A coordination mechanism with fair cost allocation for divergent multi-echelon inventory systems

In this paper we study the coordination of inventory control in divergent multi-echelon inventory systems under periodic review and decentralized control. Under decentralized control the installations decide upon replenishment policies that minimize their individual inventory costs. In general these policies do not coincide with the optimal policies of the system under centralized control. Hence, the total cost under decentralized control is larger than under centralized control. We present a simple coordination mechanism that removes this cost inefficiency. The upstream installations increases its base stock level while the downstream installations compensate their supplier for increased costs and provide it with additional side payments. We show that this mechanism coordinates the system; the global optimal policy of the system is the unique Nash equilibrium of the corresponding strategic game. Furthermore, the mechanism results in a fair allocation of the costs; all installations enjoy cost savings.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

Contracting Under Vendor Managed Inventory Systems Using Holding Cost Subsidies

Vendor managed inventory systems are becoming increasingly popular. An important issue in implementing a vendor managed inventory scheme is the contracting terms that dictate the ownership of the inventory and the responsibility of inventory replenishment decisions. Thus the performance of a vendor managed system crucially depends on these terms and on how inventory‐related costs are shared in a supply chain. We consider a system where a manufacturer supplies a single product to a retailer who faces random demand in a competitive market. The retailer incurs a fixed cost per order, inventory holding cost, and a penalty cost for a stockout (unsatisfied demand is back‐ordered). Further, the manufacturer incurs a penalty cost when there is a stockout at the retailer and a fixed replenishment cost. We assume that the players are rational and act noncooperatively. We compare the performance of retailer managed inventory systems, where the retailer places orders and makes replenishment decisions, with vendor managed inventory systems, wherein the vendor or manufacturer makes inventory and replenishment decisions. Specifically, in the vendor managed inventory system, we propose and evaluate holding cost subsidy‐type contracts on inventories offered by the retailer to improve system performance. We evaluate this contract in the context of three widely used inventory systems—deterministic economic order quantity, continuous review (Q, r) policies, and periodic review policies—and show when such contracts may improve channel performance.     

Analysis and Management of Periodic Review,Order‐Up‐To Level Inventory Systems with Order Crossover

In this article, we investigate the (R, S) periodic review, order‐up‐to level inventory control system with stochastic demand and variable leadtimes. Variable leadtimes can lead to order crossover, in which some orders arrive out of sequence. Most theoretical studies of order‐up‐to inventory systems under variable leadtimes assume that crossovers do not occur and, in so doing, overestimate the standard deviation of the realized leadtime distribution and prescribe policies that can inflate inventory costs. We develop a new analytic model of the expected costs associated with this system, making use of a novel approximation of the realized (reduced) leadtime standard deviation resulting from order crossovers. Extensive experimentation through simulation shows that our model closely approximates the true expected cost and can be used to find values of R and S that provide an expected cost close to the minimum cost. Taking account of, as opposed to ignoring, crossovers leads, on average, to substantial improvements in accuracy and significant cost reductions. Our results are particularly useful for managers seeking to reduce inventory costs in supply chains with variable leadtimes.     

A Data‐Driven Inventory Control Policy for Cash Logistics Operations: An Exploratory Case Study Application at a Financial Institution

A number of market changes are impacting the way financial institutions are managing their automated teller machines (ATMs). We propose a new class of adaptive data‐driven policies for a stochastic inventory control problem faced by a large financial institution that manages cash at several ATMs. Senior management were concerned that their current cash supply system to manage ATMs was inefficient and outdated, and suspected that using improved cash management could reduce overall system cost. Our task was to provide a robust procedure to tackle the ATM's cash deployment strategies. Current industry practice uses a periodic review system with infrequent parameter updates for cash management based on the assumption that demand is normally distributed during the review period. This assumption did not hold during our investigation, warranting a new and robust analysis. Moreover, we discovered that forecast errors are often not normally distributed and that these error distributions change dramatically over time. Our approach finds the optimal time series forecaster and the best‐fitting weekly forecast error distribution. The guaranteed optimal target cash inventory level and time between orders could only be obtained through an optimization module that was embedded in a simulation routine that we built for the institution. We employed an exploratory case study methodology to collect cash withdrawal data at 21 ATMs owned and operated by the financial institution. Our new approach shows a 4.6% overall cost reduction. This reflects an annual cost savings of over $250,000 for the 2,500 ATM units that are operated by the bank.     

提前期、构建成本和短缺量拖后率均可控的EOQ模型

传统库存模型通常将提前期和构建成本视为不可控制。事实上可以通过追加投资缩短提前期和降低构建成本。缺货期间,为减少订单丢失量和补偿顾客的损失,供应商会给予一定的价格折扣。现实库存系统中,容易得到需求的期望值和标准差,但较难得到其分布规律。基于此,考虑短缺量拖后率与价格折扣和缺货期间库存水平相关,提出了一种需求为任意分布且提前期和构建成本均可控的EOQ模型,证明了模型存在唯一最优解,给出了一种寻优算法。数值仿真分析表明,一般情况下,压缩提前期和降低构建成本能降低订购批量和安全库存,降低库存总成本;短缺量拖后系数和缺货概率对库存总成本影响较大,企业应尽量降低缺货概率,尤其在短缺量拖后系数较小时。     

Joint Lot Sizing and Scheduling of Multiple Items with Sequence-Dependent Setup Costs

The objective of this research is to investigate the effects of setup-cost estimating methods on the lot sizing and scheduling of multiple products in multiple periods. These initial setup cost estimators (ISCEs) are used to estimate sequence-independent initial setup costs from sequence-dependent setup costs. A search of the literature reveals that, although sequence-dependent setup costs are frequently found in practice and ISCEs are frequently used, there is a dearth of research concerning the effect of using ISCEs. After a review of the literature, a mixed integer formulation of the joint problem of lot sizing and scheduling is presented, followed by a discussion of the difficulty in solving the formulation. Next, the six ISCEs evaluated are presented. These ISCEs range from simple (select the minimum setup cost) to complex (use the branch-and-bound solution to a traveling salesman-type problem). Each ISCE is evaluated using a full factorial design with five independent variables: demand distribution (three levels), demand trend (three levels), setup to inventory level (six levels), setup distribution (three levels), and setup variability (two levels). Two hypotheses are researched. Do the more computationally complex ISCEs produce lower overall costs than do the simpler ISCEs? Does the reduction in total cost justify the additional computation cost? The results of this study demonstrate that it may be incorrect to use “conventional wisdom'’when selecting an ISCE.     

Integrative Cycle Scheduling Approach for a Capacitated Flexible Assembly System*

This study revisits the traditional single stage, multi-item, capacitated lot-sizing problem (CLSP) with a new integrative focus on problem structuring. Unlike past research, we develop integrative cycle scheduling approaches which simultaneously address lot-sizing, capacity, and sequencing issues. Our purposes are to (1) explore the effect of sequencing on inventory levels, (2) examine the problem of infeasibility in the economic lot scheduling problem (ELSP), and (3) provide a simple methodology of generating low-cost cycle schedules in an environment with discrete shipping, dynamic demands, limited capacity, zero setup cost, and sequence-independent setup times. Our procedures are compared to benchmark cycle scheduling approaches in terms of both inventory cost and computation time under different demand scenarios, using the operating data from a flexible assembly system (FAS) at the Ford Motor Company's Sandusky, Ohio plant.     

Setup cost reduction a multi-stage order quantity model

In this paper, a single item, multi-stage serial order quantity (MSOQ) model with constant demand is discussed. The objective of the model is to minimize the total cost which includes the setup cost and the inventory holding cost. This paper examines and analyses the investment in a one-time cost to reduce the (current) setup level and adds a per unit item amortization of this cost to the other costs associated with the MSOQ model. We consider the setup cost to be decreased on each stage with the same rate and the cost of the joint setup cost reduction is a logarithmic cost function.     

Freezing the master production schedule in multilevel material requirements planning systems under deterministic demand

This paper extends the studies by Sridharan, Berry, and Udayabhanu from single-level MPS systems to multilevel material requirements planning (MRP) systems, and examines the impact of product structure, lot-sizing rules and cost parameters upon the selection of MPS freezing parameters under deterministic demand. A model is built to simulate the master production scheduling and material requirements planning operations in a make-to-order environment. The results show that all the MPS freezing parameters studied have a significant impact upon total inventory costs and schedule instability in multilevel MRP systems. First, the order-based freezing method is preferable to the period-based method. Secondly, the study finds that increasing the freezing proportion reduces both total inventory costs and schedule instability. This finding contradicts the finding by Sridharan et al. in single-level systems. Thirdly, the study finds that a higher replanning periodicity results in both lower total inventory cost and lower schedule instability. The study also indicates that the product structure and lot-sizing rules do not significantly influence the selection of MPS freezing parameters in a practical sense under most situations. However, the cost parameter seems to significantly influence the selection of replanning periodicity.     

SETUP REDUCTION AND MACHINE AVAILABILITY

This paper is an extension of Billington, who used the framework of the economic production quantity (EPQ) to model setup cost reduction. In the present paper, we use the EPQ model as a starting point to investigate the nature of setup costs and the effect of setup time reduction on the increase in available capacity. Reducing setup is vital to a company's success because a lengthy changeover of machinery is expensive: it demands long production runs to justify its cost, and these, in turn, lead to excessive inventory and to a slow response to customer needs. As in Billington, setup reduction is modeled as a function of an annual amortized investment. The paper examines the behavior of the setup time, the inventory cost, the lot size, and the freeing up of machine time in the face of a capacity constraint. A solution algorithm is provided to find setup times that minimize the sum of setup and holding cost, subject to a constraint on machine availability. The analysis sheds light on the true nature of setup cost and on the opportunity cost of not reducing setups. In the constrained optimization, the Lagrangian multiplier gives an estimate of the marginal value of adding one time unit of machine capacity, or, alternatively, of reducing one unit of setup time.     

A new MRP/GT lot sizing heuristic: A simulation study

This paper studies the lot-sizing problem in Material Requirements Planning/Group Technology (MRP/GT) systems. A GT production cell is designed to produce many families of components. A major setup is required when switching from manufacturing one family of components to another family, and a minor setup is needed when switching from manufacturing a component type to another component type within the same family. Inventory holding cost is incurred if inventory level is positive, and inventory shortage cost is incurred if inventory level is negative, that is, backordering. The objective of the proposed lot-sizing problem is to minimize the sum of major and minor setup costs, holding and shortage costs, and regular production cost, and to meet simultaneously the demand requirements. The proposed problem is modelled into a linear integer program, a heuristic method to solve the problem is proposed, and a simulation experiment conducted to evaluate the performance of the proposed heuristic and some existing heuristics. The computational results show that the proposed heuristic is useful to reduce the total cost significantly over a wide variety of simulated environments.     

THE CLASSIC ECONOMIC PRODUCTION QUANTITY MODEL WITH SETUP COST AS A FUNCTION OF CAPITAL EXPENDITURE*

The formulation of the classic economic production quantity (EPQ) model is extended to include setup cost as a function of capital expense. Additional capital will buy reduced setup cost. Thus, the objective now is to balance holding, setup, and capital expenses. This new formulation is solved under conditions where setup cost varies exponentially and linearly as a function of capital expense. Decision rules are formulated to indicate under what conditions setup cost reduction reduces total cost. For the linear function, it is shown that once the decision to reduce setup cost is justified, the optimal choice is the minimum setup cost that is technologically feasible.     

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.     

同步物流系统下准时化生产与配送调度问题研究

对于"加工-装配"行业而言,物流管理水平的高低直接决定了供应链绩效的好坏。本文以Supply Hub运作模式为背景,研究同步物流下装配系统中各节点的生产与配送调度问题。建立供应链各参与方的生产与配送模型,并通过规划求解得到供应商和制造商的最优生产周期、零部件的最优配送间隔以及零售商的最佳采购周期。最后,结合数值实验,对同步物流模式和传统物流模式下的供应链绩效进行了对比分析。研究结果表明:较之传统物流模式,基于同步化物流方式的装配系统总成本更低,这主要得益于库存成本的下降;由于采取拉动式的生产模式,因此同步物流系统下供应链中的生产和配送活动更加频繁;生产调整成本的增加提高了制造商的平均总成本,由此可见在同步物流系统下,供应商、制造商和零售商之间更需要相互协商和收益共享,从而实现多赢。     

An Experimental Analysis of Capacity-Sensitive Setup Parameters for MRP Lot Sizing

Most material requirements planning (MRP) systems apply standard costing (absorption costing) approaches to define setup costs that are used as fixed (time invariant) setup parameters in single-level lot-sizing methods. This paper presents a computationally simple approach for estimating more appropriate setup parameters based on estimates of work-center shadow prices. These setup parameters then are used in traditional single-level MRP lot-sizing procedures. The shadow price of capacity at each work center is calculated as the increase in the overall inventory carrying cost for each additional hour of capacity lost to setups. The opportunity cost of a setup for an order subsequently is determined based on the routing information for each order and is used by traditional MRP lot-sizing procedures to calculate lot sizes. A simulation experiment compares the performance period order quantity lot sizing with capacity-sensitive setup parameters with the fixed accounting-based setup parameters. The simulation replicates the planning and control functions of a typical MRP system. The results of the experiment show that capacity-sensitive setup parameters can make significant reductions in both carrying cost and lateness and can achieve many of the benefits of optimized production technology in the context of an MRP system.     

A multicriteria model for supporting setup reduction investment decisions

One critical manufacturing challenge of the 1990s is for firms to effectively apply new operations management techniques while embracing wider philosophies such as total quality management (TQM) and computer integrated manufacturing (CIM), etc. Setup cost and/or time reduction is one such technique capable of producing many benefits for manufacturing firms, including reduced inventory, better equipment utilization, and improved quality. It is thereby viewed as an important component of just-in-time (JIT) manufacturing practice. Existing problems with the setup reduction decision include the many factors that must be considered, as well of an absence of validated and usable models for estimating potential benefits from setup reduction investment made in different contexts. This paper discusses the attainment of gains from setup reduction mainly by improving existing equipment and work practices rather than purchasing new equipment or technology. The model proposed in this paper is based on the application of the analytic hierarchical process (AHP) on seven weighted factors to obtain a preliminary indication as to whether investment in setup reduction is desirable in a given manufacturing context, and the expected benefits of such investment. A flexible scaling system, thus obtained, allows the model to handle a wide range of managerial predispositions to setup reduction.     

Quick response and supply chain structure with strategic consumers

This work explores the impact of quick response on supply chain performance for various supply chain structures with strategic customer behavior. By investigating pricing and inventory decisions in decentralized supply chains under revenue-sharing contracts and in centralized supply chains, we study the performance of four various systems and compare the value of quick response in different supply chain structures. The results show that if the extra cost of quick response is relatively low, the value of quick response would be greater in centralized systems than in decentralized systems. On the other hand, if the extra cost is high, decentralized supply chains reap more incremental profits from adopting quick response. We also find that revenue-sharing contracts enable a decentralized supply chain to outperform a centralized supply chain, but only allow limited flexibility of allocating total profits between a manufacturer and a retailer.     

The value of VMI beyond information sharing in a single supplier multiple retailers supply chain under a non-stationary (Rn,Sn) policy

This study aims to determine the value of vendor-managed inventory (VMI) over independent decision making with information sharing (IS) under non-stationary stochastic demand with service-level constraints. For this purpose, we utilize mixed-integer linear programming formulations to quantify the benefits that can be accrued by a supplier, multiple retailers and the system as a whole by switching from IS to VMI. More specifically, we investigate the incremental value that VMI provides beyond IS in terms of expected cost savings, inventory reductions, and decrease in shipment sizes from the supplier to the retailers by conducting a large number of computational experiments. Results reveal that the decision transfer component of VMI improves these performance measures significantly when the supplier׳s setup cost is low and order issuing efficiency is high. The benefits offered by VMI are negligible under the problem settings where the supplier׳s order issuing efficiency is low and the production setup serves solely a single replenishment under IS.