مدل سازی و تجزیه و تحلیل مشکل تدارکات تعیین اندازه دسته تولید تک آیتمی چند دوره ای با توجه به عدم پذیرش و تحویل دیرهنگام

Integer linear programming approach has been used to solve a multi-period procurement lot-sizing problem for a single product that is procured from a single supplier considering rejections and late deliveries under all-unit quantity discount environment. The intent of proposed model is two fold. First, we aim to establish tradeoffs among cost objectives and determine appropriate lot-size and its timing to minimize total cost over the decision horizon considering quantity discount, economies of scale in transactions and inventory management. Second, the optimization model has been used to analyze the effect of variations in problem parameters such as rejection rate, demand, storage capacity and inventory holding cost for a multi-period procurement lot-sizing problem. This analysis helps the decision maker to figure out opportunities to significantly reduce cost. An illustration is included to demonstrate the effectiveness of the proposed model. The proposed approach provides flexibility to decision maker in multi-period procurement lot-sizing decisions through tradeoff curves and sensitivity analysis.

Multi-period procurement lot-sizing decision seeks best tradeoffs among multiple cost objectives to determine appropriate lot-size and its timing to minimize total cost over the decision horizon. The multiple cost objectives are purchasing cost, transaction (ordering and transportation) cost, inventory holding cost and/or shortage cost. Supplier offers discounts, which tend to encourage buyer to procure larger quantities to obtain operating advantages such as economies of scale and reducing the cost of ordering and transportation. In such a scenario, product could be carried forward to a future period, incurring inventory holding cost. This means that in each period either procurement takes place or buyer has inventory carried forward from the preceding period. Smaller lot-size procurement strategy reduces inventory holding cost but increases purchasing cost and transaction cost. Procurement of larger lot-size reduces purchasing cost and transactions cost but leads to higher inventory cost. Supply chain risks such as rejections and late deliveries also affect the procurement lot-sizing decisions. Therefore, decision maker considers tradeoffs among purchasing cost, transaction cost, inventory holding cost and/or shortage cost in multi-period procurement lot-sizing decisions to minimize total cost over decision horizon. Material Requirement Planning (MRP) involves procurement lot-sizing decisions to be made when demand is both stable as well as lumpy and the approach is spread over a finite time horizon. In the restricted case, when demand is stable and known over the decision horizon, the simple static EOQ model can find the optimum solution. Both methods fail to consider realistic constraints regarding supplier capacity, rejections, late deliveries and time dependent variations in problem parameters. The exact solution in more general situations has been obtainable by Dynamic Programming (DP). Wagner and Whitin (1958) presented a dynamic programming solution algorithm for single product, multi-period inventory lot-sizing problem. Even though DP algorithms (Aggarwal and Park, 1993, Federgruen and Tzur, 1991, Heady and Zhu, 1994 and Silver and Meal, 1973) provide an optimal solution, these are considered difficult to understand and require high computational resources. To our knowledge, there is no multi-period linear programming model available in the literature for procurement lot-sizing problem which can substitute EOQ model and DP model to overcome their limitations, and also considers price breaks and realistic constraints as well as supports Material Requirement Planning. This paper applied an integer linear programming approach to solve multi-period procurement lot-sizing problem for single product and single supplier considering rejections and late delivery performance under all-unit quantity discount environment. The purpose of this paper is to: • Develop a mathematical model to establish tradeoffs among cost objectives and determine appropriate lot-size to procure and its period to minimize total cost over the decision horizon. • Investigate the effect of variation in problem parameters such as rejection rate, demand, storage capacity and inventory holding cost on total cost. The paper is further organized as follows. Section 2 presents a brief literature review of the existing quantitative approaches related to procurement lot-sizing problem. In Section 3, an integer linear programming formulation is developed for multi period procurement lot-sizing problem considering all-unit quantity discounts. Section 4 presents an illustration with solution to demonstrate the effectiveness of the proposed approach. Finally, conclusions are provided in Section 5.

Multi-period procurement lot-sizing decisions simultaneously determine what quantity is to be procured and in which period it should be procured so as to minimize total cost by striking tradeoffs among purchasing cost, inventory holding cost and transaction cost. Lot-sizing decision is also influenced by quantity discounts, quality and delivery performance. This paper presents an integer linear programming approach for procurement lot-sizing problem in the real world situation. By formulating the multi-period lot-sizing problem as an integer linear programming, we have captured the realistic constraint at all levels over a finite planning horizon. The proposed model can support MRP system in realistic situations. The computation analysis shows that problem of reasonable size can be solved using any commercial software in a few seconds of computer time via the proposed formulation. However, as the number of quantity discount levels and/or periods increases, the model could become very large with hundreds of binary variables and may become computationally intractable. Hence, the future research work may explore exact solution approaches such as branch and bound or cutting plane methods, or heuristics and approximate algorithms. Future research might also include several products. If there were two products, both managed by a single supplier, consolidated shipments of a mixed load could be dispatched to buyer. Two or more products may allow additional economies in inventory or transportation decisions. Further, the proposed model focuses on the buyer’s benefits. The issue of coordination between buyer and supplier can also be studied to optimize the whole supply chain benefits in a multi-period procurement lot-sizing decision making process.