Optimal pricing and core acquisition strategy for a hybrid manufacturing/remanufacturing system

Remanufacturing is one of the product recovery options where the quality of used products (cores) is upgraded to ‘as-good-as-new’ conditions. In this article, we consider a monopolist firm selling new and remanufactured products to quality-conscious primary customers and price-sensitive secondary customers, respectively, with one-way substitution, i.e. some primary customers may substitute new products by remanufactured products while secondary customers can never afford to buy new products. We develop economic models under two scenarios – when the supply of cores is unconstrained and when manufacturers have to procure cores at an acquisition price. The major observations of the article are as follows. A firm is better off when there is no constraint on the supply of cores. Even when cores have to be acquired at an acquisition price, the profitability is higher than that when the firm does not engage in remanufacturing activities. When a larger number of primary customers replace new products with remanufactured products, there is partial cannibalization of new product sales; however, the combined market share and profitability of the firm increase. When core supply is constrained and customers are less sensitive to core prices, the limited supply of cores may render remanufacturing an infeasible option for the firm. Therefore, firms should not only generate awareness among primary customers to buy remanufactured products, but also step up efforts to ensure a steady supply of cores. We conclude the article with managerial implications and directions for future research.     

Optimal core acquisition and pricing strategies for hybrid manufacturing and remanufacturing systems

In this study, we combine two aspects of remanufacturing, namely product acquisition management and marketing (pricing) of the remanufactured products. We consider an original equipment manufacturer (OEM) who decides on the acquisition prices offered for returns from different quality types and on selling prices of new and remanufactured products, in a single period setting. We develop a procedure for determining the optimal prices and corresponding profit of the OEM, and conduct a sensitivity analysis to understand the effect of different model parameters on the optimal strategies and profit. An important managerial insight is that the optimal solution is not to have the same profit per remanufactured item for all return types, but to if the minimum cost for acquisition and remanufacturing of some core type is lower.     

Optimal acquisition policy in remanufacturing under general core quality distributions

The quality of acquirable used products (cores) is highly variable, which has made production planning and control of remanufacturing systems difficult. This paper studies an acquisition problem in presence of uncertain core quality. In order to derive optimal acquisition policy, the problem is formulated as a non-linear integer programming model in the framework of order statistics. The model is a strictly discrete convex problem with a unique global minimal solution. Then, a single bisection method is developed to obtain the optimal solution under a general continuous quality distribution. Moreover, the expressions of the optimal solution in some frequently used quality distributions are derived. Furthermore, the model is extended to the case of a general remanufacturing cost function, and corresponding results are presented. Finally, numerical experiments are conducted to test the effects of quality distribution, cost relationships of acquirable cores and remanufacturing cost function.     

Analysis of the steady state probability distribution of a manufacturing system under the prioritised hedging point control policy

In order to evaluate the average production cost of a multi-product-type, multi-stage and multi-parallel-machine manufacturing system (denoted as mP/mS/mM), one of the effective ways is to obtain its steady-state probability distribution. Because the two-product-type and multi-parallel-machine system that demand backlog is not allowed can be considered as a basic building block of the mP/mS/mM system, we begin by investigating the method of obtaining its steady-state probability distribution under the prioritised hedging point control policy. Although the shape of the distribution domains of the work-in-process (WIP) levels influences the steady-state probability balance equations, we develop a unified form of the marginal probability balance equations for all the possible shapes of distribution domains, which can be used to calculate the marginal probability distribution for each product type for the two-product-type and multi-parallel-machine system. Furthermore, we extend this analysis method to both the multiple-product-type, multi-parallel-machine, and single-stage system and the more complex mP/mS/mM system, and propose a method to obtain their approximate marginal probability distributions of the WIP levels. Finally, numerical experiments are conducted to verify the accuracy of the proposed method of analysing the steady-state probability distribution of an mP/mS/mM system.     

Optimal design of a hybrid push/pull serial manufacturing system with multiple part types

The objective of this research is to investigate the possibility of integrating Manufacturing Resource Planning (MRP)/push and Just in Time (JIT)/pull strategies in a multiproduct multistage serial manufacturing system. Each workstation is able to undertake different operations and so to produce more than one type of in-process item. A modified version of a horizontally integrated hybrid push/pull production system is developed. The system can be optimized by locating points of integration, and determining the optimal values of safety stocks for the push part and numbers of Kanbans for the pull part. A modification of genetic algorithm (GA) chromosomes and crossover procedures is developed for the optimization. The optimization involves evaluations of stochastic performance measures by a discrete event simulation model. The motivating case study of a tube shop in an aerospace manufacturer is presented. This research extensively explores the question of whether each part type should have its own junction point (less constrained) or whether there should be one common junction point for the overall system (easier to implement).     

Hybrid manufacturing/remanufacturing lot-sizing and supplier selection with returns,under carbon emission constraint

This paper addresses a lot-sizing problem in manufacturing/remanufacturing systems. The studied system is a single manufacturing line where both regular manufacturing and returns remanufacturing processes are carried out, with different set-up costs for each process. We consider also a returns collection phase from customers/distributors with deterministic returns quantities at each period of the planning horizon. The environmental aspect is assumed in this study by considering a carbon emission constraint for the manufacturing, remanufacturing and transportation activities. A mixed integer programming model to minimise the management cost and meet the customer’s needs under different manufacturing constraints is proposed. Otherwise, An adaptation of the well-known Silver and Meal (SM) heuristic and two hybrid method approaches (HM1 and HM2) providing approximates solutions are developed. The mixed integer model was tested on Cplex (Software optimizer), and the obtained results were compared with the ones provided by the adapted heuristic SM and the hybrid methods. The numerical analyses show that hybrid methods provide good-quality solutions in a moderate computational time. The proposed model establishes a collegial and an integrated process that sets values, goals, decisions and priorities along the considered supply chain while taking into account the environmental aspect.     

Optimal manufacturing policy in a reverse logistic system with dependent stochastic returns and limited capacities

The stochastic models of systems with reverse logistics usually assume that the quantity of products returned is independent of sales. This hypothesis is obviously not true and can lead to suboptimal production policies. In this paper a new sales-dependent returns model is described. In this model, the returns depend on the useful life of the products sold and on the probability of an end-of-life product being returned. A Markov decision problem is formulated in order to obtain the optimal manufacturing policy. A numerical example is provided to illustrate the use of the defined model. An approximated Markov decision model is defined where the optimal policy is easily obtained. The optimal policies of the original and the approximated models are compared.     

A robust optimisation model for hybrid remanufacturing and manufacturing systems under uncertain return quality and market demand

In remanufacturing research, most researchers predominantly emphasised on the recovery of whole product (core) rather than at the component level due to its complexity. In contrast, this paper addresses the challenges to focus on remanufacturing through component recovery, so as to solve production planning problems of hybrid remanufacturing and manufacturing systems. To deal with the uncertainties of quality and quantity of product returns, the processing time of remanufacturing, remanufacturing costs, as well as market demands, a robust optimisation model was developed in this research and a case study was used to evaluate its effectiveness and efficiency. To strengthen this research, a sensitivity analysis of the uncertain parameters and the original equipment manufacturer’s (OEM’s) pricing strategy was also conducted. The research finding shows that the market demand volatility leads to a significant increase in the under fulfilment and a reduction in OEM’s profit. On the other hand, recovery cost reduction, as endogenous cost saving, encourages the OEM to produce more remanufactured products with the increase in market demand. Furthermore, the OEM may risk profit loss if they raise the price of new products, and inversely, they could gain more if the price of remanufactured products is raised.     

Two-level hedging point control of a manufacturing system with multiple product-types and uncertain demands

This research is motivated by the co-operative production process of networked manufacturing systems (NMS). Manufacturing resource sharing and flexible production scheduling are two features of NMS. For an individual manufacturing system in an NMS, ‘flexible production scheduling’ means that it can produce multiple product-types and the switching of products is quick enough to respond to the demand fluctuation. ‘Manufacturing resource sharing’ means the utilisation of extra production capacity from other manufacturing systems in the NMS. Of course, that will bring extra cost. This paper focuses on the optimal production control problem of such a situation: one manufacturing system, multiple product-types, and uncertain demands. Here, it is assumed that there are two demand-levels for each product-type: the lower one and the higher one. The total normal production capacity is larger than the total lower demands and smaller than the total higher demands. If the total demands cannot be satisfied and the work-in-process (WIP) of all product-types decrease to a certain level, e.g. zero WIP, the extra production capacity may be utilised. For such a system, a new two-level hedging point policy is proposed, in which two hedging points (a higher one and a lower one) are given for each product-type. Different from the prioritised hedging point (PHP) policy which is usually applied to one-machine and multiple part-type systems, our control policy considers all part-types at the same prioritised level and keeps the work-in-process states of all product-types on a straight line in the state space. Thus, the total costs for WIP inventory and the occupation of extra capacity can be obtained in a closed form, which is a function with respect to the hedging points. Then the method for optimising the hedging points is proposed and the special structure of the optimal hedging point is obtained. Numerical experiments verify the optimality and the special structure of the hedging point obtained by our method.     

Optimal policies in hybrid manufacturing/remanufacturing systems with random price-sensitive product returns

We study a production planning problem in which a manufacturer aims to meet a random market demand by manufacturing new product and remanufacturing returned product. The product returns are random and price-sensitive. To maximise his profit, the manufacturer needs to optimally decide on the acquisition price for the returned product as well as the quantities of the new product to be manufactured and the returned product to be remanufactured. We investigate two cases based on the relative lengths of the manufacturing and remanufacturing lead times. (1) In the case with a shorter manufacturing lead time, the manufacturer first decides his acquisition price for the returned product before the production starts, and then decides the quantities of manufacturing/remanufacturing after the product returns are realised. (2) In the case with a shorter remanufacturing lead time, the manufacturer first decides the manufacturing quantity and the acquisition price simultaneously, and then the remanufacturing quantity based on the quantity of manufactured and returned products. Each case is formulated as a two-stage stochastic optimisation problem, and the corresponding optimal polices of both are characterised and derived.     

Robust production control policy for a multiple machines and multiple product-types manufacturing system with inventory inaccuracy

Inventory inaccuracy often exists in manufacturing systems, which has great negative impact on the performance of production control, e.g. very high work-in-process holding cost or backlog penalty. To hedge against inventory inaccuracy, the robust production control problems will be investigated for a multiple machines and multiple product-types manufacturing system with uncertain production capacity. The objective of our problem is to minimise the average production cost. To solve this problem, a robust production control policy is developed, which is insensitive to the inventory record errors, and whose robustness is better than the traditional hedging point policy for optimal production control. Finally, numerical experiments are conducted to examine the performance of the proposed robust production control policy against inventory inaccuracy. Based on the experimental results, the conditions of applying the proposed policy are also obtained.     

Optimal configuration of remanufacturing supply network with return quality decision

This research studies the configuration problem of a remanufacturing production network together with the decision for return quality thresholds, in which, the manufacturer has multiple remanufacturing facilities to satisfy different market demands. Quality of returns is stochastic, while demand for remanufactured products is either stochastic or deterministic. The problem we considered is to determine facilities to operate, minimum quality to accept into each operating facility, return quantity and demand allocation simultaneously so that the system’s profit is maximised. The problem is formulated as a mixed integer non-linear programming model. Through the use of a numerical example, the impact of quantity of returns, total spending, quality uncertainty, demand uncertainty and transportation cost on the remanufacturing system is analysed.     

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.     

Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy

This paper investigates a reward-driven policy, employed in a closed-loop supply chain (CLSC), for acquiring used products earmarked for remanufacture. Under the examined model, a single manufacturer sells products through a retailer as well as directly to end users in a forward supply chain. In the reverse supply chain, three different modes of collection are employed to capture used products for remanufacture: they are through a third party, directly by the manufacturer and from the retailer. Mathematical models for both non-cooperative and centralised scenarios are developed to characterise the pricing decisions and remanufacturing strategies that indicate individual and overall supply chain performance. Optimality of all the proposed models is examined with theory. To coordinate and achieve a win–win outcome for channel members, we proposed a three-way discount mechanism for the manufacturer. Extended numerical investigation provides insights on ways to manage an efficient reward-driven CLSC in a dual-channel environment.     

Environmental issue in an integrated production and maintenance control of unreliable manufacturing/remanufacturing systems

This paper addresses a joint production and maintenance problem under environmental constraints and reliability issues in a manufacturing/remanufacturing context. The manufacturing system is composed of one machine producing one type of product. The remanufacturing system, also composed of one machine, retrieves returned products from the market in order to refurbish them. The manufacturing and remanufacturing systems aim to satisfy random demands under a given service level. Moreover, the entire system generates harmful emissions. Exceeding carbon emission limits defined by authorities may risk sanctions. We aim to propose a compromise between ecologic and economic production and maintenance plan by calling on green subcontracting in order to satisfy the demand and avoid emission excess. Three models are proposed in this paper. These models tackle mainly the basic production problems and propose alternative equivalent solution schemas for future extensions. The robustness and usefulness of the proposals are illustrated with various examples and sensitivity analyses.     

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

Lot-splitting approach of a hybrid manufacturing system under CONWIP production control: a mathematical model

This paper discusses the advantages of lot splitting in hybrid manufacturing environments where cellular and functional layouts are combined under Constant Work in Process (CONWIP) production control. The proposed model fills a research gap in the related literature by applying lot splitting and pull production simultaneously. A linear CONWIP control mathematical model that minimises the average flow time is developed in case of lot splitting. The developed model has sequence-dependent set-up times. The demand level, coefficient of variation (CV) impact and set-up time reduction effect on CONWIP production control are also investigated. The model is solved using GAMS21.6 optimisation software; the optimal backlog list, the number and size of sublots are reported. The proposed model is compared with lot production under push control in different settings as well as with two different heuristics from the literature. Experimental results indicate that in all settings, the lot splitting is more advantageous than lot production in terms of average flow time. CV has a greater effect than set-up time reduction on average flow time.     

The impact of information transparency on the dynamic behaviour of a hybrid manufacturing/remanufacturing system

A combined manufacturing/remanufacturing system is modelled and its dynamic behaviour is investigated using a control engineering approach. The model is an extension of the automated pipeline, inventory and order based production control system (APIOBPCS), which is well understood from a dynamic perspective. It is assumed that the remanufacturing process is based on a PUSH policy. Utilising different levels of information transparency from the remanufacturing process, three system types are developed and compared. Mathematical and simulation analyses of the system types were undertaken and their robustness to remanufacturing process uncertainties were tested. Our analysis indicates that the greater the degree of information transparency, the greater the robustness of the hybrid system.     

Optimal acquisition decision in a remanufacturing system with partial random yield information

When making decisions to acquire used products or components (cores), a remanufacturer faces limited information on the quality or proportional yield of cores during the recovery process. In this paper, we propose and analyse a robust optimisation model for studying the remanufacturing decision problem with partial random yield information, that is, when the quality information of cores is partly unknown in a remanufacturing system. Regarding the impacts of unknown yield information, we only require the support and mean of the proportional yield rather than the true distributions. The closed-form solutions of acquisition quantities are derived based on the minimax regret approach. In addition, to validate the effectiveness of the analytical results, particularly the acquisition of yield information, numerical experiments are designed and implemented using (1) the support and mean of the proportional yield based on the manufacturer’s knowledge and (2) a sampling inspection to evaluate the performance of the robust optimisation approach, the benchmark, and the naïve approach. We observe that the minimax regret approach slightly underperforms compared to the benchmark but performs much better than the naïve approach. As an acceptable choice, this approach is less complicated and extremely easy to implement to meet the needs of practical situations based on its robust closed-form solutions.     

Optimal production plan for a multi-products manufacturing system with production rate dependent failure rate

This study deals with the problem of dependence between production and failure rates in the context of a multi-product manufacturing system. It provides an answer about how to produce (i.e. the production rates) and what to produce (i.e. which product) over a finite horizon of H periods of equal length. We consider a single randomly failing and repairable manufacturing system producing two products P_a and P_b . The product P_a is produced to supply the strategic demand d(k) of the principal customer via a buffer stock S over k periods (k?=?1,?2,?…?,?H). The second product P_b is produced to meet a secondary but very profitable demand. It is produced during a given interval at the end of each period k. We develop a genetic algorithm to determine simultaneously the optimal production rate of the first product during each period k and the optimal duration of the production interval of the second product, maximising the total expected profit.