Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment

This paper proposes a scenario-based two-stage stochastic programming model with recourse for master production scheduling under demand uncertainty. We integrate the model into a hierarchical production planning and control system that is common in industrial practice. To reduce the problem of the disaggregation of the master production schedule, we use a relatively low aggregation level (compared to other work on stochastic programming for production planning). Consequently, we must consider many more scenarios to model demand uncertainty. Additionally, we modify standard modelling approaches for stochastic programming because they lead to the occurrence of many infeasible problems due to rolling planning horizons and interdependencies between master production scheduling and successive planning levels. To evaluate the performance of the proposed models, we generate a customer order arrival process, execute production planning in a rolling horizon environment and simulate the realisation of the planning results. In our experiments, the tardiness of customer orders can be nearly eliminated by the use of the proposed stochastic programming model at the cost of increasing inventory levels and using additional capacity.     

Multi-item capacitated lot-sizing with demand uncertainty

We consider a stochastic version of the classical multi-item Capacitated Lot-Sizing Problem (CLSP). Demand uncertainty is explicitly modeled through a scenario tree, resulting in a multi-stage mixed-integer stochastic programming model with recourse. We propose a plant-location-based model formulation and a heuristic solution approach based on a fix-and-relax strategy. We report computational experiments to assess not only the viability of the heuristic, but also the advantage (if any) of the stochastic programming model with respect to the considerably simpler deterministic model based on expected value of demand. To this aim we use a simulation architecture, whereby the production plan obtained from the optimization models is applied in a realistic rolling horizon framework, allowing for out-of-sample scenarios and errors in the model of demand uncertainty. We also experiment with different approaches to generate the scenario tree. The results suggest that there is an interplay between different managerial levers to hedge demand uncertainty, i.e. reactive capacity buffers and safety stocks. When there is enough reactive capacity, the ability of the stochastic model to build safety stocks is of little value. When capacity is tightly constrained and the impact of setup times is large, remarkable advantages are obtained by modeling uncertainty explicitly.     

Robust disassembly line balancing with ambiguous task processing times

Disassembly line balancing problem (DLBP), which is to select disassembly process, open workstations and assign selected tasks to opened workstations, plays an important role in the recycling of End Of Life products. In real-world disassembly operations, task processing times are usually stochastic due to various factors. Most related works address the uncertain processing times by assuming that the probability distribution is known and the task processing times are independent of each other. In practice, however, it is difficult to get the complete distributional information and there is always underlying correlation between the uncertain processing times. This paper investigates the DLBP with partial uncertain knowledge, i.e. the mean and covariance matrix of task processing times. A new distributionally robust formulation with a joint chance constraint is proposed. To solve the problem, an approximated mixed integer second-order cone programming (MI-SOCP) model is proposed, and a two-stage parameter-adjusting heuristic is further developed. Numerical experiments are conducted, to evaluate the performance of the proposed method. We also draw some managerial insights and consider an extension problem.     

Assessing the benefits of labelling postponement in an export-focused winery

Supporting wine production operations in an increasingly global market has grown ever more challenging. Export-focused wineries supply many foreign clients, often requiring different labels for the same kind of wine. Order forecasts tend to be highly inaccurate, and wineries must be able to quickly react to changes, making lot-sizing an important consideration. One tool to reduce product misallocation is postponing product differentiation, where the natural decoupling point for premium wine is the labelling process. However, the double handling involved incurs additional costs and time penalties. We analyse the performance impact of postponing the labelling of bottled wines by developing a multi-stage mixed-integer stochastic programming model with full recourse for demand scenarios. The underlying data and policies are based on an unnamed Chilean export-focused winery. The model supports lot-sizing under several winery production policies. We experiment with different levels of capacity tightness, demand variability and demand correlation between wines, optimising for reducing order backlogs, inventory levels and line set-ups. While we find that some amount of postponement will always be recommended, the exact mix and degree depend on these external factors. Postponement has the most benefits when production capacity is moderately tight, demand variability is high and wines have negatively correlated demands.     

Periodical capacity setting methods for make-to-order multi-machine production systems

The paper presents different periodical capacity setting methods for make-to-order, multi-machine production systems with stochastic customer required lead times and stochastic processing times to improve service level and tardiness. These methods are developed as decision support when capacity flexibility exists, such as, a certain range of possible working hours a week for example. The methods differ in the amount of information used whereby all are based on the cumulated capacity demand at each machine. In a simulation study the methods’ impact on service level and tardiness is compared to a constant provided capacity for a single and a multi-machine setting. It is shown that the tested capacity setting methods can lead to an increase in service level and a decrease in average tardiness in comparison to a constant provided capacity. The methods using information on processing time and customer required lead time distribution perform best. The results found in this paper can help practitioners to make efficient use of their flexible capacity.     

System reliability of a manufacturing network with reworking action and different failure rates

From the perspective of network analysis, the manufacturing system can be constructed as a stochastic-flow network, since the capacity of each machine is stochastic (i.e. multistate) owing to the failure, partial failure, and maintenance. Considering reworking action and different failure rates of machines, the input flow (raw materials/work in process) processed by each machine might be defective, and therefore the output flow (work in process/products) would be less than the input amount. To evaluate the capability of the manufacturing system, we measure the probability that the manufacturing network can satisfy demand. Such a probability is defined as the system reliability. A decomposition method is first proposed to divide the manufacturing network into one general processing path and one reworking path. Subsequently, two algorithms are utilised for different network models to generate the lower boundary vector of machine capacity to guarantee that the manufacturing network is able to produce sufficient products fulfilling the demand. The system reliability of the manufacturing network can be derived in terms of such a capacity vector afterwards.     

VOLUME AND CAPACITY INTERACTION IN FACILITY DESIGN

This paper addresses the joint facilities design problem of determining both demand and capacity with stochastic demand arrivals and stochastic processing throughput. Using a simple M/M/1 queueing model of a profit maximizing firm, we link marketing and production decision variables by recognizing appropriate congestion costs, and show that coordinated decision-making provides results superior to making demand and capacity decisions sequentially. Sensitivity analysis indicates that the model is robust with respect to its assumptions and parameters. An example illustrates the approach and demonstrates the application of the model.     

Channel coordination in an assembly system facing uncertain demand with synchronized processing time and delivery quantity

Supply chains need to be synchronized to increase system efficiency. With increasing globalization, an assembly or a manufacturing firm may receive supplies from all over the world. Synchronization of such a system becomes difficult for two reasons: first, each supplier has certain capacity and can supply materials with a fixed but different order processing time; second, each supplier has a different cost structure and, therefore, production quantities differ due to incentives conflicts, which leads to local optimization of profits by the suppliers. In the existing literature, this problem is generally tackled by focusing either on the synchronization of order processing time or on order quantity determination. However, when system coordination is of the essence, simultaneous consideration of both becomes imperative. A model to synchronize the assembly process is proposed and the optimal order quantities in a two-echelon assembly system with one assembler (facing a stochastic demand) and multiple suppliers with deterministic order processing times is determined. A numerical study conducted shows that risk sharing and proper safety stock placement lead to better system coordination and improve system performance.     

A new distribution-free model for disassembly line balancing problem with stochastic task processing times

Effective conduct with End of Life (EOL) products is a hot research topic in green and smart manufacturing. For EOL product recycling and remanufacturing, a fundamental problem is to design an efficient disassembly line under consideration of stochastic task processing times. This problem focuses on selecting alternative task processes, determining the number of opened workstations, and assigning operational tasks to the workstations. The goal is to minimise the total cost consisting of workstation operational cost and hazardous component processing cost. Most existing works assume that the probability distribution of task processing times can be estimated, however, it is often not likely to access the complete probability distribution due to various difficulties. Therefore, this study investigates disassembly line design with the assumption that only the mean, standard deviation and an upper bound of task processing times are known. Our main contributions include: (i) a new decomposition color graph is proposed to intuitively describe all possible processes, (ii) a new distribution-free model is proposed, and (iii) some problem properties are established to solve the model. Experimental results show that the distribution-free model can effectively deal with stochastic task processing times without given probability distributions.     

An integrated approach to inventory and flexible capacity management subject to fixed costs and non-stationary stochastic demand

In a manufacturing system with flexible capacity, inventory management can be coupled with capacity management in order to handle fluctuations in demand more effectively. Typical examples include the effective use of temporary workforce and overtime production. In this paper, we discuss an integrated model for inventory and flexible capacity management under non-stationary stochastic demand with the possibility of positive fixed costs, both for initiating production and for using contingent capacity. We analyze the characteristics of the optimal policies for the integrated problem. We also evaluate the value of utilizing flexible capacity under different settings, which enable us to develop managerial insights.     

Hierarchical cross-training in work-in-process-constrained systems

We study Work-In-Process (WIP)-constrained flowlines staffed by partially cross-trained workers with hierarchical skill sets. We characterize the optimal worker-to-task assignment policy for CONWIP systems with two workers and general stochastic processing times. This leads us to the “fixed-before-shared” principle, which states that a flexible worker should process a task he/she is uniquely qualified for before helping other workers with shared tasks. To provide insights on the performance opportunity of hierarchical cross-training in systems with limited WIP, we provide a complete characterization of the optimal policy and closed-form expressions of the resulting throughput for the case of exponential processing times. We extend our results to the more general case of floater workers, and illustrate their applicability to various real-world systems. Our analysis shows that hierarchical cross-training can provide significant benefits, but should be implemented with care in WIP-constrained environments such as those making use of pull systems.     

A multi-stage stochastic programming approach for production planning with uncertainty in the quality of raw materials and demand

Motivated by the challenges encountered in sawmill production planning, we study a multi-product, multi-period production planning problem with uncertainty in the quality of raw materials and consequently in processes yields, as well as uncertainty in products demands. As the demand and yield own different uncertain natures, they are modelled separately and then integrated. Demand uncertainty is considered as a dynamic stochastic data process during the planning horizon, which is modelled as a scenario tree. Each stage in the demand scenario tree corresponds to a cluster of time periods, for which the demand has a stationary behaviour. The uncertain yield is modelled as scenarios with stationary probability distributions during the planning horizon. Yield scenarios are then integrated in each node of the demand scenario tree, constituting a hybrid scenario tree. Based on the hybrid scenario tree for the uncertain yield and demand, a multi-stage stochastic programming (MSP) model is proposed which is full recourse for demand scenarios and simple recourse for yield scenarios. We conduct a case study with respect to a realistic scale sawmill. Numerical results indicate that the solution to the multi-stage stochastic model is far superior to the optimal solution to the mean-value deterministic and the two-stage stochastic models.     

Optimization-based planning for the stochastic lot-scheduling problem

We describe a finite-horizon stochastic optimization model for the stochastic lot-scheduling problem and procedures for finding near-optimal solutions. Several different products are produced by a single-stage process with significant changeover times and costs, and the demand for these products is random. The deterministic version of this problem, the economic lot-scheduling problem, is the subject of a great deal of research. However, the problem with random demand for the products is commonly found in practice but is not as well researched. The models developed in this paper address the problem of dynamically planning the timing and size of production runs in this kind of production environment. We also report some computational results that indicate the quality of the resulting production schedules.     

Supply chain capacity and outsourcing decisions: the dynamic interplay of demand and supply uncertainty

We study the interplay of demand and supply uncertainty in capacity and outsourcing decisions in multi-stage supply chains. We consider a firm's investment in two stages of a supply chain (Stage 1 models the “core” activities of the firm, while Stage 2 are the “non-core” activities). The firm invests in these two stages in order to maximize the multi-period, discounted profit. We consider how non-stationary stochastic demand affects the outsourcing decisions. We also consider how investment levels are affected by non-stationary stochastic supply when the market responds to the firm's investments. We characterize the optimal capacity investment decisions Tor the single- and multi-period versions of our model and focus on how changes in supply and demand uncertainly affect the extent of outsourcing. We find that as the responsiveness of the market to investments made by the firm increases, the reliance on outsourcing generally increases. While greater supply and greater demand have the expected effect on investments, decreases in variability are not as straightforward. Greater supply uncertainty increases the need for vertical integration while greater demand uncertainty increases the reliance on outsourcing. In the multi-period model, we find that the nature of adjustments in capacity based on changes in demand or supply follows from the comparative statics of the single-period model, although whether outsourcing increases or decreases depends on the costs of adjusting capacity.     

A decomposition method for multi-product kanban systems with setup times and lost sales

We consider kanban controlled production systems with three or more different products processed on a single manufacturing facility. Customers for a product arrive according to a Poisson process. If a customer's demand cannot be met from stock, the customer leaves and satisfies his demand elsewhere (lost sales). Between the production of different products setup changes must be performed that take a significant time. Setup times and processing times are product-specific and follow exponential distributions. A production run continues until the target inventory level given by the number of kanbans for the product has been reached (exhaustive processing). Then the manufacturing facility is set up for the next product according to a fixed setup cycle. The exact model is mathematically intractable even for smaller systems. Therefore, we propose a decomposition-based approximation method for estimating steady-state performance measures     

A multi-objective distribution-free model and method for stochastic disassembly line balancing problem

End-of-life product recycling is a hot research topic in recent years, which can reduce the waste and protect the environment. To disassemble products, the disassembly line balancing is a principal problem that selects tasks and assigns them to a number of workstations under stochastic task processing times. In existing works, stochastic task processing times are usually estimated by probability distributions or fuzzy numbers. However, in real-life applications, only their partial information is accessible. This paper studies a bi-objective stochastic disassembly line balancing problem to minimise the line design cost and the cycle time, with only the knowledge of the mean, standard deviation and upper bound of stochastic task processing times. For the problem, a bi-objective chance-constrained model is developed, which is further approximated into a bi-objective distribution-free one. Based on the problem analysis, two versions of the ?-constraint method are proposed to solve the transformed model. Finally, a fuzzy-logic technique is adapted to propose a preferable solution for decision makers according to their preferences. A case study is presented to illustrate the validity of the proposed models and algorithms. Experimental results on 277 benchmark-based and randomly generated instances show the efficiency of the proposed methods.     

Capacity investment and the value of operational flexibility in manufacturing systems with product blending

A distinct feature of process industries such as food, chemical and consumer packaged goods is the blending of intermediates into finished goods. In the context of such manufacturing systems the levels of different inputs that can be blended to process a final good define the range of flexibility. Likewise, the cost for using (blending) different inputs defines the mobility element of flexibility. In this paper, we investigate capacity investment and the value of flexibility in the presence of such product blending constraints. We are motivated by recent case studies of food manufacturers, in particular, those manufacturers that seek to increase flexibility via blending of intermediates. We analyse stochastic programs under demand uncertainty of such manufacturing systems. We provide analytical insights into trade-offs when range and mobility are interdependent. Our analytical work gives structural insights into subtle complementarity and substitution effects between dedicated and shared resources in the presence of blending. We analytically show that there is a degradation in the cost performance of such systems with an increase in correlation. We characterise the optimal blending fraction that balances the benefits of higher range with higher costs (lower mobility). Our numerical work shows that a moderate level of blending can significantly improve flexibility and that well-known guidelines for designing limited flexibility change in the presence of blending. For example, blending, even if optimally designed, weakens the appeal of chaining configurations. Overall our work guides resource configuration in industries where product blending is an integral part of the production process.     

基于设备使用周期的备件库存控制模型研究

由于设备系统的复杂性、设备故障的随机性,备件的需求难以准确确定,相关费用也难以做出准确评估,从而使得备件这一类库存控制问题变得相当复杂.基于备件的需求量与设备使用周期密切相关这一关键点,从设备的整个使用周期入手,结合设备的使用情况,在备件需求率随时间变化的情况下,对备件库存控制问题进行了研究,建立了在设备整个使用周期内使备件总订货成本和存储费用最低的数学模型,给出了备件最佳订货次数、订货时间和订货批量的计算公式.最后给出了一个算例以证明模型的实用性.     

The effect of supply and demand uncertainties on the optimal production and sales plans for new products

When introducing a new product, firms face a hierarchy of decisions at the strategic and operational levels including capacity sizing, time to market or starting sales, initial inventory required by the product’s release time and production management in response to changes in the demand (hereafter referred to as production-sales policies). The goal of this paper was to show the importance of considering both supply and demand uncertainties in the determination of the production-sales policy which has been overlooked in the existing literature. More specifically, we test two main hypotheses: (1) ignoring supply and demand uncertainties may lead to potentially incorrect decisions; and, (2) the decision could be different if risk is used as the primary performance measure instead of the commonly used expected (mean) profit. We perform extensive experimentation with a Monte Carlo simulation model of the stochastic supply-restricted new product diffusion and use different statistical procedures, namely, the Welch’s t-test and a nonparametric double-bootstrap method to compare the average and percentiles of the profit for different policies, respectively. The results indicate that the correctness of the two hypotheses depends on the diffusion speed, consumers’ backlogging behaviour, production capacity, price and variable production and inventory costs. The findings also have important implications for managers regarding market entry time, parameter estimation, production strategy and the implementation of the proposed model.     

Subcontracting with availability guarantees: production control and capacity decisions

We present a simplified model of a system with a producer, a subcontractor and a random demand. The demand level alternates between a high level and a low level with exponential switching times. The producer does not have enough capacity to meet the high demand. Therefore, it either produces to stock in advance or uses a subcontractor to receive additional capacity when it needs. The subcontractor serves a number of manufacturers and guarantees a long-term availability that is defined as the long-term probability that the subcontractor will be available when it is requested, to each manufacturer. Therefore, a manufacturer may not receive the requested capacity from the subcontractor immediately and waits until the subcontractor becomes available. The times that the subcontractor is available and not available are also exponential random variables. The producer uses a threshold-type policy that depends on the state of the inventory/backlog to decide how much to produce and how much to request from the subcontractor. This system is modeled analytically based on a stochastic flow rate control problem with continuous flow and discrete states in a Markovian setting. A numerical analysis of the model is used to analyze the effects of guaranteed availability on the manufacturer's and subcontractor's performances. Extensions to the producer's and subcontractor's capacity decisions and the subcontractor's pricing decisions are also discussed.