Extension of multi-commodity closed-loop supply chain network design by aggregate production planning

Supply chains with product recovery differ, depending on the characteristics of the product, the recovery activity which is used and whether this activity is done by the original equipment manufacturer or a third party [6]. In general, supply chains with product recovery can be distinguished into open-loop and closed-loop supply chains (CLSC). If there is hardly any connection of the forward and return product flows, the supply chain is open-loop and the forward and reverse product flows are managed separately. The forward product flow can be described by the traditional supply chain management theory, and the reverse product flow is planned independently by reverse supply chain management [25]. If the forward and return product flows are related, e.g. customers supply their used products as production inputs, the supply chain is closed-loop. In this case, often an integrated management of both flows is necessary to achieve an optimized CLSC; for further details see [8, 9].

In this work, a supply chain is studied which is closed by component remanufacturing. Remanufacturing is also called value-added recovery, since it describes a series of operations which restore the value of a product after usage [11]. A supply chain with remanufacturing is extended by the following activities: collecting, cleaning and testing returned products. Then, remanufacturable products are disassembled into components, which are remanufactured, e.g. repaired or refurbished. After testing these components, they are reassembled and sold in secondary markets as remanufactured items or reintegrated to the original supply chain and used as as-new items [11], as in the supply chain studied in this work. High-value products, e.g. copiers and automobiles, are suitable for component remanufacturing. A further discussion of product characteristics that enable remanufacturing can be found in [18].

Whether the supply chain is open- or closed-loop, product recovery forces supply chain management (SCM) to consider a reverse product flow. In addition to the planning, realization and control of all operations, production, inventory and distribution quantities and information flows from the product origin to the point of consumption, all problems concerning the way back through the supply chain, i.e. after consumption, have to be considered in a SCM with product recovery. These decision problems can be differentiated regarding their planning horizon: some are made on a yearly basis and determine the framework for decisions, which are made on a weekly or monthly basis [26]. Then again, these decisions constrain the operational decisions, which occur every day [20].

The network design, decisions regarding the product and material programme, supplier selection, collection strategy, take-back arrangements and supply chain coordination are strategic decision problems and belong to long-term planning. Decision problems regarding inventory management and production planning are tactical and have a mid-term planning horizon. Operative decision problems, as disassembly planning, material requirement plans, scheduling and routing in the remanufacturing shop have a short-term planning horizon [4, 5, 7, 28].

In order to achieve an optimized CLSC the tactical planning has to be considered by strategic management [14, 21, 26]. Long-range forecasts of aggregate product demand are the input for strategic planning [5]. They are used by the mathematical model developed in this work to derive a cost-optimally network design, i.e. cost-optimal facility locations and capacity equipment, with cost-optimal procuring, transportation, production and storage quantities. The quantities are planned on an aggregate level; therefore, fluctuations of data are neglected and the modelling approach is deterministic.

In the facility location problem (FLP), facilities are located and quantities of goods are allocated and distributed in the network a cost-optimal way, e.g. in [2]. In the special case of a CLSN with reverse product flows these models support the procuring decision, i.e. when to recover returned products and use them as production inputs, as well, e.g. in [8, 9].

In the literature so far, location/allocation models in a CLSCN consider opening costs of product recovery facilities, but costs for volume capacity and costs for installing technology or hiring workforce for the operations at the respective facilities of the network, especially for product recovery operations, are neglected. However, to determine a cost-optimal procurement policy, i.e. to decide when to recover returned products and use the resulting items as production inputs instead of new items procured from suppliers, these costs have to be included.

Since remanufacturing is a labour-intensive operation (see [13] for an extended discussion), labour hour costs are relevant for the decision to process returned products. The well-established aggregate production planning (APP)-framework is used to plan the production and workforce at facilities cost-optimally in this work. In APP, the length of the planning horizon is usually between 6 and 24 months [3] and quantities are planned on an aggregate level. In the following this APP-approach is described and a multi-period facility location problem extended by capacity and aggregate production planning is developed.

The consideration of different product compositions, component remanufacturing and component commonality is possible with this modelling approach, and the influence of different return rates can be investigated. Hence, different realistic SC settings can be captured.

The rest of the paper is organized as follows: relevant selected literature regarding network design and aggregate production planning is presented and discussed in the next section. Here, the differences between other contributions and the approach taken in this work are also discussed. The CLSCN and the production planning problem are presented in detail in Sect. 3. Afterwards the planning problem is described mathematically in Sect. 4. In Sect. 5, it is solved for an example data set and the results are presented. Furthermore, a sensitivity analysis is performed and selected results are discussed in Sect. 5, too. Finally, conclusions and possibilities for further research are stated.

Networks with product recovery are mathematically optimized by extending the classical Warehouse Location Problem (WLP) to capture reverse product flows. Mostly these problems are described by Mixed Integer Programming (MIP) and Mixed Integer Linear Programming (MILP) models. In the following, selected papers are discussed, which present the state of research, and have influenced this study. A more detailed review of network design literature concerning supply chains with product recovery is offered in [1].

As one of the first, Marin and Pelegrin [19] study a network with reverse product flows: customers get products at plants and return them to plants. The objective is to find the optimal plant location and shipping quantities, such that the costs for opening facilities and for transportation are minimized. Marin and Pelegrin’s [19] model is an uncapacitated Facility Location Problem (FLP), whereas the other models discussed in the following are capacitated FLP.

Following [19], in this work it is assumed that customers return their products to those facilities from which the products are distributed. Unlike [19], in the network studied here, these facilities are not plants, but facilities for distribution and collection of products, called distribution and collection centres (DCCs). Furthermore, in [19] a single product type is considered, whereas in this work multiple product types are studied.

A remanufacturing network with multiple product types is examined by Jayaraman et al. [15]. Used products are shipped from collection zones to remanufacturing centres, where they can be remanufactured or stored. Remanufactured products are distributed, i.e. are used to fulfil customer demand, or stored. The shipping quantities between collection zones, customers and remanufacturing/distribution locations are to be determined optimally; the objective is cost minimization.

In this work, following [15], it is assumed that returned products can be stored at remanufacturing centres. As in [15], the storage capacity at remanufacturing facilities is assumed to be limited. Additional to storage capacities, capacities for operations at facilities are planned in this work, too.

Operative capacity equipment is studied by Schultmann et al. [24]. The model by [24] allocates the optimal operative capacity equipment to open facilities of an existing reverse supply chain. The capacity at facilities is needed for operations, as e.g. inspection and sorting, of multiple product types. The objective is to minimize costs, caused by capacity equipment, production and distribution quantities.

Unlike in [24], in this work a closed-loop system is studied, i.e. in addition to reverse product flows, forward product flows are considered. Fleischmann et al. [8] and Fleischmann et al. [9] study such a closed-loop system as a three echelon network, consisting of warehouses, plants and test centres, where products are recovered. These facilities have to be located optimally, and the quantities of the forward and reverse product flows of the network are to be determined such that costs for opening, transport and for unsatisfied demand and not-collected returned products are minimized under capacity limitations for the product flows between facilities of different network echelons.

Salema et al. [23] extend the model from [9] to study multiple product types. Furthermore, in [23] the product flow capacity at facilities is limited by maximum and minimum capacity bounds for the facilities.

As in [9, 23], the CLSCN studied in this work has three facility levels. Here, the three facility levels of the CLSCN are DCCs, plants and suppliers and remanufacturing centres, both delivering components to plants. The production system of the CLSCN consists of two stages: at the first stage components are delivered from remanufacturing centres or from suppliers to plants, where they are assembled to products. This way, component remanufacturing, unlike product remanufacturing as in [9, 15, 19, 23], with different product and component types and component commonality in the assembly of different product types can be modelled.

In contrast to [9, 15, 23], the capacity for storage and product and component flows at facilities are decision variables, i.e. have to be determined out of a parameter range and induce costs. In addition, capacity for the operations at facilities is determined by the model stated in this work. Hence, the influence of different capacity types on the facility location decisions and on the decision to produce, remanufacture, store or distribute is studied.

All studies discussed above have a single time period planning horizon. Following [15, 21] consider inventory in a single time period planning facility location problem and study the trade-off between storing and distributing products. Further discussions of inventory in distribution networks and the interdependence of inventory, transportation and facility location can be found in [21] and different approaches to extend facility location problems by inventory management can be found in [26].

In this work, the planning horizon of the CLSCN design problem is modified to a multi-period setting, as in [22] and [30]. Pishvaee and Torabi [22] use a multi-objective approach to combine cost minimization of the CLSCN with the minimization of delivery tardiness for the single product case. In this work, the objective is to minimize costs and the production and capacity planning problem at open facilities in a network with multiple commodities is considered in a MILP-approach.

In this work, a FLP for a closed-loop supply chain with component remanufacturing is extended by production planning on an aggregate level, using the idea of APP, as in Steinke and Fischer [30]. In APPs, the different products are aggregated to product types and the capacities are not product specific, but are summarized and stated in common units, e.g. labour hours. APP is used to determine cost-optimal manufacturing and storage plans, which match the limited means in terms of workforce or working stations, respectively, and production input with forecasted demand [20]. The planning horizon of an APP can vary; usually it consists of 6–24 months, [3]. In particular, when adjustments of capacities are allowed in each period, the periods have to be sufficiently long.

Jayaraman [16] studies the production planning problem of a company, which offers recovered mobile phones for a secondary market. He states the Remanufacturing APP (RAPP) model, which minimizes costs by determining the optimal disassembly, disposal, remanufacturing, procurement and storage quantities under fixed workforce capacities.

In this work, the approach of [16] is followed to model the production system. While in [16] the reverse product flow is managed, here, a closed-loop system is studied, and the model is extended accordingly, i.e. the remanufactured components are reintegrated into the original supply chain instead of being shipped to secondary markets. Moreover, in contrast to [16], capacities in volume units and labour hours at facilities are not fixed but can be adjusted over the planning horizon.

In the RAPP proposed by [16] only one site for remanufacturing is considered, whereas in this work, multiple possible facility locations exist. Hence, the APP for a closed-loop system is integrated into a FLP. Extending a yearly FLP for a CLSCN with component recovery by an APP on a monthly basis leads to a model with extensive solution times. Furthermore, the considered capacities cannot be adjusted within one month; especially, decisions regarding the volume capacity are made on a strategic level. Therefore, also the APP is extended and the APP is modelled for a strategic, yearly, planning horizon.

With such an extended strategic planning model, decisions regarding the location of facilities and their capacity equipment for operations and storage can be studied jointly. Furthermore, different product and component types are considered and the interdependence of processing, storing and distributing them is examined. Moreover, by considering capacity costs and operative capacity in addition to storage capacity, the cost effects of the decisions regarding the returned products, i.e. if they are remanufactured, stored or disposed, are captured completely unlike in facility location problems without capacity and production planning.

Following [9, 19, 23, 30], a fixed relation between demand and returned products is assumed in this work; the returned product quantity is determined as a fraction of the sold product quantity. As in [30], the CLSCN is studied over multiple time periods, and hence, there is a time lag between the selling and the returning of a product. In [30] it is assumed that products are returned by customers after one period of usage. However, products can stay longer with the customers, i.e. the residence time of a product, defined as the number of periods a product is used by a customer, can be longer. Furthermore, products are returned not only in a specific period following the buying, but in all subsequent periods of the planning horizon. In this work, the model in [30] is extended to capture these aspects.

Moreover, the FLCAPPR model developed in this work determines cost-optimal volume capacities and optimal workforce size at the facilities for every period. In contrast, in [31] the capacity planning is integrated in a more simplified way, such that overcapacities can occur: whenever a facility is opened, its volume capacity and workforce are set to their respective upper limits and adjusted to the actual required levels only in the last period. Furthermore, while in [30] total costs are minimized, here discounting is considered in the objective function, too.

In this section the network structure of the CLSCN with component remanufacturing is introduced and the respective planning problem is described in detail.

The CLSCN consists of nodes, which represent customers and facilities with their operations, and arrows, which show the flows of multiple commodities through the network, see Fig. 1. There are five different types of nodes: costumers, DCCs, remanufacturing centres, plants and suppliers. Customers demand different product quantities in each period, and they return their products to DCCs in a later period, i.e. it is assumed that a known fraction of products shipped to customers in one period is returned in a later period of the planning horizon. The residence time of products can be different, but there is a given number of periods the product has to stay with a customer before it is returned and considered as remanufacturable. The minimum residence time can be interpreted as the minimum number of periods a product is in full working condition. Demand quantities are assumed as deterministic and known; therefore, the returned product quantities are deterministic and known, too. Demand is lost whenever it is not met, i.e. it cannot be backlogged.

The CLSCN consists of three facility levels: DCCs, plants, remanufacturing centres and suppliers. The latter are summarized to one level since both provide components. Supplier locations are given, whereas the locations of DCCs, remanufacturing centres and plants have to be determined. These facilities can be opened in one period and then remain open or are closed in a later period. It is assumed that once a facility is closed, it cannot be opened again.

Capacities at facilities are determined in volume and labour hours. The volume capacity restricts the volume of commodity flows passing a facility and, if existent, the volume of stocked products and components, respectively. The labour hour capacity limits the available hours of the workforce needed for remanufacturing and assembly at remanufacturing centres and plants, and for handling products at DCCs.

Capacity levels at facilities are determined once a facility is opened and can be adjusted in a later period, i.e. they can be expanded or reduced in fixed steps in every period.

The product and component flows through the network are described by three different types of arrows, see Fig. 1. The solid arrows show the forward product flows, which are shipped from plants to DCCs and further to the customer locations. The dotted arrows describe the component flows leaving suppliers or remanufacturing centres, respectively, to plants. The dashed arrows represent the reverse product flows, i.e. the flows from customers to DCCs and from DCCs to remanufacturing centres. In this CLSCN redistribution is possible, i.e. products and components can be shipped between facilities of the same type.

DCCs are bi-directional facilities, because products flow through DCCs to customers and customers return used products to DCCs. At DCCs returned products are collected, visually inspected and, afterwards, they are shipped either to remanufacturing centres or to the disposal unit.

The decomposition of returned products into components and the remanufacturing of those components to an as-new condition is performed at remanufacturing centres. It is assumed that components can be remanufactured repeatedly in the planning horizon, i.e. the limited number of possible remanufacturing cycles for components is not reached. However, there is a known and constant fraction of components that cannot be remanufactured to the quality standards of as-new components with a reasonable given effort and therefore has to be disposed. Moreover, at remanufacturing centres it is possible to store returned products, instead of remanufacturing them immediately.

At plants, components are assembled to products of different types. Product types differ regarding their combination of components, i.e. at least one component in the product composition has to be different in different products. Components can be product type-specifically or commonly used among different product types. They are shipped from suppliers or remanufacturing centres to plants and can be held on inventory at plants. No final products are stored in the studied network and products are assembled only if an order exists (MTO). Since the planning horizon is strategic, no lead-times for operations or transport are considered.

For each planning period the demand and return product quantities are known, while facility locations and capacity equipment at the facilities, as well as procurement, transportation, production and inventory quantities, have to be determined with the objective of total cost minimization. To support these decisions, the planning problem is formulated as a MILP, presented in the next section.

In this section, the planning problem described above, the Facility Location, Capacity and Aggregate Production Planning with Remanufacturing (FLCAPPR) Problem, is stated and explained using the notation listed in Tables 1, 2 and 3, presented below. The model presented here is an extension of the model given in [30], as described in Sect. 2 above.

The objective function of the FLCAPPR problem minimizes the discounted total costs of the CLSCN over multiple time periods. As the model combines multi-period facility location, capacity and aggregate production planning, the objective function consists of cost terms for opening, running and closing facilities, for the volume capacity equipment and the labour force at open facilities, for processing and storing goods at facilities, for procuring components at suppliers, for transporting goods in the network and for disposing returned products and components.

The discounted total costs are described by the following objective function (1). For the sake of clarity the objective function is split up into three different cost functions. The first cost function presents the costs induced by multi-period facility location, the second function includes the costs resulting from capacity planning, and the costs of aggregate production planning are described by the third function. Below the functions are introduced followed by the respective explanations.withIn the multi-period FLP studied in this work, the facilities can be opened in one period and in the later periods they can stay open or are closed. The variables \(Y^{y}_{Et}\), \(Y^{y}_{t}\) and \(H^{y}_{t}\) describe the respective state of a facility. The costs for opening, i.e. building, a facility, occur just once and are listed in line one and two. For every period in which a facility remains open it induces costs; these costs are captured by the terms in line three. In line four the costs for closing a facility are stated.

The cost terms in the next line are for procuring and shipping components from suppliers to plants. Costs for transporting components from remanufacturing centres to plants are listed in line six.

The transportation costs of the forward product flow, the flow of products from plants to DCCs and from DCCs to customers, and the penalty costs for unsatisfied demand are stated in line seven and eight.

The cost terms in line nine and ten are the shipping costs of the reverse product flow, i.e. the flow of products which are returned by customers to DCCs and flow further in the network to remanufacturing centres or to the disposal unit. In the latter case, costs for disposing occur. The disposal costs for returned products and remanufactured components are listed in line eleven. The costs for distributing products or components, respectively, on the same facility level are listed in line 12–15.At facilities, certain volume capacities in \(\hbox {m}^3\) are available and they can be increased or decreased within one period. These adjustments induce costs or revenues, as reflected by the cost terms in line 1 and 2 or revenues in line 3 and 4, respectively.Remanufacturing components at remanufacturing centres and assembling products at plants induces costs, see lines one and two. Labour hours of the workforce are needed for performing the respective operations at the facilities. The respective costs occur in every period and are stated in line 2 and 3.

Holding products and components at remanufacturing centres and holding components at plants induces costs, which are captured by the cost terms in lines 4 and 5.

The costs stated in lines 1–5 occur in every period, and hence, these costs have to summed up over the planning horizon. At the end of the planning horizon the remaining items on stock at the facilities are disposed, and the respective cost terms are stated in the last two lines.

In the following, the constraints of the problem are presented, but before that, important variables are explained.

The variables \(Y^{y}_{Et}\), \(Y^{y}_{t}\) and \(H^{y}_{t}\) are interrelated. If a facility is opened in one period, then it is running in this period; therefore, both variables \(Y^{y}_{Et}\) and \(Y^{y}_{t}\) take value 1 and \(H^{y}_{t}\) is zero.

In the next period this facility can be still open, then \(Y^{y}_{t+1} = 1\) and \(Y^{y}_{Et+1} = 0\), because the facility is already opened, and \(H^{y}_{t+1} = 0\). However, the open facility can be closed in \(t+1\), then \(H^{y}_{t+1}\) takes value 1, and \(Y^{y}_{t+1} = Y^{y}_{Et+1} = 0\).

It is assumed that a facility cannot be opened again after it is closed. The constraints (2)–(6) define these interrelations.A facility can be opened just once in the planning horizon.If a facility is opened in the first planing period, it is open in period 1.If a facility is opened and not closed in one of the periods \(t \le s\), where \((s,t) \in T\), then the facility is open in period s.These constraints indicate the closing of facilities by comparing the opening indicator variables of two successive periods.Closing of facilities is allowed to happen once within the planning horizon.

The next set of constraints, constraints (7)–(19), describes the forward and reverse product flows in the network and the inventory balance at plants and remanufacturing centres.Products are shipped from DCCs to satisfy demand of customer k for product p in period t. Unsatisfied demand is captured by \(U^{k}_{pt}\). After mr periods, products can be returned for the first time. In period t a proportion of products sold in period o, \(q_{kpo}^{t}\), is returned to DCCs. Every returned product is collected in DCCs.These constraints represent the inventory balance equations for components at plants.The inventory balance equations for returned products at remanufacturing centres are stated in (11).Components can be stocked at remanufacturing centres, too. The inventory balance is determined by the equations (12). The constraints (13) and (14) define the balance of the respective inventory at the end of the first period. Products and components remaining in the respective inventories at the end of the last planning period, LT, are captured by (15) and (16).Since no inventory at DCCs is allowed, every product entering a DCC in period t also has to leave it in period t.There is no product inventory at plants, i.e. every assembled product in a plant in period t is shipped to DCCs in the same period.Every returned product is shipped from DCCs either to remanufacturing centres or to the disposal unit D.

The constraints (20) and (21) define the disposal quantities in the network.At least a proportion of \(md_{t}\) of the returned products has to be disposed in period t, because of failing the inspection at the DCCs.After remanufacturing, at least a proportion of \(md^c_{t}\) of the components does not comply with the requirements for as-new components and is disposed.

The following constraint sets, the constraints (22) and (23), describe the disassembly and assembly operations at the remanufacturing centres and plants, respectively.The number of as-new components, derived by disassembling returned products and remanufacturing the respective components, is defined by the equations above.The number of components required for product assembly at plants is defined by these equations.

At facilities capacity in labour hours and volume are considered and have to be planned over the planning horizon. The next sets of constraints, the constraints (24)–(43), describe the capacity planning.The capacity level in terms of labour hours at facilities is the product of one worker’s labour hours per period, le, multiplied by the workforce available in t, determined by \(LCap^{v}_{t}\) for DCCs. The constraints above adhere that the labour hours needed for handling products at DCCs do not exceed the available capacity level.The labour hours used for remanufacturing at a remanufacturing centre cannot exceed the respective available capacity.At plants, capacity in terms of labour hours is needed for assembling products. It is limited by the capacity level at a plant.The capacity in labour hours at an open facility is restricted by upper and lower bounds, forced by operations and the availability of workers.The volume capacity at the facilities is a multiple of e. The volume of components stocked at an open plant cannot exceed its available volume capacity.At an open remanufacturing centre, the volume of stored products and components has to comply with the volume capacity.The volume of components flowing into a plant is restricted by the available volume capacity.The product flow through a plant adheres to the volume capacity restriction of a plant.The volume of the components and products flowing into a remanufacturing centre is limited by its volume capacity restriction.The volume of the components and products leaving a remanufacturing centre has to be less or equal than the respective capacity level.The volume of products flowing through a DCC has to comply with its capacity.The volume capacity level of a facility is a multiple of e and is limited by given upper and lower bound.Volume capacity at facilities can be expanded or reduced within one period.In the first planning period, the number of capacity steps at a facility is identical to the capacity expansion carried out in period 1.The variable \(YCCapU^{y}_{t}\) takes value 1, if the respective variable \(CCap^{y}_{t}\) is bigger than zero, i.e. the capacity of facility y is increased in period t.Capacity increase is assigned to the variable \(CCapU^{y}_{t}\).The upper capacity bound of a facility limits the capacity increase.The variable \(CCapD^{y}_{t}\) captures the capacity decrease.Capacity decrease at a facility cannot be higher than the respective upper capacity bound.Capacity can just be increased at an open facility.Unsatisfied demand, the flows of products or components between different echelons and between facilities of one echelon, the produced units, the units on stock, the capacities at the facilities and the capacity increase are described by positive integer variables.Variables describing the change of capacities at facilities are integers and can be positive or negative.The variables that determine the volume capacity decrease are negative integer variables.Binary variables indicate the opening and closing of facilities and the capacity increase.

In this section, the previously stated FLCAPPR model is solved for an example data set. At first, the example, its data and the solution are described, and then, the sensitivity of the network to changes in the data is studied. The influence of the cost parameters on the decision to remanufacture is explored. Furthermore, the robustness of the solution with respect to the quantity of returned products and the length of the planning horizon is examined by varying the return rate and the number of periods in the planning horizon. Selected interesting results are discussed.

In this work, the strategic CLSCN design is extended by capacity and production planning on an aggregate level. The resulting FLCAPPR model determines the cost-optimal network design, the facility locations and capacity equipment at open facilities, and the cost-optimal procurement, production and distribution quantities in the CLSCN over a finite planning horizon consisting of multiple periods. It is solved for an example from the copier industry with input data based on previously published research [8]. Furthermore, possible effects of the extended planning approach on the network design, especially on the decision to recover returned products, are studied in a sensitivity analysis. Thereafter, the robustness of the network design and the production and distribution quantities regarding the return rate, i.e. the quantity of returned products, is examined. In a further study the influence of the planning horizon length is investigated.

Extending a single-period FLP to the FLCAPPR model leads to new and different results concerning the decision to remanufacture and the effect of the return rate on the network. In contrast to a previous study [8], in this setting, it is cost-optimal to dispose returned products instead of recovering them and use the resulting components in the product assembly based on the FLCAPPR model. When capacity costs, especially labour hour costs at the remanufacturing centre, are included, remanufacturing is cost-optimal only if the remanufacturing costs are sufficiently low compared to the procurement costs for new components from suppliers. Hence, production costs, in particular remanufacturing costs, have a large impact on facility location and capacity equipment decisions. Furthermore, the interdependence between the capacity equipment at the remanufacturing centre and the procuring decision, the processing and storing quantities at the remanufacturing centre is determined. Hence, these decisions have to be optimized jointly, as in the FLCAPPR model.

The decisions regarding facility locations and capacity equipment are robust for low return rates. From return rates of 40% remanufacturing takes place, if remanufacturing costs are sufficiently low. Moreover, for high return rates, rates of 80% and more, the facility location decisions and the distribution system are changed compared to the results for lower rates. Therefore, the forward and reverse product flows in the network have to be planned together.

The multi-period setting of the FLCAPPR model enables a study of the influence of the planning horizon on the decision to remanufacture and provides new information compared to single-period FLPs, as in [8]. Product recovery is cost-optimal only if remanufacturing costs are sufficiently low compared to procurement costs and the planning horizon is sufficiently long. For the studied data setting, this means that there has to be product demand for at least 5 periods, i.e. five years; only then remanufacturing can be cost-optimal.

Following the CLSC-Management definition in [12], a CLSCN has to be studied over the total product life-cycle with consideration of varying demand and returned product quantities and qualities. Hence, in the future the FLCAPPR problem should be solved with data sets consisting of varying demand and returned product quantities in order to study possible product life-cycle effects.

Moreover, when residence times are longer than one period, the reverse product flow starts later in the planning horizon. This can affect decisions regarding the facility locations and capacity equipment and, therefore, the remanufacturing decision. Hence, different assumptions regarding the residence times of products should be examined in the future.

Linear costs and revenues for adjusting capacity are assumed here, and the effects of economies of scale and learning effects gained by higher production quantities and bigger facilities are not considered. Furthermore, the possibilities to increase or decrease labour hours at facilities by overtime or part-time, respectively, is not modelled. These aspects require further model extensions, but it has to be noted that the FLCAPPR model is already large scale with rather lengthy solving times.

Finally, uncertainties regarding the quantity and quality of reverse product flows are an issue of CLSCM [11‐13]. They are not considered here, because an APP framework is used. However, other approaches integrating uncertainties might be developed; this is left for future research.