Keywords

1 Introduction

Global competition, decreased profit margins and market turbulence are forcing supply chains to become dynamic networked structures usually named as Virtual Enterprises (VE), Virtual Organizations (VO), Dynamic Virtual Organizations (DVO), etc. [2]. Within this new paradigm, the concept of Dynamic Manufacturing Network (DMN) has emerged as a manufacturing industry application of VEs that rely on common business processes, real time (or close to real time) information sharing, centralized decision making and optimized operational planning [7, 10].

Despite their numerous benefits such as time savings, cost reduction and visibility, DMNs are hard to plan and vulnerable in their operations [5, 6]. DMN formation requires quick and detailed planning to satisfy demand characteristics (buyer location and expected lead time) through the partner pool (capacities, competencies). Moreover, due to the autonomy of partners, a DMN does not completely control their internal operations, this bringing a behavioral risk to its operation. There are also further risk factors that arise from their dispersed structure, such as transportation disruptions and international problems [8]. While facing many disruption risks, reliability is a major performance criterion for DMNs [6]. For these e-commerce based networks, a failed batch not only means a lost order and lost profit, but also possibly significant lost future demand. There is a clear need for mitigating the risks involved in DMN processes.

In this study, reactive flexibility strategies are considered as a factor in DMN planning along with cost. Through integrating two flexibility measures: Slack Time and Slack Capacity into DMN planning, we managed to increase the reactivity of the network to disruptions. For this purpose, a multi-objective mixed integer linear programming (MILP) has been developed. This model aims at finding balanced solutions with minimum total network costs and maximum flexibility.

2 Context

A typical VE goes through a life cycle that is composed of formation, operation, evolution and dissolution stages [11]. In this context, the DMN life cycle is presented in Fig. 1. In the formation stage of DMNs, a business opportunity is received via an e-marketplace, and the DMN formation and planning modules are triggered, to use real time data on partners’ capacities and costs. After the network has been formed and the demand has been confirmed, the DMN enters its operation stage. In the operation stage, the DMN monitoring module tracks the execution of the initial plan with the aim of controlling operations.

Fig. 1.
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DMN life cycle

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In case there is a disruption in the execution phase, the necessary actions should be performed to maintain on time delivery [7]. Within the DMN context, we use the term disruption as the deviation from the initial plan, characterized by delays in production or transportation, quality problems, etc. When an operational disruption is tracked and on time delivery is jeopardized, the customer needs to be contacted and recovery actions have to be negotiated. In fact, such a situation will decrease the reliability of the network as perceived by the customer. However, if it is still possible to reconfigure the network, the new real time partner data will be used for re-planning purposes. This may not mean a total reconfiguration of the network, but rather switching partners or transportation modes. Our aim is to do the initial planning by anticipating future disruptions.

For a prompt formation of DMNs, when real time data is available, optimized approaches are required. However, traditional deterministic cost models fail to respond to the flexibility needs of DMNs. A pure cost model may not allow space for reconfiguration if a disruption is detected. Since disruptions are naturally random, and assigning them probabilities is impossible in practice, we chose to increase the reactivity of the network by incurring in a reasonable cost.

3 The Approach

Mixed Integer Linear Programming (MILP) models are commonly used in integrated network formation and operational planning problems, due to their flexibility in encompassing different practical features, and to the reasonable easiness in solving problems to optimality, through commercial solvers. Therefore we have modeled the DMN Planning problem as a deterministic MILP model, with flexibility concerns.

Under the assumption of time independent production and transportation costs, a minimum cost solution is achieved via forward scheduling of the operations. The main reason for adopting forward scheduling is to avoid any stock that would result in extra holding costs for the system. On the other hand, maximum flexibility solution leads to backwards scheduling, selecting all the companies and assigning production as early as possible. However, from a purely economic perspective this is far from ideal. Our aim is to find a trade-off solution, in terms of flexibility measures and cost.

3.1 Flexibility Concerns

Supply chain flexibility can be used as a strategy to deal with potential operational risks and disruptions [3]. Instead of other network formation criteria such as cost, lead time, or quality, flexibility does not represent a fixed performance measure but rather a potential to deal with risks of unknown probability. In the manufacturing context, it can be defined as the capability of a manufacturing system to deal with both internal and external disruptions, while maintaining the competency and profitability levels [4].

In terms of the way to approach risk mitigation, supply chain flexibility strategies can be classified in two main classes: proactive flexibility and reactive (adaptive) flexibility. While proactive strategies are effective in mitigating internal risks, adaptive strategies are utilized to deal with the consequences of disruptions [9]. At this stage reactive flexibility strategies are required to quickly reconfigure the supply chain, in order to compensate disruptions and prevent losses. The reactive (buffering) strategies are safety stock, slack capacity, supplier backups, and slack lead times [1].

In this work we have developed two flexibility measures as total slack lead time and total slack capacity. These two measures will be used as the objectives of the MILP model to maximize total reactive flexibility.

3.2 Model

We present now a generic MILP model to support DMN formation and operational planning. The model is based on the assumption that manufacturing processes of production orders can be broken into several serial production stages.

This generic model allows us to change production stages, if different operations are included in the process. We considered a multi-order \( (\forall k \in K) \), multi-customer \( (\forall c \in C), \) multi-partner \( (\forall n \in N), \) multi-echelon \( (\forall i \in O) \) DMN structure, where each order k goes through manufacturing stages \( O_{k} \) that are a subset of O \( (O_{k} \subset O) \). Moreover, for each operation i \( (i \in O), \) there is a subset of partners \( ( N_{i} \subset N) \) that are capable of performing operation i. The production allocation and lot sizing decisions will be given within a discrete time horizon, where a unit time period is denoted by t and where the last planning period is denoted as T. The network general characteristics are presented in Fig. 2, and a verbal, synthetic formulation of the model is given in Table 1. To solve the multi-objective problem we have used a weighted sum method.

Fig. 2.
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Network structure

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Table 1. Verbal formulation of the model
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4 Results

The developed multi-objective MILP model was implemented in and solved with the CPLEX 12.5 optimization software. For assessing the approach, an illustrative network was designed. This network has 3 operations, 6 time periods, and 9 partners, where each echelon has 3 different potential partners to be assessed for assigning production (P1, P2, P3 for operation 1; P4, P5, P6 for operation 2 and P7, P8, P9 for operation 3). Each partner shares their available capacities and detailed costs for the planning horizon. The system also takes into account transportation costs in-between partners. For an easy illustration of the model, we have first considered a single order from a single customer, with a lot size of 200 units to be delivered at time 6. Figure 3 presents three alternative plans we have reached by considering different objective weights. Please note that for this data set, the maximum lead-time is 18, the maximum capacity is 26767, and the minimum cost is 17285 Plan 1, which is the “pure cost” solution, includes one partner per operation (P1, P5, and P12) and forward schedules mainly, with a small slack lead-time of 2.5. Plan 2 is the “pure slack time” solution, where production is totally forward scheduled, with 4 partners (P3, P4, P5, and P10). Plan 3 is a multi-objective solution, with equal weights for each objective, composed of P1, P5 and P12 and has a close to maximum slack lead-time value, with slightly higher cost (5 %). In fact, capacity stays at its minimum (8258) at the balanced solution, since the capacity utilization for this example is low.

Fig. 3.
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Solutions to the example

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While an increase in slack time requires back scheduling and an increasing inventory holding cost, an increase in slack capacity requires adding more partners to the network. This is obviously a higher level decision, inducing a higher cost. Further tests also revealed that with multiple orders and high capacity usage, it becomes less costly to include more partners to the network, and split batches among different partners.

5 Conclusions

In this study we have presented a multi-objective model for the formation and operational planning of Dynamic Manufacturing Networks (DMN) that simultaneously minimizes total cost and maximizes reactive flexibility measures. A DMN network is defined as a multi-echelon serial structure, with multiple customers and multiple orders. The total cost function covers production, transportation, holding and network formation costs, from the first echelon to order shipment to the customer. Slack lead time and slack capacity measures were developed, as a way to measure the reactive flexibility of the network. The model allows the decision maker to recognize and understand the trade-offs between cost and flexibility, and to choose the network configuration that best suits to the external conditions, such as how prone the operations are to disruptions and how much the DMN broker is willing to pay for flexibility.