1、東海大學博士班研究生出席國際會議報告97 年 9 月 2 日報告人姓名 許天成 就讀系所及年級 工工系四年級會議期間 97.8.12 - 97.8.19 會議地點 中國，烏魯木齊會議名稱(中文) (英文) International Association for Information and Management Science 2008發表論文題目(中文)(英文) An efficient search algorithm for obtaining the optimal replenishment strategies in assembly-type just-in-time su
2、pply chain systems報告內容包括下列各項：一、 參加會議經過本次國際會議共有百餘篇來自全球各地的論文分資訊科學（Information Science）與管理科學（Management Science）兩大主題，以數十個場次進行發表與討論。研討會每日上午進行大會議程(Plenary Talks Session)，安排來自世界知名學者與業界人士，就近期工業工程管理與資訊領域之重要學術發現進行報告。與會過程中，來自歐澳洲及日本重量級學者提出了許多學術相關待解決的問題，期盼與來自世界各地相關的學者共同合作來解決的問題。比較特殊的是今年有來自台灣清華大學的教授針對地震的預測提出了新的發
3、現與看法。二、與會心得參加此次的國際研討會，讓我有機會與世界知名工業工程與管理領域的學者與業界人士進行討論並交換研究心得，收穫很多。他們也針對我報告的論文提出看法與建議以供我未來修正與改進。同時，從其他學者的研究論文與報告中了解到目前在工業工程與管理領域研究發展的重要趨勢，相信這對自己在尋找新研究主題或修正研究方向有很大的助益。三、發表論文全文An efficient search algorithm for obtaining the optimal replenishment strategies in assembly-type just-in-time supply chain sys
4、temsTien-Cheng Hsu, Ming-Jong Yao, Tsueng-Yao TsengDepartment of Industrial Engineering and Enterprise Information,Tunghai University, P.O. Box 985, Taichung 407, TaiwanAbstract: An assembly-type supply chain system is composed of a main serial supply chain and several branching serial supply chains
5、 merging to the main supply chain. Under constant demand rate assumption, a kanban controlled serial-type supply chain system can be modeled as a mixed-integer non-linear programming (MINLP) problem. Kanban controlled assembly-type supply chain systems can be modeled based on serial-type supply chai
6、n systems. To obtain optimal replenishment strategies for a kanban controlled assembly-type supply chain system require solving a MINLP problem. We propose a search algorithm to solve the assembly-type supply chain system problem. The proposed algorithm is efficient and guarantees global optimal sol
7、ution.Keywords: Kanban, Supply chain, Just-In-Time, Mixed integer nonlinear programming, Piecewise convex, Junction points.I. IntroductionSerial supply chain systems controlled by kanban mechanism are studied in 1. It is defined that the material flow and information flow between two adjacent manufa
8、cturing plants form a kanban stage. When there exist two or more kanban stages, it is called a multi-stage supply chain system (MSSCS). Obvious, a serial-type supply chain system controlled by kanban is a MSSCS. In such a just-in-time supply chain system, suppliers provide raw materials to the manuf
9、acturing plant in the first kanban stage, semi-finished products moved between the intermediate kanban stages and then end-products are delivered from the plant in the last kanban stage to the warehouses or directly to the customers. We assume that the demand rate is constant. A mixed-integer non-li
10、near programming (MINLP) problem is constructed from the perspective of just-in-time delivery policy. Optimal number of kanbans between any two manufacturing plants and the total production quantity of the system are determined by solving the MINLP problem. In 1, a greedy heuristic to solve this MIN
11、LP problem is proposed. However, the heuristic fail to demonstrate itself to be efficient, nor the solution quality is guaranteed.Contrast to a serial supply chain system, an assembly-type supply chain system is composed of a main serial supply chain and several branching serial supply chains mergin
12、g to the main supply chain, as shown in Fig.1. It is not difficult to see that an assembly-type supply chain system is more complex than a serial-type supply chain system. In 2, the just-in-time assembly-type supply chain system is formulated based on serial-type supply chain systems. The assembly-t
13、ype problem is solved by treating the main supply chain and each of the branch supply chains as a serial supply chain. Each of the serial supply chain is solved separately then followed by a solution improvement procedure. The scheme proposed in 2 is not only inefficient but also difficult to implem
14、ent. In addition, we are able to demonstrate that it fails to obtain global optimal solution given certain parameter settings.R a wm a t e r i a lF i n i s h e dg o o d sR a wm a t e r i a lR a wm a t e r i a lM a i n l i n eB r a n c h 2B r a n c h 1Figure 1: A sample assembly-type supply chain sys
15、tem controlled by kanban.In this study, we tackle the problem in different approach. We conduct thorough theoretical analysis on the mathematical model of the assembly-type supply chain system as a whole, main line and branch supply chains all together. The characteristics of the optimal-costs of th
16、e model are fully explored. Several important findings are derived.1. The optimal cost function associated with the concerned problem is piecewise convex.2. The point where two adjacent piecewise convex curves concatenate is referred as junction point.3. The number of kanbans, or kanban multipliers,
17、 for all kanban stages are invariant within each piecewise convex curve.4. At least one kanban multipliers must be different between any two piecewise convex curves.By utilizing these findings, we propose an efficient search algorithm. Through extensive numerical experiments, we are able to demonstr
18、ate that the proposed algorithm is efficient and effective. The experiment results indicate that the concerned problem can be solved in almost linear order of the problem size and global optimal solution is guaranteed.II. Literature ReviewThe importance of pull production system has been recognized
19、in the early 1980s. In general, it indicates ordering and manufacturing only when needed, or just-in-time (JIT) replenishment. The core concept of JIT production is to eliminate waste, especially in referring to minimizing inventories. Kanban is the main mechanism used in a JIT production system, wh
20、ere kanban is used to control material flows as well as information flows between production workstations. Since kanban-controlled technique has served as efficient mechanisms to control the inventory and the operations of a manufacturing system, many researchers extended the idea to the supply chai
21、n systems. Several studies (for instance 3, 4, 5, 6, 7 and 8 etc.) considered the operations of kanbans between two adjacent production plants; however, did not consider the coordination of raw material supply and the distribution of finished goods. Sarker and Balan (9 and 10) proposed mathematical
22、models for determining the optimal number of kanbans required to transport materials between two adjacent workstations for both single-stage and multi-stage systems. In their decision-making scenario, the number of lots and the number of kanbans in different stages are assumed to be the same. Fujiwa
23、ra, Yue and Sangaradas 11 studied kanban-controlled multi-stage assembly systems. However, they did not focus on determining the optimal number of kanbans, rather, on the evaluation of the system performance. Many studies address the issue of optimal lot splitting strategies in JIT environments (see
24、 12 and 13). The major concerns of these studies are the derivation of optimal production and delivery policies, but limited to the coordination of a single supplier and a single buyer. Although 14 claimed a multi-stage linkage, it is restricted to three echelons of supplier-vendor-buyer coordinatio
25、n only.Recently, Wang and Sarker 1 proposed a mathematical model for serial-type kanban controlled multi-stage supply chain systems. Their model considered not only the kanban operations in all the stages of the supply chain, but also took into accounts the order/delivery polices of raw material and
26、 finished goods. Though two solution approaches were proposed for solving their model in 1, they either suffered from the problem of extremely long run time (for the B 0,bbiwiDAk02biwmH0i,bbisiwiDA(1)2bbbbiwiiimHkmDpfor , and all are positive real numbers.1,2.nSince the second derivative of with res
27、pect to Q is , which is positive for all stages. (,)biSCkQ3/biObviously, is convex. (,)biSCkQNext, we define a junction point of the cost function as the concatenation of two adjacent (,)biSCkconvex curves. One can easily verify that and will concatenation and the (,)bikQ1,)biQjunction point can be
28、determined by eq. (3).(3)(1,)(,)0bbi iSCkQSkBy solving eq. (3) one can derive a closed form for the location of the junction point of and (,)biSCkQas . We denote as the location of the jth junction point (1,)biSk2(1)bbwiiwiDAkmH ()bij(starting from the origin of the Q axis) for stage i of branch b a
29、s: (4)()2(1)bbbi wi wijjWe further denote as the value of which makes optimal at Q. Then eq. (4) leads *()bikbik(,)biSCkto Lemma 1.Lemma 1. For any given Q, the optimal kanban multiplier of is given by*()bikQ(,)biSk(5)*1,0,(1).(), for1:integr.bibi iQkjjjWe denote the minimum cost function at each st
30、age with respect to Q as . Then, Proposition 2 is an immediate result of Proposition 1 and *()min(,)(,)bbbbi iikSCQSQSCkALemma 1.Proposition 2. The minimum cost function is piecewise convex.()biSCQCorollary 1 provides a closed form to determine optimal multiplier for any given Q.*bikCorollary 1. Giv
31、en any value of Q, the optimal kanban multiplier at Q can be determined by(6)2*12bbwii mHQkDANow, we are ready to explore the properties of the total cost function. Define the optimal total cost as (7)10()()NbBniiTCQSProposition 3. The optimal total cost function is piecewise convex.()TCQProof. It i
32、s obvious from eq. (7). Proposition 4 links the junction points of stage cost functions to the total cost function.Proposition 4. All junction points from all kanban stages will be inherited by the function.()TCQNote that we consider the case in which is a junction point of exactly one stage, our pr
33、oof can be easily generalized to cases where is a junction point of more than one stages.Next, we defineas the vector of the optimal number of kanbans that 1*0*0*1*10 1()(),(),(),(),()NBn nnQkkQkQk obtains the optimal value for the function. Following from Proposition 3, the optimal cost curve TCbet
34、ween two adjacent junction points must be convex. For the rest of our presentation, we name it a convex interval. In another words, a junction point is the location where two neighboring convex intervals join on the function. Proposition 5 indicates an interesting property on the vector of ()TQ ()Qr
35、egarding to two adjacent convex intervals on the function.()TCQProposition 5. Suppose is a junction point of . In addition, and denote the vectors of LRthe optimal kanban multipliers for the left-hand-side and right-hand-side convex intervals regarding to . Then, can be secured from by increasing at
36、 least one of its optimal multipliers by one; RLnamely, , for some and .1bLiik0,1.NbB0,1.binThe following corollary is an immediate result from Proposition 5.Corollary 2. The vector of the optimal kanban multipliers stays invariant between two adjacent junction points.V. The Proposed Search Algorith
37、mWe need two more ingredients before we cook up our search algorithm, local optima and search range.First, let us discuss local optima. Recall that is piecewise convex, the global optimum of any ()TCQconvex interval between a pair of adjacent junction points can be easily determined. The global opti
38、ma of convex intervals are regarded as local optima of .()Proposition 6. Let and be two adjacent junction points of , with . Suppose 12 ()TCQ12is the vector of optimal kanban multipliers for the 1*0*0*1*110 1()(),(),(),(),()NBn nnQkkQkQk interval . A candidate of the local minimum in is given by2, 1
39、2,(8)11*0011*00()NbbNbbBnnsiwiinnwi bibi iDAkHmDmkp, if . Otherwise, either or is the minimum of that particular convex interval.12,Q 12Next, the integer relaxation is employed to determine the search bounds. Let us define problem (R) as:(R) Min =(,)ZX1 1000()2bb bbn nNBNBwibsiwi ii iHmDDAxQxp (1)11
40、 1,Nb bBbbiniinn , 0,0,bNiBx AQIt is obvious that the optimal objective function of problem (R) is strictly convex. Let us denote ()RQas where the global optimum of problem (R) located.Proposition 7. The global optimum of problem (R) is located at. (9)11()002()NbNbBnBnR bsi wiii imDQDAHpThen the search bounds can be determined by . We summarize the procedure to locate the search ()RQbounds as following.1. The optimal kanban multipliers of problem (P) with respect to can be computed by Corollary 1, ()RQdenoted as .()RQK
