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.     

Distribution contracts to support optimal inventory holdings under demand uncertainty

When suppliers produce products for which demand is uncertain, they face a problem of inducing downstream distributors to stock inventory levels that the suppliers prefer. This paper considers a wide array of alternative supply contracts, each of which consists of a mixture of constant per-unit wholesale prices, buy-back arrangements, and post sale payments contingent on sales made, such as revenue sharing or buybacks. We show that linear supply contracts specifying any combination of two of these three instruments can implement the vertical integrated outcome for a monopoly, thereby generating the supplier's preferred inventory configuration and price distribution. We extend our results to differentiated product oligopoly, demonstrating that each supplier obtains its preferred inventory configuration and price distribution, given the choices of its rival. Distributors choose optimal inventories from the suppliers' standpoint, even if suppliers do not know the distribution of demand uncertainty, and, given the perfect competition among distributors, all profits in the supply chain are captured by suppliers. Thus, suppliers are able to deal with demand uncertainty with remarkably little information about demand, and without the need to control dealer actions in detail. In particular, suppliers need not specify either dealer inventories or resale prices, but instead encourage distributors to order based on information in their possession and to set prices that generate desirable resale price dispersion.     

A continuous model for supply planning of assembly systems with stochastic component procurement times

This paper studies a customized product assembly scenario where some components cannot be stocked due to high component cost and risk. We consider the case where these key components are ordered after a demand has been registered with a promised delivery date. Component lead-times are stochastic and associated distribution function is known in advance. The objective is to determine the ordering time for each component such as to minimize the sum of expected holding and backlogging costs. An approach to solve this problem is proposed and the algorithm is tested on a randomly generated data set.     

A production/remanufacture model with returns’ subassemblies managed differently

This paper considers a production-remanufacturing inventory model for a single product, where constant demand is satisfied from the inventory of newly produced and remanufactured items. Although the available models in the literature imply that collected used units (or returns) are disassembled for recovery purposes, these models really do not treat them as such. Contrary, the returns are assumed to be recovered as whole units, perhaps, for simplicity. This assumption may not capture the benefits reaped from product recovery programs. This paper addresses this limitation in the literature and assumes that each unit of a used product is collected and disassembled into components, where these components are sorted into subassemblies, which are fed back into the production-remanufacturing process. The returned subassemblies are remanufactured and reassembled to represent a second source of as-good-as-new units of the end-product. For this multi-component inventory problem, the question that needs to be answered is whether, or not, extreme strategies of either pure remanufacturing or pure production are more economical than a mixed strategy (one that combines both strategies). A mathematical model is developed that accounts for the inventories of subassemblies. The results suggested that not accounting for the disassembled components of a product leads to inappropriate inventory decisions that are not environmentally sound.     

Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging

Yan and Cheng (J. Operational Res. Soc. 49 (1998), 1288–1295) presented a general production–inventory model with production rate, product demand rate and deterioration rate, all considered as functions of the time. Their model allows for shortages and partial backlogging of the unsatisfied demand at a constant rate. In this paper, we extend the results of Yan and Cheng to cover the case where the backlogging rate is a time-dependent function and we propose an algorithm for the solution of this problem. We also propose some conditions which we believe to be necessary for the validity for some of Yan's and Cheng's statements. The paper closes with numerical examples which cover each one of the cases considered in the paper.     

A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty

Manufacturers need to satisfy consumer demands in order to compete in the real world. This requires the efficient operation of a supply chain planning. In this research we consider a supply chain including multiple suppliers, multiple manufacturers and multiple customers, addressing a multi-site, multi-period, multi-product aggregate production planning (APP) problem under uncertainty. First a new robust multi-objective mixed integer nonlinear programming model is proposed to deal with APP considering two conflicting objectives simultaneously, as well as the uncertain nature of the supply chain. Cost parameters of the supply chain and demand fluctuations are subject to uncertainty. Then the problem transformed into a multi-objective linear one. The first objective function aims to minimize total losses of supply chain including production cost, hiring, firing and training cost, raw material and end product inventory holding cost, transportation and shortage cost. The second objective function considers customer satisfaction through minimizing sum of the maximum amount of shortages among the customers’ zones in all periods. Working levels, workers productivity, overtime, subcontracting, storage capacity and lead time are also considered. Finally, the proposed model is solved as a single-objective mixed integer programming model applying the LP-metrics method. The practicability of the proposed model is demonstrated through its application in solving an APP problem in an industrial case study. The results indicate that the proposed model can provide a promising approach to fulfill an efficient production planning in a supply chain.     

Optimal control of a one product recovery system with leadtimes

In this paper a recovery system for a single product is investigated. Besides a remanufacturing and a manufacturing facility the system consists of one inventory for returned and recoverable items and one for serviceable items. Demands are satisfied from serviceable inventory, which can be replenished by remanufactured returned items, which are as good as new, or by new produced items. Additionally, there is the possibility of disposing of returned items.We determine the cost optimal manufacturing, remanufacturing and disposal rates for the system under the assumptions of a linear cost structure, a finite planning horizon and deterministic and dynamic demand and return rates. Thereby we study two classes of policies, one where backorders are forbidden and another one where they are allowed. In contrast to the existing literature positive leadtimes are considered.     

An inventory control model with consideration of remanufacturing and product life cycle

This paper investigates inventory control policies in a manufacturing/remanufacturing system during the product life cycle, which consists of four phases: introduction, growth, maturity, and decline. Both demand rate and return rate of products are random variables with normal distribution; the mean of the distribution varies according to the time in the product life cycle. Closed-form formulas of optimal production lot size, reorder point, and safety stock in each phase of the product life cycle are derived. A numerical example is presented with sensitivity analysis. The result shows that different inventory control policies should be adopted in different phases of the product life cycle. It is also found that the optimal production lot size and reorder point are not sensitive to the phase length and the demand changing rate.     

Optimal inventory and pricing policies for remanufacturable leased products

In this paper we consider a company which leases new products and also sells remanufactured versions of the new product that become available at the end of their lease periods. When the amount of end-of-lease items in stock is not sufficient to meet the demand for remanufactured products, the firm may purchase additional cores from a third-party supplier. We develop a dynamic programming formulation for determining the optimal price of remanufactured products, and optimal payment structure for the leased products. Our objective is to maximize the discounted system-wide profit over a finite horizon. The profit function consists of revenues that are obtained from remanufactured product sales and leasing, remanufacturing and manufacturing costs, inventory holding and shortage costs. We consider a consumer choice based demand model for mapping a potential customer into one of the product segments (a remanufactured product customer or a customer for a leased product with a particular lease period) for a given price/lease payment vector. We explore several properties of the discounted profit function and provide insight on the behavior of pricing and inventory policies. We also investigate the effect of key product characteristics such as deterioration in age, cost of shortage in remanufacturable product inventory, and key market characteristics such as relative willingness-to-pay for buying a remanufactured product and relative willingness-to-pay for leasing a new product on optimal pricing policies through a computational study.     

Selecting make-to-stock and postponement policies for different products in a chemical plant: A case study using discrete event simulation

We present a guideline for selecting the inventory management policy for a specialty chemical plant that produces products with limited shelf life, by producing multiple grades of bulk chemical and packaging them into a large variety of bottles. The policy for each product was selected based on a cost-benefit analysis, using the multiple objectives of maximizing the on time order fulfillment, minimizing the production (cleaning and shelf life expiration) and inventory costs. To generate realistic cost estimates, we developed a discrete event simulation model that included demand variability, planning and scheduling policies, and operational details. We evaluated three different policies: make-to-stock (MTS), postponement, and combined MTS/postponement. We also evaluated different storage media and optimized the number of storage units for products selected for postponement. A combined MTS/postponement policy, in which postponement is applied to products with low to medium demand and high expiration provided lowest costs without significantly impacting the customer on time order fulfillment. For all other products, a MTS policy is applied to maximize order fulfillment on time, reduce cleaning costs and to reduce number of storage units.     

Robust optimal policies of production and inventory with uncertain returns and demand

We consider an inventory and production planning problem with uncertain demand and returns, in which the product return process is integrated into the manufacturing process over a finite planning horizon. We first propose an inventory control model for the return and remanufacturing processes with consideration of the uncertainty of the demand and returns. Then a robust optimization approach is applied to deal with the uncertainty of the problem through formulating a robust linear programming model. Moreover, properties on the robust optimization model are studied, and an equivalent robust optimization model based on duality theory is obtained which allows the solutions to be derived more efficiently. Finally, we provide a set of numerical examples to verify the effectiveness of the approach and analyze the effects of the key parameters on the solutions.     

Optimal safety stock levels of subassemblies and manufacturing components

In order to control the time to market and manufacturing costs, companies produce and purchase many parts and components before receiving customer orders. Consequently, demand forecasting is a critical decision process. Using modular product design and super bills of materials are two effective strategies for developing a reliable demand forecasting process. They reduce the probability of stockouts in diversified production contexts. Furthermore, managing and controlling safety stocks for pre-assembled modules provide an effective solution to the problem of minimizing the effects of forecast errors. This paper develops, evaluates, and applies innovative cost-based analytical models so that the optimal safety stock of modular subassemblies and components in assembly to order and manufacturing to order systems, respectively, can be rapidly quantified. The implementation of the proposed models in two industrial case applications demonstrates that they significantly reduce the safety stock inventory levels and the global logistical cost.     

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.     

基于改进TOPSIS法的供应商选择模型研究

为有效地帮助企业快速找到合适的供应商合作伙伴,采用直觉模糊集、评分函数等方法对TOPSIS评估法进行优化,并以此为基础建立了一种供应商选择模型。首先,采集和评估供应商的产品质量、产品价格、产品交货的可靠性、供应位置、财务情况、库存水平、劳资关系、发展能力和技术能力等相关信息,由专家给出主观评估信息,汇总为综合属性值;然后,通过直觉模糊熵确定各评估指标的权重;最后,综合考虑供应商选择决策过程中的多个目标和标准,应用改进TOPSIS法的对供应商进行分类选择。结果显示,基于改进TOPSIS法的供应商选择模型能够较准确地反映出各供应商的真实水平和对企业的潜在价值,可以有效地解决不确定条件下对供应商的选择问题,提高了供应商选择结果的可靠性。改进后的模型简便易行,具有良好的稳定性,对于合理制定企业供应商选择标准以及进一步优化决策模型具有一定的借鉴意义。     

Model and analysis of integrated production–inventory system: The case of steel production

The study originated from an industrial case study in the field of steel production, but it presents a larger interest, as many other manufacturing fields have similar concerns (e.g. foundries, food, textile and paper industries). A significant phase of steel manufacturing is the product cooling (likewise, drying in paper and textile production, or maturing in food production). This phase may be completed in different ways, but (1) it must be carried out in the finished product warehouse and (2) it must meet both production optimisation and customer needs. The latter requirement acquires a strategic relevance in JIT environments. The present study proposes a mathematical model to find the optimal production schedule of steel billets, based on the relevant parameters of the productive system (set-up and processing times, demand profile). In the industrial case examined, the negative impact of holding costs on cash flows is also linked to the space required by the cooling process, which depends on the production schedule adopted. In other words, the finished product storage can be considered a part of the manufacturing cycle and impacts on it. In the case of steel plants operating in JIT environments, the warehouse must be promptly emptied and carefully managed to exploit the available space. Thus, the effect of inventory costs is examined in a production–inventory system with finite capacity, where products are made to order and share the same manufacturing facility. The study is completed by an experimental analysis to investigate the effect of variations in the relevant parameters of the problem.     

Competition under capacitated dynamic lot-sizing with capacity acquisition

Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inventory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a constant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.     

Revenue Sharing and Vertical Control in the Video Rental Industry

Revenue sharing contracts, in which retailers pay a royalty on sales to their suppliers, are now widely used in the video rental industry. We show that revenue sharing is valuable in vertically separated industries in which demand is either stochastic (unpredictable) or variable (e.g., systematically declining), downstream inventory is chosen before demand is realized and downstream firms engage in intrabrand competition. Unlike two-part tariffs, revenue sharing achieves the first best outcome by softening retail price competition without distorting retailers' inventory decisions. Our theories are also consistent with trends in prices and availability following retailers' adoption of revenue sharing contracts.     

AN INVENTORY MODEL FOR DETERIORATING ITEMS WITH STOCK-DEPENDENT DEMAND UNDER THE CONDITIONS OF INFLATION AND TIME-VALUE OF MONEY

In this paper, we incorporate the effects of inflation and time-value of money in inventory decision making when demand, at each time moment rather than being constant, is considered to be dependent upon current stock level. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be linearly dependent on the amount of demand backlogged. We shall be concerned with finding the optimal number of replenishments and service rate to minimize the total relevant costs over a finite planning horizon. Numerical examples are presented to illustrate the proposed models.     

Coordination of a production network with a single buyer and multiple vendors

This article considers a single buyer sourcing a single product from a network of homogeneous suppliers. We assume a close and cooperative relationship between buyer and vendors and suggest two coordination mechanisms, which differently affect where inventory is held in the system. Accordingly, we derive analytical and heuristic solutions for both alternatives and study the relative advantage of the models in a sensitivity analysis. Finally, propositions for future research are presented.     

A Model of Supplier Integration into New Product Development*

In many industries, firms are looking for ways to cut concept‐to‐customer development time, to improve quality, and to reduce the cost of new products. One approach shown to be successful in Japanese organizations involves the integration of material suppliers early in the new product development cycle. This involvement may range from simple consultation with suppliers on design ideas to making suppliers fully responsible for the design of components or systems they will supply. While prior research shows the benefit of using this approach, execution remains a problem. The processes for identifying and integrating suppliers into the new product development (NPD) process in North American organizations are not understood well. This problem is compounded by the fact that design team members often are reluctant to listen to the technology and cost ideas made by suppliers in new product development efforts. We suggest a model of the key activities required for successful supplier integration into NPD projects, based on case studies with 17 Japanese and American manufacturing organizations. The model is validated using data from a survey of purchasing executives in global corporations with at least one successful and one unsuccessful supplier integration experience. The results suggest that (1) increased knowledge of a supplier is more likely to result in greater information sharing and involvement of the supplier in the product development process; (2) sharing of technology information results in higher levels of supplier involvement and improved outcomes; (3) supplier involvement on teams generally results in a higher achievement of NPD team goals; (4) in cases when technology uncertainty is present, suppliers and buyers are more likely to share information on NPD teams; and (5) the problems associated with technology uncertainty can be mitigated by greater use of technology sharing and direct supplier participation on new product development teams. A supplier's participation as a true member of a new product development team seems to result in the highest level of benefits, especially in cases when a technology is in its formative stages.