Simultaneous control of production, repair/replacement and preventive maintenance of deteriorating manufacturing systems

This paper presents a method to find the optimal production, repair/replacement and preventive maintenance policies for a degraded manufacturing system. The system is subject to random machine failures and repairs. The status of the system is deemed to degrade with repair activities. When a failure occurs, the machine is either repaired or replaced, and a replacement action renews the machine, while a repair action brings it to a degraded operational state, with the next repair time increasing as the number of repairs increases as well. A preventive maintenance action is considered in order to improve the reliability of the machine, thereby reducing the amount of disruptions caused by machine failures. The decision variables are the production rate, the preventive maintenance rate and the repair/replacement switching policy upon machine failure. The objective of the study is to find the decision variables that minimize the overall cost, including repair, replacement, preventive maintenance, inventory holding and backlog costs over an infinite planning horizon. The proposed model is based on a semi-Markov decision process, and the stochastic dynamic programming method is used to obtain the optimality conditions. A numerical example is given to illustrate the proposed model, and a sensitivity analysis is considered in order to confirm the structure of the control policy and to illustrate the usefulness of the proposed approach.     

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.     

Optimal production–inventory strategies for a HMMS-type reverse logistics system

The aim of the paper is to find optimal inventory policies in a reverse logistics system with special structure. It is assumed that demand is a known continuous function in a given planning horizon and return rate of used items is a given function. There is a constant delay between the using and return process. We investigate two stores. The demand is satisfied from the first store, where the manufactured and remanufactured items are stored. The returned products are collected in the second store and then remanufactured or disposed. The costs of this system consist of the quadratic holding costs for these two stores and the quadratic manufacturing, remanufacturing and disposal costs.The model is represented as an optimal control problem with two state variables (inventory status in the first and second store) and with three control variables (rate of manufacturing, remanufacturing and disposal). The objective is to minimize the sum of the quadratic deviation from described inventory levels in stores and from described manufacturing, remanufacturing and disposal rates. In this form, the model can be considered as a generalization of the well-known Holt et al. (Planning Production, Inventories, and Work Forces, Prentice-Hall, Englewood Cliffs, NJ, 1960) model with two warehouses. After solving the problem, we give some numerical examples to represent the optimal path in dependence of the demand rates.     

Production planning of a hybrid manufacturing-remanufacturing system under uncertainty within a closed-loop supply chain

This paper deals with the production planning and control of a single product involving combined manufacturing and remanufacturing operations within a closed-loop reverse logistics network with machines subject to random failures and repairs. While consumers traditionally dispose of products at the end of their life cycle, recovery of the used products may be economically more attractive than disposal, while remanufacturing of the products also pursues sustainable development goals. Three types of inventories are involved in this network. The manufactured and remanufactured items are stored in the first and second inventories. The returned products are collected in the third inventory and then remanufactured or disposed of. The objective of this research is to propose a manufacturing/remanufacturing policy that would minimize the sum of the holding and backlog costs for manufacturing and remanufacturing products. The decision variables are the production rates of the manufacturing and the remanufacturing machines. The optimality conditions are developed using the optimal control theory based on stochastic dynamic programming. A computational algorithm, based on numerical methods, is used for solving the optimal control problem. Finally, a numerical example and a sensitivity analysis are presented to illustrate the usefulness of the proposed approach. The structure of the optimal control policy is discussed depending on the value of costs and parameters and extensions to more complex reverse logistics networks are discussed.     

Integrated multi-period cell formation and subcontracting production planning in dynamic cellular manufacturing systems

In this paper, an integrated mathematical model of the multi-period cell formation and production planning in a dynamic cellular manufacturing system (DCMS) is proposed with the aim of minimizing machine, inter/intra-cell movement, reconfiguration, partial subcontracting, and inventory carrying costs. This paper puts emphasis on the effect of the trade-off between production and outsourcing costs on the re-configuration of the cells in cellular manufacturing systems (CMSs) under a dynamic environment, in which the product mix is different from a period to another resulting in the operational dynamism in the cells. The proposed model is verified by a number of numerical examples and related sensitivity analysis.     

Model and analysis of integrated production–inventory system: The case of steel production

The study originated from an industrial case study in the field of steel production, but it presents a larger interest, as many other manufacturing fields have similar concerns (e.g. foundries, food, textile and paper industries). A significant phase of steel manufacturing is the product cooling (likewise, drying in paper and textile production, or maturing in food production). This phase may be completed in different ways, but (1) it must be carried out in the finished product warehouse and (2) it must meet both production optimisation and customer needs. The latter requirement acquires a strategic relevance in JIT environments. The present study proposes a mathematical model to find the optimal production schedule of steel billets, based on the relevant parameters of the productive system (set-up and processing times, demand profile). In the industrial case examined, the negative impact of holding costs on cash flows is also linked to the space required by the cooling process, which depends on the production schedule adopted. In other words, the finished product storage can be considered a part of the manufacturing cycle and impacts on it. In the case of steel plants operating in JIT environments, the warehouse must be promptly emptied and carefully managed to exploit the available space. Thus, the effect of inventory costs is examined in a production–inventory system with finite capacity, where products are made to order and share the same manufacturing facility. The study is completed by an experimental analysis to investigate the effect of variations in the relevant parameters of the problem.     

Integrated product specifications and productivity decision making in unreliable manufacturing systems

This paper considers joint production control and product specifications decision making in a failure prone manufacturing system. This is with the knowledge that tight process specifications, while leading to a product of more reliable quality and higher market value, are at the same time associated with higher levels of non-conforming parts, a higher rate of parts rejection and thus a lowering of overall plant productivity. The decision making is further complicated by the lack of reliability of the production process, which imposes that an adequate, also to be designed, level of inventory of finished parts be maintained. The overall optimal decision policy is defined here as one that maximizes the long term average per unit time profit of a combined measure of quality and quantity dependent sales revenue, minus inventory and backlog costs, in the presence of random plant failures and random repair durations. Policy optimization is achieved via a revisited model of the Bielecki–Kumar theory for Markovian machines and a simulation and experimental design based methodology for the more general cases.     

A hierarchical planning system for energy intensive production environments

This paper describes a hierarchical production planning approach with decision support features for energy intensive industries with particular reference to a tile manufacturing factory. In the tiling industry, the facilities which contribute most to the consumption of energy (and, hence, to the production costs) are usually the kilns where the curing operation is carried out. Frequently, the kilns are also the bottleneck in terms of capacity utilization. Thus, in order to save on energy costs, a planning approach which aims at minimizing the number of active kilns throughout the year is needed besides optimizing the process design in the curing department. To achieve the latter goal, it is necessary to take into account demand fluctuations as well as detailed capacity restrictions while deciding on the lot sizes of the products and the kilns on which the products are loaded. Rather than adopting a monolithic mathematical model for developing a desirable production plan, a hierarchical approach which decomposes the problem into two sub-problems is preferred. In the first level, products and capacity are aggregated over the planning horizon to achieve an overall consideration of demand fluctuations over time. Then, the solution provided by the aggregate solution for the current planning period is disaggregated into a detailed lot sizing and loading solution. The disaggregated problem is difficult to solve and hence, a heuristic is proposed here. This planning approach is sustained by a Decision Support System which enables the elimination of possible inconsistencies in the production plan by providing an effective interaction with the decision maker.     

Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution

In hybrid control systems for simultaneous remanufacturing of used products and manufacturing of new ones, the two operations are not directly interconnected if remanufactured items are downgraded and have to be sold in markets different from those for new products. Sometimes a connection between these markets is given by a downward substitution property which allows the producer to offer a new item instead of a remanufactured one in case of a shortage of a remanufactured product. Thus, shortage costs can be avoided, but a loss in profit due to sale of a high-graded product at the price of a low-graded one has to be accepted. For a single-period problem with stochastic returns of used products and stochastic demands of serviceable ones, it is shown how the manufacturing and remanufacturing decisions have been coordinated in order to maximize the total expected profit. It turns out that under strictly proportional costs and revenues a medium-simple ‘order-up-to policy’ with two parameters and two parameter functions is optimal. However, optimal policies in situations where manufacturing leadtimes exceed leadtimes for remanufacturing turn out to be different from those in the opposite leadtime case. The research presented combines methods for policy analysis in stochastic manufacturing/remanufacturing problems and in stochastic inventory control problems with substitutable products.     

A production rate control policy for stochastic repair and remanufacturing systems

We consider the control of a manufacturing system responding to planned demand at the end of the expected life of each individual piece of equipment and unplanned demand triggered by a major equipment failure. The difficulty of controlling this type of production system resides in the variable nature of the remanufacturing process. In practice, remanufacturing operations for planned demand can be executed at different rates, referring to different component replacement and repair strategies. We formulate this problem as a multi-level control problem and propose a suboptimal control policy. The proposed control policy is described by inventory thresholds triggering the use of different execution modes. Determination of the control policy parameters is based on parameter optimization of analytical cost expressions. A numerical example based on a real case is presented. Our analysis demonstrates that the use of the proposed control approach can lead to a significant reduction in the total average cost, as compared to current practices.     

Optimal control of a one product recovery system with leadtimes

In this paper a recovery system for a single product is investigated. Besides a remanufacturing and a manufacturing facility the system consists of one inventory for returned and recoverable items and one for serviceable items. Demands are satisfied from serviceable inventory, which can be replenished by remanufactured returned items, which are as good as new, or by new produced items. Additionally, there is the possibility of disposing of returned items.We determine the cost optimal manufacturing, remanufacturing and disposal rates for the system under the assumptions of a linear cost structure, a finite planning horizon and deterministic and dynamic demand and return rates. Thereby we study two classes of policies, one where backorders are forbidden and another one where they are allowed. In contrast to the existing literature positive leadtimes are considered.     

Capacity flexibility allocation in an outsourced supply chain with reservation

We consider a contract manufacturer that serves a limited number of outsourcers (customers) on a single capacitated production line. The outsourcers have different levels of demand uncertainty and the contract manufacturer faces the question how to allocate the contractual capacity flexibility in an optimal way. The contractual capacity flexibility is a contract parameter that sets the amount of demand the contract manufacturer is obliged to accept from the outsourcers. We develop a hierarchical model that consists of two decision levels. At the tactical level, the contract manufacturer allocates the capacity flexibility to the different outsourcers by maximizing the expected profit. Offering more flexibility to the more uncertain outsourcer generates higher expected revenue, but also increases the expected penalty costs. The allocated capacity flexibilities (determined at the tactical level) are input parameters to the lower decision level, where the operational planning decisions are made and actual demands are observed. We perform a numerical study by solving the two-level hierarchical planning problem iteratively. We first solve the higher level problem, which has been formulated as an integer program, and then perform a simulation study, where we solve a mathematical programming model in a rolling horizon setting to measure the operational performance of the system. The simulation results reveal that when the acceptance decision is made (given the allocated capacity flexibility decision), priority is given to the less uncertain outsourcer, whereas when the orders are placed, priority is given to the most uncertain outsourcer. Our insights are helpful for contract manufacturers when having contract negotiations with the outsourcers. Moreover, we show that hierarchical integration and anticipation are required, especially for cases with high penalty cost and tight capacities.     

ORDER PROCESSING COST REDUCTION IN A JOINT VENDOR-BUYER INVENTORY SYSTEM VIA THE APPLICATION OF INFORMATION TECHNOLOGY

Modem information technologies have become important means for manufacturing and retailing firms to gain such competitive advantages as lower logistics costs and securer customers' loyalty. In this paper, we investigate a joint inventory system where the vendor produces a single item for its sole buyer and the buyer sells the item to consumers with backorders allowed. Each production lot is delivered to the buyer in a number of shipments and consecutive shipments will be increased by a fixed factor. Both vendor and buyer are willing to participate in order processing time reduction by applying information technologies in order to decrease their joint total cost. The order processing time can be reduced by certain expenditures and will affect the lot-size decisions. An analytical model is developed for determining the optimal expenditure in order processing time reduction and lot sizes for both vendor and buyer. The numerical experiment along with sensitivity analysis is also performed to obtain some insights of our model.     

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.     

Integrated production planning with sequence-dependent family setup times

This paper proposes an integrated optimization model of aggregate production planning (APP), family disaggregation planning, and family scheduling problems in hierarchical production planning (HPP) systems considering sequence-dependent family setup times. The model obtains the optimal production plan for each product type and product family in each period, together with the globally optimal production sequence of product families in all planning periods. The proposed model is tested with randomly generated experimental data consistent with what is prevalent in the manufacturing industry and its results are compared with those of the traditional HPP models. Our results show that the integrated model realizes greater cost savings.     

Reliability evaluation and adjustment of supply chain network design with demand fluctuations

This study focuses on supply chain network design problems by considering economies of scale and demand fluctuations. A reliability evaluation method is developed to evaluate the performance of plants under demand fluctuations. In addition, two mathematical programming models are developed to determine the optimal adjustment decisions regarding production reallocation among plants under different fluctuating demands. The judgments to adjust or to do-nothing are investigated by comparing the results if the adjustment is made or not made. Results show that making adjustments benefits the manufacturers by reducing total production cost and avoiding revenue loss, which outweighs the extra costs, especially for high value-added products. Results also suggest that the manufacturer should ignore a short period abnormal state, since the benefits to respond to it might not compensate the high allocation costs. The results of this study provide a reference for the manufacturer in their decision making process of network planning with demand fluctuations, when they have to cope with benefits and costs during abnormal states.     

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 JIT lot-splitting model for supply chain management: Enhancing buyer–supplier linkage

This study develops a buyer–supplier coordination model to facilitate frequent deliveries in small lot sizes in a manufacturing supply chain. The proposed model, based on the integrated total relevant costs of both buyer and supplier, determines optimal order quantity, the number of deliveries/setups, and shipping quantity over a finite planning horizon in a relatively simple JIT single buyer single supplier scenario. Under deterministic conditions for a single product, we show that the optimal delivery policy adopted by both buyer and supplier in a cooperative manner can be economically beneficial to both parties. It is shown that the optimal delivery size can be unique, regardless of the order quantity and the number of deliveries. Numerical results are also presented.     

Competition under capacitated dynamic lot-sizing with capacity acquisition

Lot-sizing and capacity planning are important supply chain decisions, and competition and cooperation affect the performance of these decisions. In this paper, we look into the dynamic lot-sizing and resource competition problem of an industry consisting of multiple firms. A capacity competition model combining the complexity of time-varying demand with cost functions and economies of scale arising from dynamic lot-sizing costs is developed. Each firm can replenish inventory at the beginning of each period in a finite planning horizon. Fixed as well as variable production costs incur for each production setup, along with inventory carrying costs. The individual production lots of each firm are limited by a constant capacity restriction, which is purchased up front for the planning horizon. The capacity can be purchased from a spot market, and the capacity acquisition cost fluctuates with the total capacity demand of all the competing firms. We solve the competition model and establish the existence of a capacity equilibrium over the firms and the associated optimal dynamic lot-sizing plan for each firm under mild conditions.     

Just-in-time: A cross-sectional plant analysis

This paper uses a data base of quantitative and qualitative plant-level cross-sectional data to analyze the relative performance of Just-in-time (JIT) and non-JIT plants operating in two distinct manufacturing industries: electronic components and auto-parts. A number of conjectures made by the literature concerning the relationship between JIT manufacturing and plant inventory holdings, costs and profits are tested. Consistent with many of these conjectures, the results suggest that JIT manufacturing at the plant level is associated with greater productivity in inventory usage, lower total and variable costs, but not fixed costs, and higher profits. The success of JIT plants along these dimensions is found to be related to the length of experience with JIT manufacturing, and process quality and leanness but unrelated to product quality, quality control or the extent of plant unionization.