control state to the out-of-control state following a general discrete probability distribution. Once the production process goes out of control, the production process produces some defective items. The defective item cost includes reworking and warranty costs. Thus, in order to economically operate a production-inventory system with products sold under warranty, the tradeoffs among the production setup, inventory, and defective item cost, including the reworked cost before sale and the warranty cost after sale, needed to be analysed. This objective in this paper is to determine the production lot size while minimizing the total cost per unit of time per unit of time. Various special cases are presented. Two of them are extensions of results obtained previously in the literature. Finally, a numerical example is given which uses a discrete Weibull probability distribution. Sensitivity analysis of the model with respect to cost and time parameters is also performed.     

Shelf Space Management When Demand Depends on the Inventory Level

Two factors that their influence on the demand has been investigated in many papers are (i) the shelf space allocated to a product and to its complement or supplement products and (ii) the instantaneous inventory level seen by customers. Here we analyze the joint shelf space allocation and inventory decisions for multiple items with demand that depends on both factors. The traditional approach to solve inventory models with a state‐dependent demand rate uses a time domain approach. However, this approach often does not lead to closed‐form expressions for the profit rate with both dependencies. We analyze the problem in the inventory domain via level crossing theory. This approach leads to closed‐form expressions for a large set of demand rate functions exhibiting both dependencies. These closed‐form expressions substantially simplify the search for optimal solutions; thus we use them to solve the joint inventory control and shelf space allocation problem. We consider examples with two products to investigate the significance of capturing both demand dependencies. We show that in some settings it is important to capture both dependencies. We consider two heuristics, each one of them ignores one of the two dependencies. Using these heuristics it seems that ignoring the dependency on the shelf space might be less harmful than ignoring the dependency on the inventory level, which, based on computational results, can lead to profit losses of more than 6%. We demonstrate that retailers should use their operational control, e.g., reorder point, to promote higher demand products.     

The Backroom Effect in Retail Operations

Traditional inventory models fail to take into account the dynamics between the retail sales floor and the backroom, commonly used by retailers for extra storage. When a replenishment order for a given item arrives at a retail store, it may not fit on the allocated shelf space, making backroom storage necessary. In this article, we introduce the backroom effect (BRE) as a consequence of misalignment of case pack size, shelf space, and reorder point. This misalignment results from the fragmented nature of inventory policy decision making in the retail industry and affects basic trade‐offs in inventory models. We specify conditions under which the BRE exists, quantify the expected amount of backroom inventory, derive an optimal short‐term inventory policy, and assess the impact of the BRE on the optimal inventory policy and total costs. Our results indicate that ignoring the BRE leads to artificially high reorder points and higher total costs. The paper concludes with a discussion of theoretical and managerial implications.     

A decision tree approach for selecting between demand based,reorder, and JIT/kanban methods for material procurement

In designing mechanisms for the procurement of raw materials, a manager is often faced with the task of selecting from a variety of possible methods. Since the performance of these methods is a function of the environment in which they are implemented, it is the responsibility of the manager to select the method best suited for a particular application. In this paper we present a methodology for assisting managers in the selection process. Specifically, three classes of procurement methods are considered, these are: demand based, reorder, and JIT methods. The selection methodology is structured as a decision tree, which considers the annual usage value, lead time ratio, holding cost, vendor location, vendor delivery performance, and material supply value. Each factor is evaluated on a three level scale, and on the basis of these evaluations the tree makes a selection. The application of the methodology is illustrated via some examples.     

A queuing/management consideration on Japanese production systems

A single-stage lot/cell production under a Poisson arrival and exponential service in a batch is considered. The three economic queuing models of push and pull types are presented, an economic comparison of push versus pull types is considered, and a strategic management/design consideration to the lot production is given. First, the total expected operating cost is given for the three queuing models including the Omote-Kanban type similar to VMI. Second, the push versus pull system is discussed from a view of setup time, inventory or operating cost, and it is ascertained that the three types are alternative. Finally, a strategic management basis for economic traffic, leadtime setting is given, and discussed by the introduction of production matrix on 2-stage design.     

周期性需求下基于延迟订货的库存控制

本文在假设产品需求为周期性需求,订货周期为需求周期的整数倍,不能满足的需求在一定的时间间隔内允许缺货的前提下,提出一种确定性库存模型,并在此基础上,以满足单位时间内利润最大化为目标,研究并确定了优化订货批量、订货周期的时间间隔长度和缺货的时间长度的算法,最后给出算例,并验证了算法的可行性.