The Optimal Inventory Policy of Production Management

Transcription

1 Engineering, 03, 5, ublished Online May 03 ( he Optimal Inventory olicy of roduction Management hou-mei u,, hy-der Lin Department of Applied Mathematics and Business Administration, Chung Yuan Christian University, Chung-Li City, aiwan Department of Banking and Finance, akming University of cience and echnology, aipei City, aiwan * shyder@cycuedutw, a96003@gmailcom, shyder@cycuedutw Received February 5, 03 revised March 7, 03 accepted April 6, 03 Copyright 03 hou-mei u, hy-derlin his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited ABRAC he traditional Economic roduction Quantity (EQ) assumes that the replenishments are instantaneous and the relevant cost only consists of setup cost, stock-holding cost of the finished goods and the purchasing cost of raw materials As a manager of a manufactory, there is a problem that must be taken into consideration If the establishment buys all of the raw materials at the beginning, the stock-holding cost for the raw materials should be accounted into the relevant cost he main purpose of this paper will add the stock-holding cost of raw materials to the EQ model Base on this new modified EQ model, two more useful models are established One of the new models contains the reusable raw materials instead of the raw materials he other one considers the stock-holding cost of the raw materials and the imperfect-quality items are considered We present the optimal cycle length from each of these three models Keywords: EQ Raw Materials Reusable Imperfect-Quality Items Introduction he EQ model was developed by E W aft [] in 98 he EQ model is a well-known and commonly used inventory control technique E W aft [] did not consider the stock-holding cost for the raw materials In today s factory, producers are required to prepare raw materials, parts, etc that will be used in the production in order to finish the operation schedule hese prepared raw materials, parts, etc that cause extra stock-holding cost and must be paid by the producers herefore, we add the stock-holding cost in the EQ model Up to now Lin [] is the first one to establish an EQ model taking the stockholding cost of raw materials into consideration here are three EQ models concerning about the total relevant costs in this paper he first EQ model (called model ) is based on Lin s [] model that takes the stockholding cost of raw materials into consideration We are attempting to reduce the impact of environmental impairment and increasing competition capabilities of business by recycling the repair and waste disposal which were enthusiastically concerned in the past years o the second EQ model (called model ) is based on model and Richter s [3] ideas We assume that all the raw materials are reusable raw materials and the stock- * Corresponding author holding cost of raw materials is taken into consideration For making sure the quality of products, we assume all the products are screened o the third EQ model (called model 3) is based on model and alameh and Jaber s [4] ideas We assume that all products are screened in the process of making he proportion of imperfect-quality items is fixed and the stock-holding cost of raw materials is taken into consideration he Models he mathematical models developed in this study are based on the following definitions and assumptions Definition RC : the annual total relevant cost per unit time RRC : the annual total relevant cost containing reusable raw materials per unit time IRC : the annual total relevant cost containing imperfect-quality items per unit time Q : the order size : the setup cost : the production rate D : the demand rate C : the purchasing cost per unit raw materials Copyright 03 cires

2 0 -M U, -D LIN : the reusable rate : the percentage of defective items in finished productions : the cycle length r : the discount rate h : the stock holding cost of raw materials per item per unit time h : the stock holding cost of finished products per item per unit time x : the screening rate d : the unit screening cost b : the selling price of unit imperfect-quality items t : the screening time Assumptions () roduction rate is greater than demand rate D, () roduction rate and demand rate D are known and constant, (3) hortage is not allowed, (4) A single item is considered, (5) 0, (6) 0, (7) he imperfect-quality items are sold at the end of the screening time, D (8) x D and x t here are three models considered in this paper Model : Using the total relevant cost per unit time to find the optimal cycle length (It is shown in Figure ) Raw Materials Inventory Level D D ime Figure he EQ model containing raw material he annual total relevant cost RC() consists of the following elements: he ordering cost per unit time () he purchasing cost per order per unit time CQ CD CD he stock holding cost of raw materials hd per unit time he stock holding cost of products per unit time h D D he total relevant cost per unit time can be expressed as follows: hd h D D RC CD he unique solution of above equation is hd h D D D he optimal order quantity is Q hd hd At time, the RC has a global minimum on 0, If h h h, then hd h D D hd D and Q h he optimal quantity of this model is the same as that of the traditional EOQ inventory model Model : Using the annual total relevant cost using 00% reusable raw materials to find the optimal solution (It is shown in Figure ) he topic of environmental protection in the world is enthusiastically concerned in recent years o, by the recycle of the repair and waste disposal productions, we can reduce the impact to environment and increase the ability of competition in business Also the amount of reused raw materials at the beginning is D, then the amount of D of usable raw materials can be got he annual total relevant cost with 00% reusable raw materials RRC consists of the following elements: () (3) Copyright 03 cires

3 -M U, -D LIN Figure he EQ model containing reusable raw material he setup cost per unit time CD he purchasing cost per order per unit time he stock holding cost of raw materials per unit time hd he stock holding cost of products per unit time h DD he total relevant cost per unit time can be expressed as follows: RRC CD hd h D D And the first and second derivatives of RRC are drrc hd h DD and d d et sult: d RRC 3 drrc d 0forall 0, respectively 0, then we have the following re- hd h D D 0, he unique solution of above equation is hd h D D At time, the RRC has a global minimum d RRC on 0, since 0 for all 0 d Model 3: Using the annual total relevant cost containing imperfect-quantity items to find the optimal cycle length (It is shown in Figure 3) his is an EQ model by accounting for fixed percentage imperfect-quality items and considering the issue that poor quality items were sold as a single batch with lower price than it of good quality items at the end of the screening time he annual total relevant costs IRC consists of the following elements: he ordering cost per unit time CD he purchasing cost per order per unit time dd he screening cost per unit time he stock holding cost of raw materials per unit time hd Figure 3 he EQ model containing imperfect-quality items Copyright 03 cires

4 -M U, -D LIN he stock holding cost of products per unit time DD D D D D D h x x x he money earned from selling the imperfect-quality items per unit time he total relevant cost per unit time can be expressed as follows: IRC hd CD dd bd bd DD D D D D D h x x x And the first and second derivatives of IRC are dirc hd DD D D D D D h x x x d d 3 IRC 0 for all 0, respectively d dirc et 0, and set d hd DD D D D D D W h x x x then we have the following result: W 0 then we have * ** *** 44, 0707 and Conclusion he unique solution of abo ve equation is W In this paper, we add the stock-holding cost of raw mate- At the time of ***, the IRC has a global mini- rials into this EQ model to obtain the optimal inventory d IRC policy his is an idea about modifying the traditional mum on 0, since 0 for all 0 EQ model o academic researches and practices, the d stock-holding cost of raw material has been added to the 3 Numerical Examples EQ model, the result of adding the stock-holding cost of raw materials into the EQ model is more useful and Example If we set the numbers as practical then we have 000, 000, D500, 0, 08, x800, h and h 5, 08433, 0945 and 07 Examp le If we set the numbers as 3000, 000, D500, 0, 07, x700, h and h, REFERENCE [] E W aft, he Most Economical roduction Lot, he Iron Age, Vol 0, 98, pp 40-4 [] -D Lin, he Optimal Inventory olicy of roduction Management, Across-traits Academic Conference roceedings in Management heories and ractices, Vol 3, 00, pp 99-0 [3] K Richter, he Extended EOQ Repair and Waste Disposal Model, International Journal of roduction Eco- Copyright 03 cires

5 -M U, -D LIN 3 nomics, Vol 46, No -3, 996, pp doi:006/ (95) [4] M K alameh and M Y Jaber, Economic Reduction Quantity Model for Items with Imperfect Quality, International Journal of roduction Economics, Vol 64, 000, pp doi:006/ (99) Copyright 03 cires