برنامه ریزی تولید سلسله مراتبی تصادفی برای کارگاه های اتوماسیون انعطاف پذیر

This paper presents the hierarchical stochastic production planning (HSPP) problem for flexible automation workshops (FAWs) in agile manufacturing environments, which is a multiple-period multiple-product problem with random material supply, demands, capacities, processing times, rework and waste products. To solve the HSPP problem, a mathematical model is built up first. Then, an algorithm for HSPP is deduced in detail by using a stochastic interaction/prediction approach. The corresponding software package named as stochastic interaction/prediction algorithm (SIPA) has been developed and is presented in this paper, through which examples of HSPP have been studied, and which show that the algorithm can optimally decompose medium-term random product demand plans of an FAW into short-term stochastic production plans to be executed by FMSs in the FAW. Finally, the application of the algorithm is presented in detail through one of those examples.

A manufacturing department of a manufacturer in China is usually composed of several workshops or sub-factories, each of which is usually composed of some workshop-sections. Thus, the manufacturing department of the computer integrated manufacturing system (CIMS) in such a manufacturer is also composed of several shops, each of which consists of some manufacturing cells or flexible manufacturing systems (FMSs). Secondly, in theory, the workpiece-transport time and charges can be decreased by reconfiguration of the manufacturing cells (Chung and Fang, 1993 and Rheault et al., 1995). However, because main machines in cells (or FMSs) are NC machines and machining centers that cannot be arbitrarily moved, the physical reconfiguration of cells cannot be realized and the logical reconfiguration of cells cannot obviously decrease the workpiece-transport time and charges. Thirdly, although the commercial software of manufacturing resource planning (MRP II) can directly assign manufacturing orders to manufacturing cells, these orders are usually not optimal (Zou & Su, 1994). This is because the manufacturing orders are made according to a material requirement plan that, without workcentre capacities being taken into consideration, is generated only from a master production schedule, bill and lead time of a material. After the manufacturing orders are obtained, a capacity requirement plan is developed by simulation. If the capacity requirement plan does not match workcentre capacities, these manufacturing orders are revised manually after the amount of material to be procured and/or the amount of work to be subcontracted have been changed manually, or other manufacturing orders are remade after the master production schedule has been modified manually until they match each other. Thus, those manufacturing orders are not optimal. It is better for MRP II to assign a shop the manufacturing orders that are to be optimally decomposed into short-term plans to be executed by manufacturing cells or FMSs in the shop, about which little has been written in the literature on production planning (PP). Fourthly, the solutions of PP problems in workshops will provide a theoretical basis for implementing manufacturing execution systems (Baliga, 1997) similar to shop floor controllers. Fifthly, with the increasingly keen competition for markets, there will be no manufacturer that has all the resources to win a victory. Thus, several manufacturers with complementary resources will temporarily form themselves into an agile virtual enterprise (Goranson, 1995) to take advantage of a transient market opportunity and to win a victory in the competition. In such an agile manufacturing environment, a shop is empowered to organize production autonomously according to manufacturing orders (product demand plans) not only from the manufacturer (which it belongs to) but also from the agile virtual enterprise (which it belongs to), which generates more uncertainty in the product demand than the traditional production. Besides, the equipment capacity in the shop is uncertain because of unplanned maintenance and the material supply for the shop is also uncertain because of the supplier's capacity and the material quality. Therefore, the shop can be taken as a stochastic manufacturing system to some extent. On the other hand, the production planning in a manufacturing setting is essential to achieve efficient resource allocation over time while meeting demands for finished products. It is thus clear that the study on the stochastic PP problem for a flexible automation workshop (FAW) consisting of FMSs (or cells) is of great significance. Since the scope of PP problems generally prohibits a monolithic modeling approach, a hierarchical production planning (HPP) approach has been widely advocated in the PP literature (Davis & Thompson, 1993). To model PP problems, the existing hierarchical approaches usually employ the following concepts: (1) product disaggregation (Davis and Thompson, 1993, Bitran et al., 1981, Graves, 1982, Simpson and Erenguc, 1998, Simpson, 1999 and Kira et al., 1997), (2) temporal decomposition (Malakooti, 1989, Nguyen and Dupont, 1993, Carravilla and Sousa, 1995, Qiu and Burch, 1997 and Bassok and Akella, 1991), (3) process decomposition (Villa, 1989, Yan, 1997 and Yan and Jiang, 1998), and (4) event-frequency decomposition (Gershwin, 1988). However, these articles focus on deterministic HPP problems except (Davis and Thompson, 1993, Gfrerer and Zapfel, 1995 and Kira et al., 1997) that are on the HSPP problems. The existent articles on the PP problems with uncertainties mostly focus on uncertainties of the demand, capacity and material supply in the single-period or infinite-horizon setting (Bassok and Akella, 1991, Ciarallo et al., 1994, Ishikura, 1994, Kasilingam, 1995, Metters, 1997 and Hwang and Medini, 1998). However, Davis and Thompson propose an integrated stochastic decision-making approach of integrating the techniques of mathematical programming and Monte Carlo simulation, which is employed within each implemented generic controller to rigorously address the uncertainties that are inherent to multi-period PP problems (Davis & Thompson, 1993). Gfrerer and Zapfel address hierarchical production planning for a multi-period model consisting of an aggregate planning level and a detailed planning level in the case of uncertain demand (Gfrerer & Zapfel, 1995). Kira et al. propose a stochastic linear programming approach to solve hierarchical production planning problems under uncertain demand (Kira et al., 1997). Bitran and Leong examine deterministic approximations to multi-period multi-item production planning problems in environments with stochastic process yields and substitutable demands (Bitran & Leong, 1992). Schmidt presents a Markov decision process model that combines features of engineering design models and aggregate production planning models to obtain a hybrid model that links biological and engineering parameters to optimize operations performance in biopharmaceutical production processes (Schmidt, 1996). Stecke and Raman use an open queueing network model of a flexible manufacturing system to determine the optimal configurations and machine workload assignments for the no grouping and total grouping cases (Stecke & Raman, 1994). Bonissone et al. propose a new approach to planning in the financial domain of mergers and acquisitions and in dynamic and uncertain environments (Bonissone, Dutta, & Wood, 1994). The planning is viewed as a process in which an agent's long-term goals are transformed into short-term tasks and objectives, given the agent's strategy and the context of planning (Bonissone et al., 1994). In contrast, the HSPP problem in this paper involves not only the three kinds of uncertainties (demands, capacities and material supply) in the existent PP literature, but also the uncertainties of processing times, rework and waste products. Besides, the system under consideration is also very complicated (an FAW consists of some FMSs, each of which consists of several machines) and the problem is also a multi-period multi-product one. It is thus clear that the problem gives a challenge. Because most stochastic programming problems in the literature are solved for the single-period or infinite-horizon (Bitran and Leong, 1992 and Higle et al., 1994) and the stochastic linear programming approach in Kira et al. (1997) is suitable for solving the hierarchical PP problem only under uncertain demand and because the solution of multistage stochastic optimization problems requires the tree-like decision-making structure (Mulvey & Ruszczynski, 1995) that is not suitable for the solution of the HSPP problem, it is necessary to find a new approach to solve the problem. Thus, the paper proposes a new stochastic interaction/prediction approach that can effectively solve the HSPP problem.

Because the existing papers on the PP problems with uncertainties mainly focus on uncertainties of the demand, capacity and material supply in the single-period or infinite-horizon setting and because most stochastic programming problems in the literature are solved for the single-period or infinite-horizon, we propose the new stochastic interaction/prediction approach to solve the HSPP problem for FAWs in agile manufacturing that is a multiple-period multiple-product problem with random material supply, demands, capacities, processing times, rework and waste products. In the paper, a mathematical model of stochastic production of an FAW is built up first. The stochastic interaction/prediction algorithm of HSPP for the FAW is then deduced. Based on the algorithm, the software package named SIPA has been developed and is presented in this paper. By means of SIPA, many examples of HSPP have been studied. Through one of those examples, the application of the algorithm and SIPA is introduced. As compared with the existing approaches to solve the PP and HPP problems with uncertainties, the present algorithm has the following features: 1.It solves the multiple-period multiple-product problem with more uncertainties and in a more complicated manufacturing setting (see Section 1). 2.It needs only expectations of r(k), di(k), vi(k), Ti(k) and TiT(k) Ri(k) Ti(k) and independence of Ti(k) from ui(k) and βi(k), but does not require their exact distributions. 3.On condition that expectation blanks and expectation demands for products in the FAW are given, the combinatorial optimization of the objectives, such as the work-in-process in FMSs, machine utilization, balance of loads on machines, and satisfaction of demands for products, is reached. 4.Since the FAW's optimal HSPP problem is decomposed into M FMSs’ optimal SPP sub-problems, the complexity of the problem is greatly reduced, thus speeding up the process of solving the problem. 5.The interactions View the MathML source among FMSs in the FAW can be obtained. Weight matrixes Qi(k) View the MathML source are symmetrical and (semi-) positive definite. Ri(k) and Ki(k) are symmetrical and positive definite. For simplicity, they can be taken as diagonal matrixes. Each element in them must not be too great in case the loss of significant digits in the matrix calculation makes the problem ill-conditioned. For the decomposition of the ten-day or week random product demand plans, the hour is taken as a unit of the element in Ti(k) and βi(k) in order to decrease its numeric and increase the accuracy of the matrix computation. To increase the satisfaction of the demands for products, the numeric of the element in Ki(k) can be properly increased. When some elements of View the MathML source are negative, the corresponding elements (that can be decimal) of αi(k) can be increased. SIPA has the friendly user interface. It is convenient for users to input and update both data and parameters of the algorithm. It can run by itself and also be taken as an algorithm module of algorithm base of the FAW controller if it is properly modified. It can be used not only to optimally decompose random product demand plans of FAWs but also to examine the rationality of both the expectation blank supply and the expectation product demand. If the expectation supply of blanks is not suitable to the given expectation demand for products, the expectation demand can not be satisfied, as may be imagined. Therefore, we will probe further into the problem of how to determine the expectation blank supply appropriate for the given expectation demand so as to meet it.