A master production scheduling procedure for stochastic demand and rolling planning horizons

The problem of interest is a one product, uncapacitated master production schedule (MPS) in which decisions are made under rolling planning horizons. Demand is stochastic and time varying, and effectiveness is measured by inventory holding, production setup, and backorder costs.Typically, in both the research literature and the business practice the stochastic nature of the problem is modeled in an ad hoc fashion. The stochastic MPS problem is usually solved by adding safety stock to production quantities obtained from a deterministic lot-sizing algorithm. Here, the stochastic nature of the problem is explicitly considered, as an optimal algorithm for solving the static probabilistic dynamic lot-sizing problem is adapted to rolling planning horizons. The resulting algorithm is found to dominate traditional approaches over a wide variety of experimental factors, reducing total costs by an average of 16% over traditional methods.     

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.     

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.     

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.     

Production lot sizing with a secondary outsourcing facility

An extended economic production quantity (EPQ) model under stochastic demand is investigated in this paper, where a fixed lot sizing policy is implemented to reduce the complexity of production planning and inventory control, and outsourcing with a secondary facility is used to supplement the lot sizing policy and to cope with the random demand. The considered cost includes: setup cost for the batch production, inventory carrying cost, backorder cost when the demand cannot be met immediately during the production period, and outsourcing cost when the total demand is greater than the lot size in one replenishment cycle. Under some mild conditions, the expected cost per unit time can be shown to be convex. Extensive computational tests have illustrated that the average cost reduction of the proposed model is significant when compared with that of the classical lot sizing policy. Significant cost savings can be achieved by deploying the production lot sizing policy with an outsourcing strategy when the mean demand rate is high.     

Integrated safety stock optimization for multiple sourced stockpoints facing variable demand and lead time

The safety stock placement problem of a multi-stage supply chain comprising multiple sourced stockpoints is addressed in this paper. Each stockpoint faces variability in its downstream demand and suppliers' lead time. The maximum among these suppliers' lead time is determined by employing concepts of order statistics. It is required to find the fill rate and safety stocks at each stockpoint that leads to satisfying the end customer service level at minimum safety stock placement cost. Hence, the fill rates and the safety amounts are decided from a global supply chain perspective. Two models are proposed; a decentralized safety stock placement model and a centralized consolidation model. The decentralized model finds the safety amounts at each stockpoint required to face its underlying lead time demand variability. The consolidation model finds the consolidated safety amounts that will be kept in the relevant consolidation center at each stage. A Benders decomposition technique is developed to handle the nonlinearity and binary restrictions involved in the safety stock consolidation model. Strategies proposed by the consolidation model achieve 45.2-62% reduction in safety amounts that results in a cost savings ranging between 22.2-44.2% as compared to the strategies proposed by the decentralized model.     

Stocking decisions for repairable spare parts pooling in a multi-hub system

This paper presents an analytical model for determining spare parts stocking levels in a single-item, multi-hub, multi-company, repairable inventory system in which complete pooling of stock is permitted among the hubs and companies. The objective is to minimize the total system cost which consists of inventory holding cost, downtime cost and transshipment cost. We develop an approximation method to compute the logistical system performance measures needed for calculating the cost function. To find the optimal stocking levels, a two-stage solution is proposed. In the first stage, the demands at all hubs are aggregated and treated as if occurring at a single location. The optimal number of total spare parts is determined by minimizing the sum of inventory holding cost and downtime cost. In the second stage, a heuristic procedure is developed to find the optimal allocation of the total spare parts to minimize the total transshipment cost.     

西部地区成品油合理库存探讨

针对西部地区成品油库存管理,在保障市场稳定供应的前提下,为提升成品油库周转效率,降低库存成本占用及库存油品跌价风险,本文按照油库类型、运输方式、订货周期分类,利用不确定性库存管理模型,有效测算西部地区零售(省区公司)、批发企业(大区公司)油库的合理库存;同时考虑西部地区固有的季节性产销因素,按照成品油库存淡储旺销调剂模式,确定包含季节因素的西部地区整体合理库存.测算结果与实际情况符合较好,可以有效指导销售企业进行实际库存管理.此外,文章还对西部地区合理库存测算的影响因素进行了分析,指出了改进的方向.     

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.     

采油厂修井作业物资精益生产体系的建立和运行

在油田开发建设中,修井作业是原油生产周期的重要保障。通过运用潜在失效模式与后果分析失效模式对生产周期小于400d的1 116井次油井进行分析,发现抽油杆、油管失效比例占作业井次的53.1%,将其作为重点质量改进方向。在建立精益生产体系过程中,创新性地对油管修复线节拍时间、安全库存量等进行了计算,探索出修复线每日8h修复4 000m的节拍时间7.2s,Φ62mm和Φ76mm的安全库存是400根和300根。     

Integrating noncyclical preventive maintenance scheduling and production planning for a single machine

This paper deals with the problem of integrating noncyclical preventive maintenance and tactical production planning for a single machine. We are given a set of products that must be produced in lots during a specified finite planning horizon. The maintenance policy suggests possible preventive replacements at the beginning of each production planning period, and minimal repair at machine failure. The proposed model determines simultaneously the optimal production plan and the instants of preventive maintenance actions. The objective is to minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. The problem is solved by comparing the results of several multi-product capacitated lot-sizing problems. The value of the integration and that of using noncyclical preventive maintenance when the demand varies from one period to another are illustrated through a numerical example and validated by a design of experiment. The later has shown that the integration of maintenance and production planning can reduce the total maintenance and production cost and the removal of periodicity constraint is directly affected by the demand fluctuation and can also reduce the total maintenance and production cost.     

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.     

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.     

Evaluation of postponement in the soluble coffee supply chain: A case study

This paper, through a case study, evaluates postponement as an option to improve supply chain performances in a soluble coffee manufacturer. The main focus of the paper is on the development of a numerical data-driven methodology for quantifying the benefits of postponement obtained from the total inventory reduction. Our study shows that significant cost savings are achievable by delaying the labelling and packaging processes until actual orders from retailers are known. These savings include the reduction of the cycle stock, safety stock, and obsolete stock unsold from promotional events. We also discuss the cost implications of the proposed configuration that may offset the estimated potential benefits. The methodology presented in this paper can also be used in many other supply chains, particularly in the food industry with similar environments. This paper contributes to the literature in extending the very short list of published work presenting a systematic methodology of characterising the postponement benefits in real world settings and driven by numerical data.     

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.     

Dynamic lot sizing problem with continuous-time Markovian production cost

This paper develops a polynomial algorithm for obtaining dynamic economic lot sizes in a single product multiperiod production system with the objective of minimizing total production and inventory costs over T periods. It is assumed that production costs are linear, inventory costs are concave, setup costs are zero and backlogging is not permitted in all periods. Moreover, the unit production cost is a stochastic variable, which is evolved according to a continuous-time Markov process over the planning horizon. The model is formulated as a stochastic dynamic programming (DP) optimization with the state variable being unit production cost. Then, it is solved using the backward dynamic programming approach. To justify the application of the proposed model, two practical cases are presented.     

油田开发生产成本测算初探

油田开发生产成本占到油田总成本的85％左右,是油田管理水平的直接体现。通过对油田未来各年度评价井、产建井及措施工作量的预测,结合作业成本法将油田开发成本细分为各作业中心成本,并确定油田开发生产总成本.     

A fuzzy random continuous review inventory system

A fuzzy random continuous review system has been presented in this paper with the annual customer demand assumed to be a uniformly distributed continuous fuzzy random variable. Besides the reorder point and the production lot size, the setup cost and the ‘out of control’ probability for a production process have been assumed to be control parameters in the model. Investments to reduce the setup cost and improve the process quality have been incorporated into the total cost in this regard. A methodology has been proposed to minimize this cost and it has been illustrated by way of a numerical example.     

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.