Capacity Planning to Optimize the Profit of an Apparel Manufacturer in Developing Country

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1 31 Capacity Planning to Optimize the Profit of an Apparel Manufacturer in Developing Country ader Md. MOHAFIQUL, Hirohisa NARITA, Lian-Yi CHEN and Hideo FUJIMOTO The export oriented apparel manufacturers of developing countries produce apparel on the make-to-order basis instead of make-to-sell. As a result, there is no chance of stockout of goods that could be sold or overstock that has to be liquidated at deep discount at the end of the period. But an analogy can be drawn between stock of goods and capacity of production as idle capacity or shortage of capacity exists frequently while matching capacity with orders obtained. Considering capacity as a resource in inventory to be used in the future this paper applies newsboy problem to decide its use in production. ey Words: Optimization, Newsboy Problem, Capacity Planning, Apparel Manufacturer 1. Introduction Traditional production systems produce products and stock them as inventory until they are sold (make-tostock). In order to reduce inventory and increase the level of customization, some firms have designed their production systems to produce a product only after it is ordered. Such systems are referred to as make-to-order. The readymade garments (RMG) or apparel manufacturers of developing countries like Bangladesh adopt one or both of the systems mentioned above on purpose. Some of the factories serve the domestic demand and they use the maketo-stock systems. Some serve the export demand and use make-to-order system. This paper is concerned with the export oriented firms capacity planning. World s apparel industry has a very complex supply chain. It is not uncommon for design, production of fabric, cutting and sewing of garments, and sales in retail outlets to take place in different countries spread all over the globe (1). The apparel manufacturers of Bangladesh do the cutting and sewing of garments according to the orders and specification of foreign buyers. As a result, there is no chance of stockout of goods that could be sold or overstock that has to be liquidated at deep discount at the end of the period or to carry the unsold goods as inventory to the next period. Usually this happens to the outlet of the foreign buyers. Export oriented production entirely depends on the orders received from the foreign buyers. There are several steps starting from the negotiation of the orders with foreign buyers to the shipment of the products, but the important ones are shown in Fig. 1. In this whole process, capacity planning plays a significant role, because a firm must ensure that the committed orders are delivered timely to the customer. Depending on a firm s size, marketing skill and length of experience, it may lease its production facility to others or rent from others. This paper deals with the decision making of export-oriented firms regarding their capacity utilization during production. This paper considers production facility as an asset to utilize in the future and uses the newsboy technique to make decision. The rest of the paper is followed by a literature review in section 2, apparel manufacturing scenario of Received 3th July, 24 (No ) Department of Computer Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya , Japan. kader@vier.mech.nitech.ac.jp Tsukuri College, Graduate School of Engineering, Nagoya Institute of Technology Omohi College, Graduate School of Engineering, Nagoya Institute of Technology Fig. 1 Steps in the apparel manufacturing JSME International Journal Series C, Vol. 48, No. 1, 25

2 32 Bangladesh in section 3, mathematical model and the solution in section 4, a numerical example in section 5. Finally, conclusion and direction of future research are in section Literature Review Several researches are carried out about the problems of apparel manufacturing. The impact of working capital and inventory holding costs on a firm s stockout and markdown costs is discussed by Raman and im (2). Demand uncertainty and overstocking and understocking cost of firms whose production of garments occurs in various countries like Hong ong, China, Jamaica, Bangladesh, is dealt by Fisher and Raman (1). Prospects, marketing and status of textile along with readymade garments (RMG) of Bangladesh is discussed in Bhuiyan and Hossain (3), Haque and ader (4), and Chowdhury (5). The line balancing of RMG industry in Bangladesh is studied by Mohiuddin and ader (6). None of these papers deals with capacity planning like that in this paper. On the other hand, most papers on newsboy problem discuss the pricing, ordering and marketing policies and seldom involve the policy of capacity planning. In pricing policy, the case of progressive discount to sell the excess inventory is studied by houja (7). An extension of the problem, multi-product resource constrained situation is dealt by houja and Mehrez (8). In ordering policy, a situation with two orders in a period, is considered by Lau and Lau (9), (1). A newsboy problem with centralized warehouse that outperforms one with multi-location is dealt by Cherikh (11). Considering the above situations, this paper presents the application of newsboy problem in different field, like capacity planning. 3. RMG and Its Growth in Bangladesh Bangladesh the country of world famous muslin fabric and the Great Royal Bengal Tiger has now emerged as a child labor free, apparel giant in the world textile and apparel market. The country exports its apparel products worth nearly 5 billion US$ per year to the USA, EU, Canada and other countries of the world. This is about 75% of its annual national exports earning (4). At present the country is the 6th largest apparel supplier to the USA and EU countries. The major products are nit and Woven Shirts and Blouses, Trousers, Skirts, Shorts, Jackets, Sweaters, Sportswear and many more casual and fashion apparels. Starting in late 7 s as a small nontraditional sector of export, Ready-made Garment (RMG) emerged as a promising export-earning sector of the country by the year At that time there were only 46 industries as members of Bangladesh Garments Manufacturers and Exporters Association (BGMEA), which increased to 1 65 only in 1 years in the year 1993 (6). Today BGMEA is Series C, Vol. 48, No. 1, 25 Fig. 3 Fig. 2 RMG exports of Bangladesh Order collection and production planning proud to have about 4 garment manufacturers and exporters as its members. Figure 2 provides the RMG export data of Bangladesh. 4. Mathematical Model Apparels and fashion change according to two main seasons, summer and winter. Accordingly the production in the industry changes in its types, and the manufacturer considers two periods for production, summer and winter. In the mathematical model, a firm is considered that produces a single product in each period. All the orders it collects in a period and before, is planned to produce in the next period. But the planning of capacity is done prior to the period of order collection as shown in Fig. 3. This advanced decision about capacity planning helps the firm in many ways, namely (i) the decision maker gets a number of firms to be chosen for its capacity leasing, (ii) gets the opportunity to bargain for the contract, (iii) less risk of being remain idle, etc. Considering a single product for a single period, let X random variable representing the sum of orders received in a period, follows N(µ,σ 2 ), k upper limit of the in-house capacity, JSME International Journal

3 33 Fig. 4 Leasing model of capacity capacity decided to use in the period for own order, thus when < k, k is the leased capacity and when > k, k is the rented capacity, h(x) density function of X, p profit from unit capacity employed for own production, l profit from unit leased capacity, c r unit rental cost of capacity, c p shortage capacity penalty cost (e.g. incurring from the loss of goodwill). As mentioned earlier, a firm may lease out its capacity to avoid being remained idle or rent capacity to avoid shortage of capacity required to produce goods ordered. Both of the cases will be discussed in this paper separately Leasing model Capacity is leased when either (i) a firm is newly established or (ii) having weak marketing force, or (iii) capacity is relatively large. Whatever the firm receives as orders for a period does not exceed its capacity. If the firm does not lease out its capacity to other firms its part of the capacity may remain idle losing the revenue from lease. By leasing, the decision maker commits to produce part or whole of the order of its client factory and reduces its risk of remaining idle. The revenue thus received producing a unit, l, is lower than that of its own order, p. Thus if the firm leases much capacity and misses the opportunity to produce own orders, it loses (p l) per unit capacity. Since the amount of total order is not known at the beginning of the period it may be lower or higher than as shown in Fig. 4. The profit function 1 is P()=xp+(k )l, x < =p+(k )l (x )c p, x (1) The expected profit is 1 E{P()}=(k )l+ p +p xh(x)dx h(x)dx c p (x )h(x)dx (2) The cost for maintaining the facility will be same irrespective of the order size. It can be shown that expected profit is concave downward on and thus from first derivative we get h(x)dx= P(x ) = l (3) Analysis of solution As long as > l, (3) yields the optimal capacity to use in the period under consideration. Let Φ(.) be the standard normal distribution, φ(.) be its density function, and Φ 1 (.) be its inverse function. h(x)dx= P(x ) = p+c ( p l ) µ = Φ σ t1 = φ(x)dx; t 1 = µ σ { ( ) } = max µ+σφ 1 p+cp l,o (4) It can be shown by taking appropriate derivatives that when the unit revenue of own order, p and unit shortage penalty cost, c p increase, it is better to use more capacity to increase profit or to avoid capacity shortage. On the other hand if unit revenue of leased capacity, l, increases more capacity is leased to avoid decrease of profit. After simplification with the method proposed by Silver and Peterson (12), the expression for expected profit, (2) becomes E{P()} = (k )l+ pµ ( )σg u (t) (5) 4. 2 Rental model This is the opposite situation of leasing. Capacity is rented when (i) the firm is relatively old in the industry, (ii) having a strong marketing force, (iii) capacity is relatively small. Since it cannot produce all the orders by its own capacity, it contracts others to produce for it. The firm receives a revenue as it receives from own capacity, but it has to pay the rent, c r, to the firm it rents capacity from. As the firm rents other firms to make the excess orders that it cannot produce by its own capacity during a certain period, it should not rent too much or too less. In the first case, its rented capacity remains idle and incur loss paying the rent. In the second case it may lose revenue, as its capacity does not permit to produce potential orders. According to the two situations shown in Fig. 5 the profit function is P()=xp ( k )c r, x =p ( k )c r (x )c p, x > (6) Expected profit function is E{P()}=(k )l+ p +p xh(x)dx h(x)dx c p (x )h(x)dx (7) JSME International Journal Series C, Vol. 48, No. 1, 25

4 34 Table 2 Capacity used and expected profit (L-M) Fig. 5 Rental model of capacity Table 1 Comparison of the model parameters and results To find the maximizing value we set de{p()} = dx and get h(x)dx= c r. As shown in the leasing model, using the standard normal distribution, we can show, the value{ of ( maximizing) expected } profit is = max µ+σφ 1 p+cp c r,o, and the expected profit function is E{P()} = ( k )c r + pµ ( )σg u (t) (8) The expressions for capacity decided to use,, expected profit for that capacity, E{P()}, and variation of capacity with p, c p, l and c r are shown in Table Numerical Example The examples of the two situations are provided separately. Leasing is considered first. From a certain capacity when a firm leases out, its decided capacity to use decreases. In this case its maximum capacity may be the its own capacity when it decides not to lease at all. On the other hand, when a firm rents capacity its decided capacity to use for production increases. Thus the lower limit of capacity used is its own capacity when renting no capacity Leasing model (L-M) Suppose a firm, with a capacity of producing 5 units of shirts in summer period, wants to decide about its Series C, Vol. 48, No. 1, 25 Fig. 6 Variation of expected profit (L-M) capacity leasing. The past record shows that total order size follows N(4,1 2 ). It earns 5$ when it produce a shirt from its own order and earns 4$ from its leasing. The shortage penalty cost is ignored. From calculation the optimum capacity to use for own order production is units. So it can go for a contract of making units maximum to optimize the profit. The tabular calculation and graphical variation of the expected profit with capacity used for own order production are shown in Table 2 and Fig. 6 respectively. This value of, and the expected profit will change if the value of p or l changes. For example, when the revenue from using unit capacity for own order, p increases the firm loses the probable revenue p l per unit capacity. Thus when all others remain constant, and p increases, the capacity decided to use, also increases, to avoid the shortage of capacity when order is available. Similarly, when revenue from the leased unit capacity, l increases, the value of p l decreases. That permits the decision maker to lease more, and as a result decreases. These JSME International Journal

5 35 Fig. 8 Changes of E{P()} with at different c r (R-M) (a) As l changes Fig. 9 Profit difference when is set at average ordersize 6. Conclusion Fig. 7 (b) As p changes Changes of and E{P()} with p and l (L-M) facts are shown in the following graphs (Fig. 7) Rental model (R-M) Suppose a firm, with a capacity of producing 5 units of shirts in summer period, wants to decide about its capacity leasing. The past record shows that total order size follows N(7,1 2 ). It earns 5$ when it produce a shirt from its own order and gives 3$ rent for each unit. The shortage penalty cost is ignored. As the average value of orders received is greater than the capacity of the firm it must rent capacity to satisfy the demand. By doing this it earns more revenue and approaches its expected optimum. But it should not rent much that its capacity become greater than its total orders obtained in the period, thus causing the capacity remained idle. Thus with the normally distributed demand, when the firm rents 6 8 unit capacity, it maximizes its profit to 27,66$ (curve with c r = 3.inFig.8). In the apparel manufacturing industry it is a very common practice to lease out and rent capacity to match capacity with the orders received in a period. This also happens in many other industries when capacity of a firm is not sufficient to manufacture all the orders obtained. This paper models the situation of the renting and leasing of capacity of a firm producing a single product. This study shows that mere depending on the averages in capacity planning decision in apparel manufacturing firms producing make-to-order basis is misleading, as it does not optimize the expected profit (Fig. 9). Following are the findings of the study: ( 1 ) The profit maximizing capacity can be found out systematically, which is not necessarily the average of the orders received in the period. (2) Whenp and c p increase should be increase to earn p l (during leasing) or p c r (during renting) more per unit of capacity and to avoid shortage penalty cost and vice versa. (3) When l or c r increases should be decreased with leasing more capacity or renting less capacity. Consequently the risk of capacity being idle will decrease. Though the study enhances capacity planning using JSME International Journal Series C, Vol. 48, No. 1, 25

6 36 newsboy problem in a very simple fashion, it seems that there is a very good chance to extend the research farther in future considering multiple products with capacity constraints. Another approach of importance is that of decision-making whether to lease or rent for a single firm. References ( 1 ) Fisher, M. and Raman, A., Reducing the Cost of Demand Uncertainty through Accurate Response to Early Sales, Operations Research, Vol.44, No.1 (1996), pp ( 2 ) Raman, A. and im, B., Quantifying the Impact of Inventory Holding Cost and Reactive Capacity on an Apparel Manufacturer s Profitability, Production and Operations Management, Vol.11, No.3 (22), pp ( 3 ) Bhuiyan, M.A. and Hossain, M.T.Z., Prospects of Man- Made Fiber Production in Bangladesh in View of South and Southeast Asian Countries, Presented in the Proceedings of International Conference on Manufacturing (ICM) 22, Dhaka, Vol.2 (22), pp ( 4 ) Haque, A.S.M.S. and ader, M.M., Marketing of Export Quality Yarn in Bangladesh: Problems and Prospects, Presented in the Proceedings of International Conference on Manufacturing (ICM) 22, Dhaka, Vol.2 (22), pp ( 5 ) Chowdhury, A.H., Present Status of Textile Sector in Bangladesh and Its Future Prospect, Presented in the Proceedings of International Conference on Manufacturing (ICM) 22, Dhaka, Vol.2 (22), pp ( 6 ) Mohiuddin, G. and ader, M.M., Line Balancing and the Garments Industries of Bangladesh, Presented in the 38th Annual Convention of IEB, Dhaka, January 1994, Published in the Journal of AOTS, BAAS, (1994), pp ( 7 ) houja, M., The Newsboy Problem under Progressive Multiple Discounts, European Journal of Operational Research, Vol.84 (1995), pp ( 8 ) houja, M. and Mehrez, A., A Multi-Product Constrained Newsboy Problem with Progressive Multiple Discounts, Computers and Industry Engineering, Vol.3 (1996), pp ( 9 ) Lau, H.-S. and Lau, A.H.-L., Reordering Strategies for a Newsboy-Type Product, European Journal of Operations Research, Vol.13 (1997). pp (1) Lau, H.-S. and Lau, A.H.-L., A Semi-Analytical Solution for a Newsboy Problem with Mid-Period Replenishment, Journal of Operational Research Society, Vol.48 (1997), pp (11) Cherikh, M., On the Effect of Centralization on Expected Profits in a Multi-Location Newsboy Problem, Journal of Operational Research Society, Vol.51 (2), pp (12) Silver, E.A. and Peterson, R., Decision Systems for Inventory Management and Production Planning, 2nd Ed., (1985), pp , John Wiley & Sons. Series C, Vol. 48, No. 1, 25 JSME International Journal