An Economic Production Quantity Model for Atlantic Pharmaceuticals Laboratories

--Inventory in an industry is considered like a blood in the body, and almost 50% of investment is made on inventory. Therefore, keeping the optimum level of inventory at low possible cost is the primary focus of researchers. Industries have to make good choices for inventory management in order to compete in market and meet the demands. Major issues regarding inventory in pharmaceutical industry are overstock, unjustified forecasting technique, long manufacturing lead times and lack of IT support. For these reasons, optimizing inventory is more difficult for pharmaceutical companies as compared to other manufacturing companies. Such issues are also faced by Atlantic Pharmaceuticals Laboratories (APL). In order to address these issue, inventory management is performed in APL. Inventory is categorized in three classes through ABC analysis. Class A items are further analyzed and their optimum quantity is determined by EPQ model. At the end sensitivity analyses are performed to determine the most and least critical parameters of the model.

A. Problem Description APL deals with products like syrup, suspension and infusion, the raw material which is ordered for such kind of product is through experienced guess not through technical method, which often cause the shortage of inventory or excess of inventory, and causing additional cost. Thus, developing a technique for this kind of problem and making sure that, the desired demand is fulfilled exactly when the customer needs it with minimum inventory cost associated.

B. Objectives
The main objective of the inventory management is to make an equilibrium between inventory investment and customer service. Applying the best methodology based on the inventory problem to achieve the following objectives:  Optimum inventory level  Minimum inventory cost

II.
LITERATURE REVIEW Everyone knows that inventory management plays the major role in every type of business organization to flourish it. Production Order Quantity (POQ) model is one of the most common inventory model which is used in inventory control techniques. This almost the first inventory model developed by Harris in 1913. This model calculates the quantity in order to minimize inventory cost, by determining the optimum level for the related costs. This model tells us about the level of optimum amount of items production and therefore it is mostly applicable to manufacturing organization. S.M. Samak-Kulkarni contributed in the determination of finest inventory model for decreasing inventory cost [1]. Inventory is the stuff of raw material, WIP and finished goods used in organization. To solve order related problems, they present some models on which they work to solve inventory related problem which will reduce the total inventory cost and will optimize the inventory level. These papers take into consideration lot by lot size, economic order quantity (EOQ), periodic order quantity (POQ) and Wagner Within algorithm. In this paper total inventory cost for many items are determined for each method so in the results after calculation for each model the Wagner Within algorithm gives the optimum cost in each case. Lt Col Gupta researched to control the inventory of medical store by using ABC-VED analysis in a combination to divide the whole inventory in three categories I, II, and III [2]. The methods which were used by the authors in this case study are ABC-VED analysis, and the economic analysis of the Pharmaceutical Spending of Priced Vocabulary Stores (PVMS) section 01 hospital for the year 2003 was under consideration which was consists of 190 bedded service. The total drugs were 493 drugs in PVMS Section 01, and in these drugs only 325 were being used in the reference hospital which costs about 55,23,503 rupees. So this 325 drugs were categorize in such a way that 47 drugs (about 14.4%) were added to category A which consume 70% of the total expenditure because these drugs were high in the cost but were low in the amount (about 14.4% ) as mentioned earlier, Hooshang researched on inventory management by using ABC Classification and decision support system with a clinical laboratory application [3]. For this clinical laboratory the ABC classification is based on the criteria of annual dollar volume which categorize the items intro three classes. The Pareto principle is usually applicable to ABC classification which suppose that 20% of the items will generate 80% of the annual dollar volume of the demand. So, this idea motivate inventory controller to concentrate on few of the items of the inventory which are the most critical items regarding annual dollar value. The class A items are the highest annual dollar demand items (about 78-80 %) of the budget which are forcefully managed which requires a high attention from both class B and C items. The 15-20 % of the total items of the laboratory include in class A which is less but very critical due to its annual dollar value while 15-25% annual dollar volume generates by class B which included 25-30% of the items and class C with low annual dollar volume values but includes large portion of the inventory. The Class B and Class C items are placed at a higher level than Class A items. The company uses ABC classification for the 47 items in which the first 8 items were classified in Class A which accounted for 77% of the annual demand cost. 4 items were classified in Class B and the remaining 17 items were classified in Class C using Lean Production, Organizational Performance and Inventory Management [4]. The purpose of this case study was to check the hypothesis that with the implementation of lean inventory management will leads to improve the financial performance of a firm. Now in this case study they analyze the data which came from the ICAP database, which includes financial information. The data were taken in between 2000 and 2002 period which was the sample period for the data analysis. The industrials sectors which were selected in Greece were Food, Textiles and Chemicals. Initial results, from this analysis obtained that the higher the level of inventories conserved by a firm, the lower will be its rate of return. This kind of inventory models has attracted the attention of several researchers such as Sarkar, Chaudhuri, & Sana [5], Sarkar, Sana, & Chaudhuri [5,6,7], Sarker, Jamal, & Mondal [8], Sana & Chaudhuri [6] , Chug [9], Sarkar [10,11,12], Widyadana and Wee [13], Chang, Su, Yang, & Weng, [14]) and Cárdenas-Barrón, Sarkar, & Treviño-Garza [15], Cárdenas-Barrón, Taleizadeh, & Treviño-Garza [16] , just to name a few works. MS Mahatme, et al [17] researched an integrated Economic model analysis of a Teriary Care Hospital in Central India. Financial study plays an essential role in the management of medical store. Hospital inventory management system should ensure the optimum stock of all the required items to keep the supply without any interruption. About one third of the hospital revenue is spent on the materials and pharmaceuticals. So, this gives importance to manage and control the important drugs in the medical store. The main purpose of this case study was to control the inventory of the medical store by controlling VED analysis with EOQ after the comparison of indexed cost and the actual cost.
III. METHODOLOGY As mentioned before the industry, which is selected for the proposed work is Atlantic Pharmaceuticals Laboratories (APL). The production process of any pharmaceuticals industry for syrup and suspension production is given in figure 1. APL deal with different products like syrups, suspension and infusion and they follows the same process. First of all, solid ingredients are dissolved into liquid (mostly purified water) and then through dosing systems are fed into the production tanks according to the formulation. The dosing system is powered by an electric motor and has a controller that turns the pump on and off and managed the flow rate. In production tanks the solution is taken to the required temperate and necessary production processes are performed. After the production, the solid particles are separated from the solution through the process of filtration. All the products dispense extemporaneously are stored in the storage tanks and then filled in the bottles when required.

A. Data Collection
APL produces three kinds of products i.e. Syrups, Suspension and Infusions. Table I given below tells about the type of product its registration number their package size and cost associated per unit. For example, look at the product no 1, it shows that it is syrup by name of Acitral having registration no 62316 with a generic name of Sodium acid citrate. The packing of Acitral is 120 ml per pack or bottle with a unit cost of Rs.19. Table I. Detail of the products in Atlantic Pharmaceuticals Laboratories.
In data collection the first thing is to know how many different kinds of products in the industry producing. APL is producing 32 types of products which include syrups (syp), Suspensions (Susp) and infusions (Inf). The monthly demand of each item from January to December is shown in the table below. The Demand given here is in cottons. Look at the item no 1 with registration no 62316, it shows that the demand of this particular item in January is 300 cottons, in February 308 cottons and so on as shown in Table II At the end of the year the average monthly demand is 301 cottons and as 1 cotton contains 70 units, therefore is 21070 units demand in average for this particular item.

B. Data Analysis
Data is analyzed so that it becomes easier to understand the data and become more help full in problem solving.
Here ABC analysis technique is followed, which divides the on-hand inventory into three classes A, B and C on the basis of annual dollar volume as shown in Table III. The detail of each class is discussed in an earlier chapter.  1000 1030 990 990 1014 1020 980 995 1018 1025 995 1000 1005 100 100500  10 62315 800 810 812 791 792 807 812 800 796 794 796 810 802 100 80200  11 73363 500 488 495 508 505 505 495 496 520 516 494 502 502 100 50200  12 62325 125 120 130 128 112 120 133 132 125 128 127 130    Now the total cost here is calculated on the basis of optimum production quantity Q * p. After that the sensitivity analysis comes which helps in finding the most critical variable or variables which can affect the TC with large scale when they are manipulated.

IV. NUMERICAL COMPUTATION AND SENSITIVITY ANALYSIS
This includes the sensitivity analyses for all the items of class A which were selected as a critical product and are more responsible for inventory cost. The analysis performed for each is given below in detail.

V.
RESULTS AND DISCUSSION APL produces a total of 32 items. By using ABC analysis technique on the inventory items, they were classified in three classes A, B and C. Six items belongs to A class and 9 to class B and 17 to C. Class A items were taken for further analysis because both of them contributes to 80% cost monthly inventory cost. For these class A items the optimum production quantity * was determined by using POQ model. After that the total cost was determined for each item. For example, the * for item 1  Similarly, it is done for the rest of fourteen items. After these calculations the sensitivity Analysis is performed so that we know the critical factor or variable with is more responsible for the increase or decrease of cost for the particular item. Sensitivity Analysis is performed by changing one variable and keeping all other variables fixed in the Cost equation.

VI.
CONCLUSION The proposed research develops the economic production quantity (EPQ) model for different items in Atlantic Pharmaceuticals Laboratories. The managers of Atlantic Pharmaceuticals Laboratories as well as of other industries of similar sectors will be benefited by the outcomes of the results as the optimal solution has been modelled in the most realistic manners. It is concluded from sensitivity analysis that holding cost (H) and quantity per order (Q) are the critical/sensitive parameters as compared to demand rate (D) and setup cost (S). The Effect of variable demand and setup cost are somehow same. Thus, by keeping holding cost and quantity per order in the right level the inventory can be controlled and reduced for each item cost up to 50% of the cost which is available in present time. Furthermore, to check the influence of all parameter on the total cost, all parameters are manipulated separately. First of all demand is manipulated in a percentage so for 50% increase in demand the total cost is increased by 29.7%, and for 25% increase its influence is 14.8%. Similarly, for 50% decrease in demand has increased the total cost by -29.7% and for 25% decrease the total cost is decreased by -14.8%. Secondly, order quantity is manipulated in a percentage so for 50% increase in order quantity the total cost is increased by 49.5%, and for 25% increase its influence is 24.7%. Similarly, for 50% decrease in order quantity has increased the total cost by -49.1% and for 25% decrease the total cost is decreased by -24.6%. Now, setup cost is manipulated in a percentage so for 50% increase in setup cost the total cost is increased by 29.7%, and for 25% increase its influence is 14.8%. Similarly, for 50% decrease in setup cost has increased the total cost by -29.7% and for 25% decrease the total cost is decreased by -14.8%. Further, holding cost is manipulated in a percentage so for 50% increase in holding cost the total cost is increased by 49.7%, and for 25% increase its influence is 24.8%. Similarly, for 50% decrease in holding cost has increased the total cost by -49.7% and for 25% decrease the total cost is decreased by 24.8%.