目前企業在全球競爭的壓力下,必須在不同地區擁有多家製造工廠,總公司必須在短時間內以人力將所有訂單的產品需求指派至適當的工廠生產,其指派結果往往會影響到顧客之需求與企業之營運目標的績效,然而,過去研究大多針對廠內製造相關成本最小化,鮮少將工廠與訂單指定配送地點的運輸成本納入考量。因此,發展有效的方法求解整合生產與運輸規劃的多廠區訂單分配問題是相當值得探討的。 本研究將多廠區訂單分配問題區分為「單產品多廠區訂單分配問題」和「多產品多廠區訂單分配問題」,在產能資源限制下,分別建構混合整數規劃數學模式,以訂單分配後的系統總成本(包括整備成本、製造成本、存置成本及運輸成本)最小化為目標,求解各廠在各時期的生產計畫。由於多廠區訂單分配問題在工廠數、產品數、訂單數及規劃時期數增加時,無法以正確解法在合理時間求得最佳解,因此本研究發展以拉氏鬆弛法為概念且具有次梯度法的拉氏演算法求解此問題,在求可行上限解時,將不可行的訂單先在各廠間的同時期交換,若仍不可行時則將訂單提前生產,獲得系統總成本最小化。 本研究利用自行隨機產生的題庫進行驗證,並且與LINGO軟體求解的結果作比較,結果顯示在大型問題中,LINGO軟體須花費較長的時間才可獲得一個可行解,本研究的演算法能夠在短時間內獲得不錯的結果。另外也分析各項相關成本對訂單分配之決策,以影響系統總成本及工廠選擇與數量分配,其中以各廠的製造成本和與訂單指定地點的運輸成本影響最大,可供作為企業選擇工廠準則的參考。
Global production becomes the trend for firms to compete in conforms of customer’s quick response requirement. Nowadays, a firm would accept orders from all customers and assign the orders to a proper plant for manufacturing goods based on the setup cost, manufacturing cost, inventory holding cost, and the capacity constraint at different plants. The transportation cost that is seldom considered may cause a higher total supply chain cost for fulfilling an order. Thus, order allocation for multi-plant multi-item multi-period based on the total system cost is discussed in this research. In this research we first formulate the problem based on one item problem. The objective is to minimize the total system cost that takes into account the setup cost, manufacturing cost, inventory holding cost, and the transportation cost for deliver the items to the order’s destination. Then extend the problem into multi-item production problem. Lagrangian-based approach is a popular approach to solve many practical optimization problems. Thus, we propose a Lagrangian relaxation-based algorithm that relaxes the capacity constraint, while Lagrangian multipliers are updated by using a subgradient method. At each iteration, a feasible solution of the original problem is constructed from the solution of the relaxed problem with an order shifting and backwarding approach. About 12 randomly generated instances of the single-item and multi-item problem have been solved, respectively. The same instances are also solved by LINGO. It has been found that Lagrangian heuristic works quite “efficiently” for this problem. The results of sensitivity analysis in different parameters show that the manufacturing cost and transportation cost are two most important factors to be considered for multi-plant multi-item multi-period order allocation problem.