An integrated production-inventory model with reprocessing and inspection

Competitive pressures continually force management to examine cost and quality levels of production systems. In this paper these issues are addressed via a model that synthesizes several potential features of production systems: production processes, quality control procedures, in-process inventory and reprocessing. For any specified inspection configuration the model can be used, for serial production systems, to obtain closed-form expressions for two important decision variables: optimal lot size and reprocessing batch size, which minimize the total system costs. A numerical example highlights the interdependencies and the role of various system features in determining the values of the decision variables and hence in reducing the total costs. The paper also discusses the managerial implications of the model.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

Infinite horizon production planning with periodic demand: solvable cases and a general numerical approach

In this paper, we consider a single part-type pull manufacturing system, which controls its production rates in response to periodic demand. When tracking the demand results in a product surplus, an inventory storage cost is incurred. Likewise, if an overall shortage occurs then a backlog cost is paid. In addition, production costs accrue when the system is not idle. Given an infinite planning horizon, the objective is to determine the cyclic production rates in order to minimize the total cost. With the aid of the maximum principle, extremal behavior of the system is studied and the continuous-time production planning problem is reduced to a discrete problem with a limited number of switching points at which time the production rates change. Using this result, an efficient numerical algorithm is proposed, which will yield an approximation to the optimal solution within any desired level of accuracy. In addition, we determine the analytical solution to the problem for three special cases: (i) the system capacity is not limited and the inventory storage cost factor is equal to the backlog cost factor; (ii) the production cost is negligible; and (iii) the surplus and shortages costs are negligible.     

Joint production and shipment lot sizing for a delivery price-based production facility

A joint economic production quantity (EPQ) and delivery quantity model for a production system is investigated in this paper. More specifically, an EPQ policy is implemented in the production system, while a smaller shipping quantity is periodically dispatched to the customer. The production system is also responsible for the shipment cost, i.e. a delivery price-based procurement from the customer. The considered cost includes setup cost to launch the batch production, inventory carrying cost, and transportation cost, where the transportation cost is a function of the delivery quantity. A per unit time cost model is developed and analysed to determine the optimal production and delivery quantities. Under some mild conditions, it can be shown that the joint cost function is convex with respect to the production quantity; and the number of delivery is an integer in each replenishment cycle. Computational study has demonstrated the significant impact of the joint decision model on the operating cost. In particular, the reduction in total cost can be more than 15% when inventory carrying costs, and/or transportation costs, are high.     

Simulation of an integrated age replacement and spare provisioning policy using SLAM

This paper presents a SLAM simulation model for determining a jointly optimal age replacement and spare part provisioning policy. The policy, referred to as a stocking policy, is formulated by combining age replacement policy with a continuous review (s, S) type inventory policy, where s is the stock reorder level and S is the maximum stock level. The optimal values of the decision variables are obtained by minimizing the total cost of replacement and inventory. The simulation procedure outlined in the paper can be used to model any operating situation having either a single item or a number of identical items. Results from a number of case problems specifically constructed by 5-factor second order rotatory design have been presented and the effects of different cost elements, item failure characteristics and lead time characteristics have been highlighted. For all case problems, optimal (s, S) policies to support the Barlow-Proschan age policy have also been determined. Simulation results clearly indicate the separate optimizations of replacement and spare provisioning policies do not ensure global optimality when total system cost has to be minimized.     

The Acquisition of Automation Subject to Diminishing Returns

In this paper, it is assumed that the purchase of automation has the effect of reducing the per unit production and in-process inventory costs. The optimal dynamic mix of automation and manual output is derived to minimize the cost incurred over the planning horizon due to (1) deviating from the future goal levels of output, (2) production, (3) inventory, (4) changing the level of manual output, and (5) acquiring automation. The cost of purchasing automation and the effectiveness of automation on reducing the per unit. production and in-process inventory costs are expressed as functions of time to include the impact of learning or anticipated technological advancement. Furthermore, the effectiveness of automation on reducing the per unit production and in-process inventory costs is assumed to decrease as the level of automation held by the organization increases due to diminishing returns. We show that it is rarely optimal to increase automation without simultaneously modifying the level of manual output. In addition, a numerical solution algorithm is presented to compute the optimal times and levels of changes in automation and manual output.     

Effects of forecast errors on optimal utilisation in aggregate production planning with stochastic customer demand

The hierarchical structure of production planning has the advantage of assigning different decision variables to their respective time horizons and therefore ensures their manageability. However, the restrictive structure of this top-down approach implying that upper level decisions are the constraints for lower level decisions also has its shortcomings. One problem that occurs is that deterministic mixed integer decision problems are often used for long-term planning, but the real production system faces a set of stochastic influences. Therefore, a planned utilisation factor has to be included into this deterministic aggregate planning problem. In practice, this decision is often based on past data and not consciously taken. In this paper, the effect of long-term forecast error on the optimal planned utilisation factor is evaluated for a production system facing stochastic demand and the benefit of exploiting this decision’s potential is discussed. Overall costs including capacity, backorder and inventory costs, are determined with simulation for different multi-stage and multi-item production system structures. The results show that the planned utilisation factor used in the aggregate planning problem has a high influence on optimal costs. Additionally, the negative effect of forecast errors is evaluated and discussed in detail for different production system environments.     

An integrated model for inventory and production planning in a two-stage hybrid production system

A two-stage hybrid flow-shop production system is considered. The first stage is a process production system and the second stage is a job-shop production system. The two stages are separated by an intermediate warehouse to introduce flexibility (some independence) in the planning of production at both stages. The inventory level at the warehouse should be optimized to provide a trade-off between the cost of carrying the inventory of the semi-finished products, the minimum batch size requirement in the first stage, and the required service level at the second stage. An integrated model for planning the production in these hybrid flow-shop production systems types is developed. The objectives of optimizing the production and inventory costs at the two stages of the system, including the warehouse, while satisfying customer demands, are considered. An algorithm to solve the suggested model is described in detail, and a solution is provided for a real world case, which has inspired the study. A computational study to measure the performance of the approach was also carried out and the results are reported.     

回收努力影响下循环物流包装库存策略优化

目的 解决循环物流包装放置混乱造成循环物流包装返回率低、循环物流包装运营成本增加的问题。方法 在循环物流包装库存模型中引入回收努力作为决策变量,建立非线性规划模型,分析循环物流包装的最优检查周期、购买周期和最优回收努力水平的决策问题,设计迭代算法进行求解。比较分销商投入回收努力与不投入回收努力情况下系统的总成本和决策变量。结果 包装的最优检查周期为2.78,最优购买周期为4.88,分销商最优努力水平为230.96,系统总成本降低了42%,循环物流包装的检查周期缩短了49%,购买周期缩短了13%。结论 在循环物流包装的应用中,加强对循环物流包装管理流程的培训力度有利于循环物流包装系统更有效的运行。     

Effective investment to reduce lost-sales rate in a periodic review inventory model

In 1973 Montgomery et al. proposed an (R, T) type of a periodic review inventory model in which the lost-sales rate caused by stockout is given. The purpose of this article is to investigate in this heuristic periodic review inventory model with partial lost-sales to effectively increase investment and to reduce the lost-sales rate. We discuss two models: complete (normal distribution) and partial (distribution free) information about the protection interval (i.e., review period plus lead time) demand distribution. For each model, two commonly used investment cost functional forms, logarithmic and power, are employed for lost-sales rate reduction. That is, for these two investment cost functions, we first assume that the protection interval demand follows a normal distribution, and then we assume that only first and second moments of the probability distribution of protected interval demand are known. Two algorithms are developed to find the optimal investment decision, and six numerical examples are given to illustrate the results.     

Flexible work-in-process production system in supply chain management under quality improvement

For a complex product production, any flexible manufacturing system with a work-in-process inventory is recommended for a supply chain management (SCM) system. Building a flexible manufacturing system increases the total cost of the supply chain; for this reason, a discrete investment is important. For flexible production systems, production rate within a finite specific interval of production rate as work-in-process inventory is calculated. The aim of the supply chain is to reduce the total cost when demand during the lead time is a random variable with a normal distribution. A crashing cost is utilised to reduce the duration of lead time within the supply chain system. A model is proposed to obtain the optimal flexible production rate with the reduced total cost of the supply chain. A classical optimisation technique is employed to obtain the closed-form and quasi-closed-form solutions of the decision variables. An improved algorithm is designed to obtain the global minimum cost of SCM under the framework of a flexible production system. An illustrative numerical example and sensitivity analysis are given to test the model. A numerical study proves that this model obtains the minimum cost with the optimal decision variables.     

A membership function approach to lot size re-order point inventory problems in fuzzy environments

Inventory models play an important role in logistics and supply chain management for reducing cost and increasing customer satisfaction. This paper develops an approach to derive the fuzzy objective value and decision variables of the fuzzy lot size re-order point inventory problem with parameters being fuzzy numbers and the shortages are backordered with extra cost incurred. Different from the existing studies, the idea is based on Zadeh's extension principle. A pair of mixed integer nonlinear programs (MINLP) parameterised by the possibility level α is formulated to calculate the lower and upper bounds of the minimal total cost per unit time at α, through which the membership function of the minimal total cost per unit time is constructed. At the same time the membership functions of the optimal order quantity and the optimal re-order point are also provided. A numerical example studied by previous studies is solved successfully to demonstrate the validity of the proposed method. Compared with previous studies, the obtained results which precisely and completely conserve the fuzziness of the input information are more informative for finding the best inventory policy since they are expressed by membership functions rather than by crisp ones. Moreover, to provide representative crisp solutions for designing inventory systems, the Yager's ranking index method is adopted to defuzzify the obtained membership functions. The successful extension of inventory models to fuzzy environments permits inventory models to have wider applications in practice.     

SETTING SAFETY LEADTIMES FOR PURCHASED COMPONENTS IN ASSEMBLY SYSTEMS

We consider the problem of setting appropriate safety leadtimes in an assembly system where all components are purchased and the only manufacturing operation is final assembly. First, we describe two formulations of this problem: (1) minimize total inventory carrying and tardiness costs and (2) minimize inventory carrying costs subject to a service constraint. Second, we discuss how these formulations sometimes fail to adequately provide a decision maker with sufficient information to establish leadtimes when applied independently but how they can be used together to provide a useful decision support system. Finally, we describe a procedure similar to ABC analysis that allows us to solve a much smaller related problem whose solution provides a good approximation to the solution of the original problem. We conclude the paper with numerical examples and a discussion of an actual implementation.     

Development of an optimal core steel slitting and inventory policy

The objective of this investigation is to develop an optimal slitting and inventory policy for a deterministic demand of steel over a finite planning horizon. The cost function includes the inventory carrying cost and the cost of scrap steel generated besides the usual fixed costs. The minimum of this cost function is obtained by using a combination of dynamic programming and integer linear programming which provides a practical and sound procedure. Actual data is used to determine the optimal solution for a planning horizon of ten weeks.     

Capacitated dynamic lot sizing with capacity acquisition

One of the fundamental problems in operations management is determining the optimal investment in capacity. Capacity investment consumes resources and the decision, once made, is often irreversible. Moreover, the available capacity level affects the action space for production and inventory planning decisions directly. In this article, we address the joint capacitated lot-sizing and capacity-acquisition problems. The firm can produce goods in each of the finite periods into which the production season is partitioned. Fixed as well as variable production costs are incurred for each production batch, along with inventory carrying costs. The production per period is limited by a capacity restriction. The underlying capacity must be purchased up front for the upcoming season and remains constant over the entire season. We assume that the capacity acquisition cost is smooth and convex. For this situation, we develop a model which combines the complexity of time-varying demand and cost functions and of scale economies arising from dynamic lot-sizing costs with the purchase cost of capacity. We propose a heuristic algorithm that runs in polynomial time to determine a good capacity level and corresponding lot-sizing plan simultaneously. Numerical experiments show that our method is a good trade-off between solution quality and running time.     

区间数多产品多计划期生产计划问题的目标规划求解方法

针对多目标、多产品、多计划期和需求、生产费用、生产能力等参数不确定的综合生产计划问题进行了研究。引入区间数描述生产计划问题中存在的不确定性,建立了以生产成本最小和设备利用率最大为优化目标的目标规划模型。为求解模型,运用区间规划理论和基于区间序关系的可能度定义,实现了区间目标规划模型的清晰等价转换,并采用Lingo软件完成模型求解。该方法解决了传统不确定优化方法在获取概率分布和模糊隶属度函数较为困难的不足,能根据决策者的偏好以交互方式分析出不同置信水平对目标的影响,为决策者在不确定环境下进行生产计划决策提供理论依据。最后,通过算例说明方法的有效性和灵活性。     

A CAPACITY PLANNING MODEL FOR A MULTI-PRODUCT FACILITY

A deterministic capacity planning model for a multi-product facility is analyzed to determine (he sizes to be expanded (or disposed of) in each period so as to supply the known demand for N products on time and to minimize the total cost incurred over a finite planning horizon of T periods. The model assumes that each capacity unit of the facility simultaneously serves a prespecified number of demand units of each product, that costs considered include capacity expansion costs, capacity disposal costs, and excess (idle) capacity holding costs, and all the associated cost functions are nondecreasing and concave, and that backlogging is not allowed. The structure of an optimal solution is characterized and then used in developing an efficient dynamic programming algorithm that finds optimal capacity planning policies. The required computational effort is a polynomial function of N and T.     

Optimal production control policy in unreliable batch processing manufacturing systems with transportation delay

This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuously meet a constant demand rate. The main objective of this work is to jointly determine the optimal lot sizing and optimal production control policy that minimise the total expected cost of inventory/backlog and transportation, over an infinite time horizon. The decision variables are the lot sizing and the production rate. The problem is formulated with a stochastic dynamic programming model and the impulse control theory is applied to establish the Hamilton–Jacobi–Bellman (HJB) equations. Based on a numerical resolution of the HJB equations, it is shown that the optimal control policy is governed by a base stock policy for production rate control and economic lot size for batch processing. A thorough analysis and practical issues are addressed with a simulation-based approach. Thus, a combined discrete–continuous simulation model is developed to determine the optimal parameters of the proposed policy when the failure and repair times follow general distributions. The results are illustrated with numerical examples and confirmed through sensitivity analysis.     

订单式生产下汽车零配件企业采购决策研究

为解决传统JIT模式下供应链非主导的汽车零配件厂面临的巨大交付压力与高昂存货管理成本问题,基于MTO订单式生产下汽配厂的原材料供应现状,对其原材料进行两步分类得出3类原材料,分别建立以最小化存货成本的多周期动态规划模型,并推出其最优采购策略。最后,采用M企业实际运营数据进行对比分析,发现最优策略下的原材料存货周转天数显著缩短、库存成本显著降低,验证了优化策略的可行性及有效性。     

Optimal leadtimes planning in serial production systems with earliness and tardiness costs

We consider a production system consisting of N processing stages. The actual leadtimes at the stages are stochastic. The objective is to determine the planned leadtimes at each stage so as to minimize the expected total inventory costs, tardiness penalties, and a backlog penalty for not meeting demand due date at the last stage. Recursive relationships are used for automatic generation and efficient computation of the objective function. The efficiency of the proposed algorithms allows us to obtain new insights regarding operating policies, leadtime delivery reliability, and production line design. The problem is formulated as a convex non-linear programming problem. The latter is then solved using classical convex optimization algorithms. For the special case of exponentially distributed leadtimes, the objective function is derived in a closed form.