A dynamic lot sizing model with exponential machine breakdowns

This paper addresses the dynamic lot sizing model with the assumption that the equipment is subject to stochastic breakdowns. We consider two different situations. First we assume that after a machine breakdown the setup is totally lost and new setup cost is incurred. Second we consider the situation in which the cost of resuming the production run after a failure might be substantially lower than the production setup cost. We show that under the first assumption the cost penalty for ignoring machine failures will be noticeably higher than in the classical lot sizing case with static demand. For the second case, two lot sizes per period are required, an ordinary lot size and a specific second (or resumption) lot size. If during the production of a future period demand the production quantity exceeds the second lot size, the production run will be resumed after a breakdown and terminated if the amount produced is less than this lot size. Considering the results of the static lot sizing case, one would expect a different policy. To find an optimum lot sizing decision for both cases a stochastic dynamic programming model is suggested.     

Solving the Generalized Machine Assignment Problem in Group Technology

Many existing solution methodologies for machine assignment problems in group technology do not consider factors such as part demand, operation sequence and cost of intercellular moves. We formulate a 0-1 quadratic programming model that takes into account these factors in machine assignment. Two approaches are proposed to solve this problem. The first is an A*-based approach that generates optimal solutions. The second is a heuristic approach developed to solve problems with large number of machines and/or parts. The heuristic approach is shown to be efficient in producing good solutions in a computational study.     

An economic production lot-size model with shortages and time-dependent demand

In the present article, a production-inventory model is developedover an infinite plan ning horizon where the demand varies linearlywith time, unit production cost is taken as a function of theproduction rate, and shortages in inventory are permitted andare fully back-ordered. The machine production rate, which isassumed to be flexible, is treated as a decision variable. Theassociated nonlinear programming problem is modified by usingthe barrier-function method, and then a search technique isused to find the solution numerically. The analysis of the presentmodel of the production system points to optimality under conditionsthat are commonly recognized as ‘just in time’.     

Knapsack-based Algorithms for Designing Cellular Manufacturing Systems

In this paper, we use a 0–1 linear programming model for the machine assignment problem in cellular manufacturing. The formulated machine assignment problem considers many manufacturing factors such as machine utilization cost, cost of intercellular moves, part demand, and operating time capacity. The problem is shown to be NP-complete. Two designing algorithms are proposed to exploit the problem structure of the knapsack problem. Computational experience of the two algorithms is also reported.     

Fuzzy programming and profit and cost allocation for a production and transportation problem

In this paper, we deal with a real problem on production and transportation in a housing material manufacturer, and consider a production and transportation planning under the assumption that the manufacturer makes multiple products at factories in multiple regions and the products are in demand in each of the regions. First, we formulate mixed zero–one programming problems such that the cost of production and transportation is minimized subject to capacities of factories and demands of regions. Second, to realize stable production and satisfactory supply of the products in fuzzy environments, fuzzy programming for the production and transportation problem is incorporated. Finally, under the optimal planning of production and transportation, we show a profit and cost allocation by applying a solution concept from game theory. Using actual data, we show usefulness of the fuzzy programming and a rational allocation scheme of the profit and cost.     

Optimal deteriorating items production inventory models with random machine breakdown and stochastic repair time

This study develops deteriorating items production inventory models with random machine breakdown and stochastic repair time. The model assumes the machine repair time is independent of the machine breakdown rate. The classical optimization technique is used to derive an optimal solution. A numerical example and sensitivity analysis are shown to illustrate the models. The stochastic repair models with uniformly distributed repair time tends to have a larger optimal total cost than the fixed repair time model, however the production up time is less than the fixed repair time model. Production and demand rate are the most sensitive parameters for the optimal production up time, and demand rate is the most sensitive parameter to the optimal total cost for the stochastic model with exponential distribution repair time.     

随机需求下考虑半成品库存的多周期生产决策优化

为了更好地应对需求的不确定性,在需求实现之前,企业既可以生产成品直接满足需求,亦可生产部分半成品,在观察到实际需求之后短时间内迅速完成剩余生产环节以满足需求。未加工的半成品和未售出的成品可用于满足后续周期的需求。作为一种提高生产灵活性的手段,分阶段生产的方式会产生更高的成本。企业需要在成本和灵活性之间作出权衡,优化生产决策。模型通过动态规划的方法,研究需求不确定情况下考虑半成品库存的多周期生产决策问题,通过分析目标函数以及最优值函数的结构性质,推导出最优的多周期生产策略为修正的目标库存策略,并且分析了不同参数对最优策略的影响。     

An improved stochastic programming model for supply chain planning of MRO spare parts

The maintenance, repair and operation (MRO) spare parts that are vital to machine operations are playing an increasingly important role in manufacturing enterprises. MRO spare parts supply chain management planning must be coordinated to ensure spare part availability while keeping the total cost to a minimum. Due to the specificity of MRO spare parts, randomness and uncertainties in production and storage should be quantified to formulate the problem in a mathematical model. Given these considerations, this paper proposes an improved stochastic programming model for the supply chain planning of MRO spare parts. In our stochastic programming model, the following improvements are made: First, we quantify the uncertain production time capacity as a random variable with a probability distribution. Second, the upper bound of the storage cost is modeled as a multi-choice variable in the constraint. To derive the equivalent deterministic model, the Lagrange interpolating polynomial approach is used. The results of the numerical examples validate the feasibility and efficiency of the proposed model. Finally, the model is tested in the supply chain planning of continuous caster (CC) bearings.     

A stochastic programming approach for multi-site aggregate production planning

Production planning problems play a vital role in the supply chain management area, by which decision makers can determine the production loading plan—consisting of the quantity of production and the workforce level at each production plant—to fulfil market demand. This paper addresses the production planning problem with additional constraints, such as production plant preference selection. To deal with the uncertain demand data, a stochastic programming approach is proposed to determine optimal medium-term production loading plans under an uncertain environment. A set of data from a multinational lingerie company in Hong Kong is used to demonstrate the robustness and effectiveness of the proposed model. An analysis of the probability distribution of economic demand assumptions is performed. The impact of unit shortage costs on the total cost is also analysed.     

A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment

In this study, a fuzzy multi-objective joint replenishment inventory model of deteriorating items is developed. The model maximizes the profit and return on inventory investment (ROII) under fuzzy demand and shortage cost constraint. We propose a novel inverse weight fuzzy non-linear programming (IWFNLP) to formulate the fuzzy model. A soft computing, differential evolution (DE) with/without migration operation, is proposed to solve the problem. The performances of the proposed fuzzy method and the conventional fuzzy additive goal programming (FAGP) are compared. We show that the solution derived from the IWFNLP method satisfies the decision maker’s desirable achievement level of the profit objective, ROII objective and shortage cost constraint goal under the desirable possible level of fuzzy demand. It is an effective decision tool since it can really reflect the relative importance of each fuzzy component.     

基于时间约束的生产过程优化问题研究

本文提出一个实际的生产过程优化问题:基于时间约束的生产过程优化问题。客户要求企业在规定时间内完成指定批量工件的生产任务,该问题便是从中引出的。该问题的目标是在满足生产时间的条件下最小化总生产成本。本文为该问题建立了整数规划模型。然后以某厂工作缸生产过程为例,采用数学规划软件Cplex 9.0求解模型。     

A Simple Model for Computing the Trade-Offs between Plant Capacity and Operating Strategies

A method is presented for determining the optimal capacity of a production system which encounters a strong seasonal demand for its output. A model is developed for analysing the trade-offs between plant capacity and different production strategies. The production strategies are computed by linear programming for a range of plant capacities and a given demand pattern. The annual capital costs of the plant are calculated as a function of plant capacity and the two costs are added in order to determine the plant capacity corresponding to the least cost.     

A partial-postponement decision cost model

A number of factors, including product proliferation and increased customer service-level requirements, have led many companies to consider adopting postponement as a supply chain strategy. Packaging postponement is the process of delaying packaging of a common item into a final product configuration until the customer order is received. For a given product, a portion of demand is known with a high level of certainty and would not benefit from postponement. The remaining portion of demand is known with little certainty and would benefit from delaying the differentiating stage of the operation until demand is known. We develop a single-period, two-product, order-up-to cost model to aid in setting the levels of finished-goods inventory and postponement capacity. Minimum-cost optimal solutions to inventory levels and capacity are obtained by solving the derived analytical expressions using a non-linear programming formulation. We examine the sensitivity of the model to different levels of the model parameters to generate managerial insights beyond those of previous work. We show that changing product value, packaging cost, cost of postponement, holding cost, fill rate, and demand correlation can decrease expected total cost and increase postponement capacity.     

Production planning via scenario modelling

Several Linear Programming (LP) and Mixed Integer Programming (MIP) models for the production and capacity planning problems with uncertainty in demand are proposed. In contrast to traditional mathematical programming approaches, we use scenarios to characterize the uncertainty in demand. Solutions are obtained for each scenario and then these individual scenario solutions are aggregated to yield a nonanticipative or implementable policy. Such an approach makes it possible to model nonstationarity in demand as well as a variety of recourse decision types. Two scenario-based models for formalizing implementable policies are presented. The first model is a LP model for multi-product, multi-period, single-level production planning to determine the production volume and product inventory for each period, such that the expected cost of holding inventory and lost demand is minimized. The second model is a MIP model for multi-product, multi-period, single-level production planning to help in sourcing decisions for raw materials supply. Although these formulations lead to very large scale mathematical programming problems, our computational experience with LP models for real-life instances is very encouraging.     

Time and inventory dependent optimal maintenance policies for single machine workstations: An MDP approach

In this work the problem of obtaining an optimal maintenance policy for a single-machine, single-product workstation that deteriorates over time is addressed, using Markov Decision Process (MDP) models. Two models are proposed. The decision criteria for the first model is based on the cost of performing maintenance, the cost of repairing a failed machine and the cost of holding inventory while the machine is not available for production. For the second model the cost of holding inventory is replaced by the cost of not satisfying the demand. The processing time of jobs, inter-arrival times of jobs or units of demand, and the failure times are assumed to be random. The results show that in order to make better maintenance decisions the interaction between the inventory (whether in process or final), and the number of shifts that the machine has been working without restoration, has to be taken into account. If this interaction is considered, the long-run operational costs are reduced significantly. Moreover, structural properties of the optimal policies of the models are obtained after imposing conditions on the parameters of the models and on the distribution of the lifetime of a recently restored machine.     

A Chance-Constrained Integer Goal Programming Model for Capital Budgeting in the Production Area

The selection of capital projects in a production environment is complicated by the existence of multiple and conflicting goals. Typical production objectives for cost minimization often conflict with goals for quality, environmental standards, labor relations, etc. This problem of project selection is further complicated by the uncertainty inherent in product demand, the key factor in production management. This paper approaches these complications by employing an integer goal programming (to compensate for multiple conflicting objectives) with chance-constrained capabilities (to reflect uncertainty in product demand). The approach is demonstrated via an in-depth case example of a production problem.     

The coordination of transportation and batching scheduling

We study a coordinated scheduling problem of production and transportation in which each job is transported to a single batching machine for further processing. There are m vehicles that transport jobs from the holding area to the batching machine. Each vehicle can transport only one job at a time. The batching machine can process a batch of jobs simultaneously where there is an upper limit on the batch size. Each batch to be processed occurs a processing cost. The problem is to find a joint schedule of production and transportation such that the sum of the total completion time and the total processing cost is optimized. For a special case of the problem where the job assignment to the vehicles is predetermined, we provide a polynomial time algorithm. For the general problem, we prove that it is NP-hard (in the ordinary sense) and present a pseudo-polynomial time algorithm. A fully polynomial time approximation scheme for the general problem is obtained by converting an especially designed pseudo-polynomial dynamic programming algorithm.     

A decomposition algorithm for solving certain classes of production-transportation problems with concave production cost

This paper addresses a method for solving two classes of production-transportation problems with concave production cost. By exploiting a special network structure both problems are reduced to a kind of resource allocation problem. It is shown that the resultant problem can be solved by using dynamic programming in time polynomial in the number of supply and demand points and the total demand.The author was partially supported by Grand-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Grant No. (C)05650061.     

Application of Mathematical Programming to a Large-scale Agricultural Production and Distribution System

This paper addresses an actual production planning problem for a large seed corn production company. Various scenarios are included in different mathematical programming models in order to help the management make production decisions. A linear programming package and a mixed-integer programming package are combined by a designed heuristic program to solve the problem. The solutions obtained and an accompanying sensitivity analysis provide the management with insight into the system's operation and potentials of cost savings.     

两阶段随机线性规划的费用型鲁棒模型

Vladmiron和Zenios曾引进了限制补偿的概念,给出了关于具有补偿的两阶段随机线性规划的鲁棒优化的新的表述。为适应决策者对补偿在技术操作上的稳定性与经费预算上的稳定性的需求,我们提出了费用型鲁棒模型以及混合型鲁棒模型,并转化为序列修正的线性规划的求解问题．