Task assignment with imprecise information for real-time operation in a supply chain

Abstract

Real-time operation is often required in a supply chain, where it is desirable to re-optimize the schedules each time a new order is submitted. An organization in a supply chain may not be able to perform all the tasks it has received completely due to lack of resources. It has to delegate those subtasks which it cannot perform to its suppliers in the supply chain. In a practical situation, the suppliers may be parts of more than one supply chain. Hence the organization does not have a complete control over the schedules of its suppliers. There should be coordination within and across organizations for producing the schedules. Usually, multiple objectives (or criteria) like quality, cost, and duration are associated with a task. Preference ratings, assigned by the end-user or the organization itself, may be associated with these criteria. The preference ratings may be specified in an imprecise manner by using ordinal values or linguistic terms. The assignment of the tasks to the suppliers, which is a multiobjective decision making problem, has to be done quickly for real-time operation.

In this paper, a supply chain is first modeled using a multiagent framework and an architecture for the agents located at every organization in the chain is presented. We then propose a real-time scheduler that can schedule new orders with soft real-time deadlines. An algorithm for the task assignment using the fuzzy set approach for the real-time operation in a supply chain is then proposed. Comparison of the algorithm versus other commonly used heuristic methods for task assignment is done in a simulated environment. The experimental results show significant performance gains for a large range of task arrival rates. However, the performance deteriorates for very high arrival rates. In order to overcome this limitation, we present a hybrid algorithm that augments the fuzzy technique and does not suffer from performance degradation even for high arrival rates.

Introduction

A supply chain can be defined as a network of autonomous or semi-autonomous business entities collectively responsible for procurement, manufacturing, and distribution activities associated with one or more families of related products [13]. Coordinating the activities of the various entities in a supply chain is important for improving performance in terms of multiple objectives such as on-time delivery, quality assurance, and cost minimization. A typical supply chain is shown in Fig. 1. It shows the upstream entities which are the suppliers and the downstream entities which are the consumers. As is evident, a supply chain is a distributed system.

Usually, there are three phases of decision making in supply chain management depending on the frequency of each decision and the time frame over which a decision phase has an impact [4]. These are the supply chain strategy phase, the planning phase, and the operation phase. In supply chain operation, the time horizon is weekly or daily, and companies make decisions regarding individual customer orders. Here, firms allocate individual orders to inventory or production, set a date that an order is to be filled, allocate an order to a particular shipping mode, set delivery schedules of trucks, etc. For many situations, it is desirable to re-optimize the schedules each time a new order is being considered [11]. This would enable details for scheduling the new order to be efficiently integrated with all other unscheduled orders. A new order may have a deadline associated with it and hence the whole operation has to be modeled with soft real-time constraints. This is referred to as real-time operation in a supply chain.

Multiagent systems consist of multiple autonomous or semi-autonomous agents where knowledge and control is distributed and agents communicate through messages [3]. Since supply chain operation is concerned with coordination among multiple decision makers, a multiagent framework for modeling it is a natural choice. In the current scenario, the consumer demand is ever changing and there are fluctuations in resource costs and availability. Hence companies must respond rapidly to maintain consumer satisfaction and profits. As these changes are occurring at increasing speeds, scales and complexity unmanageable by humans, the need for automated techniques becomes acute [14].

Let us consider a part of a supply chain with a focal organization H₀ and its upstream entities (the suppliers) as shown in Fig. 2. H₀ may not have all the required resources to completely perform all the subtasks of a task submitted to it. Those subtasks, which cannot be performed at H₀, have to be assigned to its suppliers quickly in real-time operational environments. As depicted, in a practical situation, the suppliers of H₀ may belong to more than one supply chain. Hence H₀ does not have a complete control of the scheduling activities of its suppliers. At the same time, more than one supplier may have the resources to perform a subtask. H₀ has to make a decision to choose one of the suppliers to which a subtask needs to be delegated. A similar task assignment decision has to be done by all the suppliers for the tasks delegated to them.

Usually there are multiple objectives (or criteria) like minimizing cost and time, maximizing quality, etc. associated with a task. Moreover, different preference ratings may be assigned to each of the criteria. These preference ratings, which are the relative importances for each of the criteria, may be assigned by the focal organization, downstream entities, or the end-users themselves. The problem of the assignment of a task to a node (we will henceforth use the common term node for an organization, a company, or a firm in a supply chain) is important since a good assignment would make it feasible to satisfy the criteria. Thus, task assignment in a supply chain is a multiobjective decision making problem.

In practice, it is convenient to assign ordinal values to the preference ratings. Linguistic terms like low, moderate, very high, etc. could also be used. There is imprecision implicit in the system under consideration. The first source of the imprecision is in the subjective specification of the preference ratings using ordinal values. Since we are considering a dynamic distributed system, another source of imprecision arises. A node does not have a complete view of the entire chain and hence does not have the global system state. Hence the global state has to be collected before the task assignment. Since the utilization of the resources and hence the schedules at various nodes change continuously, it is not possible to get a precise system state. Hence the decision making needs to be done allowing for tolerance for the imprecision.

In this paper, a model for the supply chain as a multiagent system is presented first with an agent located at each of the nodes. We design a real-time scheduler for the agents that would integrate schedules of new orders having soft real-time deadlines with the already existing schedules. To deal with the imprecision mentioned, a fuzzy set approach [16] is used in the context of multiobjective decision making for task assignment. We adapt the multiobjective decision process using fuzzy sets for the task assignment problem in a supply chain management system. The proposed technique is evaluated against other commonly used heuristic approaches for task assignment. It is seen that for a large range of task arrival rates the fuzzy technique has superior performance. However, its performance deteriorates for very high arrival rates.

To overcome this limitation, we next design a hybrid algorithm which augments the multiobjective decision process using fuzzy sets. This approach does not suffer from performance degradation even at very high task arrival rates. The hybrid algorithm is compared with other techniques and it is found that it out-performs all of them for all arrival rates.

An example where the proposed approach could be applied is the apparel industry. In this industry, outsourcing for various kinds of clothes is common and an apparel manufacturing company typically has many suppliers for the same types of clothes, each having different quality, cost, and lead times. A supplier may be part of different supply chains catering to more than one apparel manufacturing companies. A task here corresponds to the making of a trouser, suit, etc. Due to the ever changing market conditions, the manufacturer has to operate with real-time constraints to be competitive.

The paper is organized as follows. In Section 2, we review the related works. The supply chain is modeled using a multiagent framework in Section 3. The real-time scheduler used in the agents is explained in Section 4. In Section 5, the task assignment in a supply chain is formulated as a multiobjective decision making problem. Simulation studies are presented in Section 6. In Section 7, the hybrid algorithm is proposed. Section 8 concludes the paper.