برنامه ریزی عملیات یکپارچه و زمان بندی در یک زنجیره تامین

This paper deals with the integration of process planning and scheduling, which is one of the most important functions in a supply chain to achieve high quality products at lower cost, lower inventory, and high level of performance. Solving the problem is essential for the generation of flexible process sequences with resource selection and for the decision of the operation schedules that can minimize makespan. We formulate a mixed integer programming model to solve this problem of integration. This model considers alternative resources: sequences and precedence constraints. To solve the model, we develop a new evolutionary search approach based on a topological sort. We use the topological sort to generate a set of feasible sequences in the model within a reasonable computing time. Since precedence constraints between operations are handled by the topological sort, the developed evolutionary search approach produces only feasible solutions. The experimental results using various sizes of problems provide a way to demonstrate the efficiency of the developed evolutionary search approach.

Supply chain is an integrated business process where various business entities work together in an effort to (a) acquire raw materials, (b) convert these raw materials into specified final products, and (c) deliver these final products to retailers (Beamon, 1998). A global chain covers multiple manufacturing sites and consists of suppliers, fabrication and assembly shops, as well as outsourcing entities. These supply chains’ planning and scheduling activities are very complex and have to take place within the enterprise and across the entire supply chain in order to achieve high quality products at lower cost, lower inventory, and high levels of performance. As a result, to efficiently provide global optimal solutions, enterprises are migrating from separated planning processes toward more coordinated and integrated planning processes. Recently, researchers have placed increasing attention on integrated models for supply chain planning. Process planning and scheduling are possibly the most important functions in a supply chain system. This is because these functions are essential for inventory to be available-to-promise for customers. Process planning determines how an item will be manufactured; it acts as a bridge between design, manufacturing, and scheduling. Process planning considers alternative resources. In practice, any customer order, assigned to a site for processing, can be scheduled on various resources and may have a flexible process sequence. If some orders have certain process sequences, they should be considered for an integrated model using alternative resources. Hankins, Wysk, and Fox (1984) showed that using alternative resources reduces lead-time and improves overall resource utilization. Nasr and Elsayed (1990) presented two heuristics to determine an efficient schedule for the n orders and the m resources problem with alternative routings allowed for each operation. Brandimarte and Calderini (1995) developed a two-phase hierarchical Tabu search for planning and scheduling. Palmer (1996) developed a method based on simulated annealing to solve integrated problems. However, the researchers mentioned above did not consider the precedence rule for an operation sequence; they only considered the time aspect with a non-constraint operational sequence. Tan (2000) presented a review of various research efforts considering the process planning and scheduling area and discussed the extent of applicability of various approaches in solving process planning and scheduling. Guinet (2001) proposed a primal-dual approach to solve a production planning model with a network. More recently, Moon, Kim, and Hur (2002) proposed an integrated model for flexible process sequencing and scheduling to minimize total tardiness. This model considered resource selection and precedence constraints. They developed an evolutionary algorithm approach to solve the model. Cochran, Horng, and Fowler (2003) solved parallel resource scheduling problems using a two-stage multi-population evolutionary algorithm. Tan and Khoshnevis (2004) presented a mixed integer programming model to solve process planning and scheduling problems. The main focus of our work is not only the formulation of a mathematical model that incorporates the process planning of resource selection and operation sequencing and the determination of their schedules so that the total processing time is optimized, but also the development of an efficient evolutionary search approach with a topological sort (TS) technique (Horowitz & Sahni, 1984) .This technique is to determine a set of operation sequences for orders. The evolutionary search approach has been successfully applied to a number of combinatorial optimization problems (Cochran et al., 2003, Gen and Cheng, 2000 and Moon et al., 2002). An evolutionary search approach based on a TS can generate a good solution to the model within a reasonable amount of computation time. Since precedence relations between operations are handled by the TS, an evolutionary search approach produces only feasible solutions.

We have proposed an evolutionary search approach based on a topological sort to solve the integrated process planning and scheduling problem in a supply chain. Solving the problem is essential for the generation of flexible process sequences with resource selection and for the decision of operations schedules that can minimize makespan. We have formulated a mixed integer programming model to represent the problem. The problem considers alternative resources and sequences, and precedence constraints. The objective is to find the optimal resource selection for assignments and operation sequences and to decide a schedule in order to minimize the makespan. To solve the problem, a new evolutionary search approach based on topological sort has been developed. Since precedence relations between operations are handled by a topological sort, the evolutionary search approach produces only feasible solutions. Experimental results have shown that the proposed evolutionary search approach can be a good alternative for locating an optimal solution in solving complicated process planning and scheduling situations because it produces better solutions than traditional approaches. In conclusion, the proposed evolutionary search approach can be effectively used to solve the complex and sizable problem of integrated process planning and scheduling in supply chains.