A joint economic lot size model for raw material ordering,manufacturing setup,and finished goods delivering

In this research we consider a single-manufacturer single-buyer supply chain problem where the manufacturer orders raw materials from its supplier, then using its manufacturing processes converts the raw materials to finished goods, and finally delivers the finished goods to its customer. The manufacturer produces the product in batches at a finite rate and periodically delivers the finished goods at a fixed lot size to its customer, who has a constant demand rate. An integrated inventory control model, making joint economic lot sizes of manufacturer's raw material ordering, production batch, and buyer's ordering, is developed to minimize the mean total cost per unit time of the raw materials ordering and holding, manufacturer's setup and finished goods holding, the buyer's ordering, and inventory holding. Numerical examples are also setup to illustrate that jointly considering the inventory costs above results in less mean total cost than that of considering them separately.     

Integrated procurement- production system in a just-in-time environment-modelling and analysis

Classically, economic lot size models have been used separately for procurement and production subsystems. However, when the raw materials are used in production, the procurement policies are dependent on the schedule and the batch size for the product. Hence, it is necessary to unify the procurement and production policies. The just-in-time JIT environment provides an ideal setting for such a coordination between the procurement and production policies. The model proposed here is a traditional inventory model recast into a model for a JIT system for a single product, multistage batch environment aiming at the minimization of total variable cost and thereby determining the batch sizes for the product and raw material order sizes. A JIT system aims at minimizing setup time and this feature is captured in the proposed model. The computational experience reported in this paper is based on a number of simulated problem sets. The possible domain of application is also highlighted.     

回收物流库存控制研究

本文探讨了包含回收品的库存系统。回收物流库存中既有一般生产过程的新产品,也有经再制造的回收品,使其最优库存策略非常复杂,论文推导出不同控制方式下的EOQ模型,以确定最优生产和再制造批量。此外,还对求得的最优批量进行适当的调整,以确保在循环周期中的定货次数为整数。该模型形式、结构简单易于在实践中应用。     

一种考虑原材料库存成本的变质物品EPQ模型

在库存管理研究中,单独实现产成品或原材料库存成本最小,往往无法获得整个库存系统的最优控制策略.本文提出了一种同时考虑产成品和原材料库存成本的变质物品EPQ集成模型.运用迭代寻优法得到模型最优解,得出计划期内最优原材料订购次数,原材料订购周期内的最优生产次数和最优服务水平,并对主要参数进行了灵敏度分析,为生产制造企业的库存管理提供了决策依据.     

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.     

Materials receiving capacity and inventory management

This paper analyses the optimal level of materials receiving capacity for a manufacturer that receives deliveries from many suppliers. Inventory levels and inventory carrying costs depend on the frequency of deliveries and thus, on the materials receiving capacity. An analytic model that captures the tradeoff between inventory costs and materials receiving costs is presented and discussed. The receiving cost is modeled as increasing in discrete jumps of varying sizes whenever materials receiving resources are added. Practical issues in implementing the model are highlighted and methods to reduce the marginal materials receiving cost are discussed. The paper also discusses connections to the JIT approach for production environments where materials receiving is heavily automated.     

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.     

Cost models for lot streaming in a multistage flow shop

Lot streaming is a technique used to split a processing batch into several transfer batches. In this way, overlapping operations can be performed in different manufacturing stages, and production can be accelerated. This paper proposes two cost models for solving lot streaming problems in a multistage flow shop. The purpose is to determine the optimal processing batch size and the optimal number of transfer batches that minimize the total annual cost in each model. In the first model, a more complete and accurate method is developed to compute the costs of raw materials, work-in-process, and finished-product inventories. The total cost includes the setup cost, the transfer batch movement cost, the three-type inventory holding cost, and the finished-product shipment cost. The second model contains not only the four costs in the first model, but also the imputed cost associated with the makespan time. The total annual cost functions in both models are shown to be convex, and two solution approaches are suggested. An experiment consisting of three phases was conducted to explore the effect on the optimal solution when changing the value of one parameter at a time. The results indicate that three parameters have significant effects on the optimal solution.     

A COMPARISON OF DIRECT COST SAVINGS BETWEEN FLEXIBLE AUTOMATION AND LABOR WITH LEARNING

This paper compares flexible automation with labor‐intensive manufacturing processes in a batch production environment and considers learning, forgetting, inventory carrying costs, setup costs, production demand volume, previous production experience, and the proportion of material to labor cost. While flexible automation typically can reduce setup times, and therefore inventory carrying costs through smaller optimal batch sizes, the results of this research show that the effect of forgetting on relative cost savings is difficult to predict in some situations. When using optimal lot sizes in both the automated and labor environments, cost savings from flexible automation may be smaller than expected or may occur in different ways than anticipated.     

Coordinated scheduling of production and delivery stages with stage-dependent inventory holding costs

This paper considers a problem of integrated decision-making for job scheduling and delivery batching wherein different inventory holding costs between production and delivery stages are allowed. In the problem, jobs are processed on a facility at a production stage and then delivered at the subsequent delivery stage by a capacitated vehicle. The objective is to find the coordinated schedule of production and delivery that minimizes the total cost of the associated WIP inventory, finished product inventory and delivery, where both the inventory costs are characterized in terms of the weighted flow-time and the delivery cost is proportional to the required number of delivery batches. It is proved that the problem is NP-hard in the strong sense. Thereupon, three heuristic algorithms are derived. Some restricted cases are also characterized as being solvable in polynomial time. Numerical experiments are conducted to evaluate the performance of the derived heuristic algorithms.     

Determination of economic production quantity in a multi-stage production system

In this paper two models have been suggested for determining economic production quantity in a multi-stage production system. The demand for the product is assumed constant and it is supplied by manufacturing the product in equal production runs. The production lot is transported in a number of sub-batches of equal sizes. Each sub-batch is processed on the production stages without wait during process. As a result of processing the sub-batches without wait during process, the processing on the production stages is interrupted. Expressions have been derived for the manufacturing cycle time, the total process inventory and the finished product inventory and then total variable cost models have been suggested and manipulated for obtaining the economic production quantity.     

Transportation Approach to Locating Plants in Relation to Potential Markets and Raw Material Sources

Proximity to the market place has been considered the most important locational factor in the literature so far. However, the growing need for frequent deliveries of materials in smaller lot sizes for just-in-time (JIT) manufacturing prefers plants closer to the raw materials sources. Locating plants for JIT manufacturing is, therefore, a problem of finding the right balance between the requirements of procurement and distribution. A comprehensive model is proposed in this paper to solve this problem. The model is solved by using the transportation algorithm and produces simultaneous decisions on procurement, production, and distribution. The model does not require plant sizes to be known a priori, but it allows upper limits to be placed on the size of each plant and raw material source. As such, optimal plant capacities along with the corresponding procurement and distribution quantities are all determined by the model solution.     

Lot sizing in workload control systems

An important basis for workload control (WLC) is the existence of functional relationships between the mean level of work-in-process (WIP) and the values of important goal variables, like average flow time, capacity utilization, etc. These functional relationships are largely influenced by the lot sizes. This means that the usual objective of lot sizing must be supplemented by considering the impact of lot sizes on the relationships between WIP and the other goal variables. Here it is shown that this insight leads to flow time oriented lot sizing models. This type of lot sizing models is analysed. It is argued that the derivation of simple rules for lot sizing is an important research topic, and a model for deriving such rules is presented. Some rules are derived from the model, assuming that the batches are processed by an M/G/1 server, and it is shown that these rules support insights based on simulation in the 1980s. Topics for future research are outlined as well.     

Optimizing multi-stage production with constant lot size and varying number of unequal sized batches

This paper describes a model for a multi-stage production/inventory system in which a uniform lot size is produced through all stages with a single setup and without interruption at each stage. Partial lots, called batches, may be transported to the next stage upon completion. The number of the unequal sized batches may differ across stages. Considering setup costs, inventory holding costs, and transportation costs, an optimization method is developed to determine the economic lot size and the optimal batch sizes for each stage. The method is illustrated by a computational example and further numerical simulations.     

A new EPQ model: integrating lower pricing,rework and reject situations

The economic production quantity (EPQ) is a well-known and commonly used inventory control technique. It has been used for well over 50 years to optimize lot sizes in transportation/production. The standard results are easy to apply but are based on a number of assumptions. A common assumption in the EPQ model is that all units produced are of perfect quality, this will underestimate the actual required quantity. Many researchers have studied the effects after relaxing this assumption on the EPQ model. The previous studies had considered that imperfect quality and defective items are either to be reworked instantaneously and kept in stock or rejected at a cost. The objective of this paper is to provide a framework to integrate lower pricing, rework and reject situations into a single EPQ model. A 100% inspection is performed in order to identify the amount of good quality items, imperfect quality items and defective items in each lot. This model assumes that items of imperfect quality, not necessarily defective, could be used in another production situation or sold to a particular purchaser at a lower price. The electronic and clothing industries give good examples for such situations. A mathematical model is developed and a numerical example is presented to illustrate the solution procedures. It is found that the time factor of when to sell the imperfect items is critical, as this decision will affect the inventory cost and the batch quantities.     

Discrete time-varying demand lot-sizing models with learning and forgetting effects

This paper deals with the problem of incorporating both learning and forgetting effects into discrete timevarying demand lot-sizing models to determine lot sizes. Forgetting is retrogression in learning which causes a loss of labour productivity due to breaks between intermittent production runs. Formulae are derived for calculating the production cost required to produce the first unit of each successive lot over a finite planning horizon. An optimal lotsizing model and three heuristic models are developed by extending the existing models without learning and forgetting considerations. Numerical examples and computational experience indicate that larger lot sizes are needed when the phenomenon of learning and forgetting exists. Several important conclusions are drawn from a comparison of the three heuristic solutions with the optimal solution, and suggestions for future research and for lot-size users to choose an appropriate lot-sizing technique are made.     

Process Mean Determination with Quantity Discounts in Raw Material Cost*

Setting the mean (target value) for a container-filling process is an important decision for a producer when the material cost is a significant portion of the production cost. Because the process mean determines the process conforming rate, it affects other production decisions, including, in particular, the production setup and raw material procurement policies. In this paper, we consider the situation in which quantity discounts exist in the raw material acquisition cost, and incorporate the quantity-discount issue into an existing model that was developed for simultaneously determining the process mean, production setup, and raw material procurement policies for a container-filling process. The product of interest is assumed to have a lower specification limit, and the items that do not conform to the specification limit are scrapped with no salvage value. The production cost of an item is proportional to the amount of the raw material used in producing the item. A two-echelon model is formulated for a single-product production process, and an algorithm is developed for finding the optimal solution. A sensitivity analysis is performed to study the effects of the model parameters on the optimal solution.     

Optimal two-stage production-inventory policy with whole lot and split lots

This paper deals with the problem of determining the optimal lot sizes for a two-stage production-inventory system. The first stage has a large lot to be processed in a single batch and is called the ‘whole lot’; this is split in the second stage into smaller lots of equal size called ‘split lots’. The lot in stage 1 is inspected for its conformity to standards before it is passed on to stage 2. We use a single sampling attribute plan for inspection and examine the consequences of rejecting or accepting the lot. The rejected lots are 100 % inspected and defectives are eliminated..The accepted lots contain defectives in the uninspected part which are identified during stage 2 processing. We have combined these aspects of inspection with the usual inventory costs and developed a model to determine the optimal sizes of the whole lot and split lots     

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.