THE APPLICATION OF MANAGEMENT SCIENCE IN DECISION MAKING AND FORECASTING IN MANUFACTURING COMPANIES (PZ CUSSONS AS CASE STUDY)

Transcription

1 874 THE APPLICATION OF MANAGEMENT SCIENCE IN DECISION MAKING AND FORECASTING IN MANUFACTURING COMPANIES (PZ CUSSONS AS CASE STUDY) Akintoye Oluwasegun Ogundiya 1, Usman Jibril Wushishi 2 1 (Department of Management Information Systems, Cyprus International University, Lefkosa, Cyprus erains4eva@yahoo.co.uk) 2 (Department of Management Information Systems, Cyprus International University, Lefkosa, Cyprus wushi09@live.com) ABSTRACT The primary aim of every business or organization is to maximize profit with the most minimal cost using all the available resources. Manufacturing can be defined as the production of merchandise with the use of chemical and biological processing, machines and labor, tools, or formulation (1). It could refer to a range of human activities but is commonly applied to industrial production whereby raw materials are transformed into finished goods on a large scale. PZ Cussons is a prime producer of personal healthcare products and consumer groups, having their markets around the continents of Africa, Asia, and Europe. The need for PZ Cussons to balance production in all their locations for all their brands, in order to minimize excess (surplus) produces with their resources is paramount to achieve success. This project aims at applying Management Science (Linear Programming) in the production for PZ Cussons for maximum efficiency. Keywords Constraints, Decision Variables, Forecasting, Linear programming, Operations Research, Production. I INTRODUCTION A. A BRIEF INTRODUCTION OF MANAGEMENT SCIENCE Management science can be defined as a branch of applied mathematics designated to optimal decision planning, with great bonds with economics, engineering, business, and other sciences. Management science enhances the organization s ability to authorize meaningful management decisions by meeting optimal or nearly optimal solutions to highly complex decision tasks through the use of various strategies, scientific research-based principles, and analytical methods such as mathematical modelling, numerical algorithms, and statistics. Management science is synonymously used with Operations Research and Decision Science and often regarded as the business uses of Operations Research (2). The most prominent mathematical model used in management science or operations research is the use of linear programming to solve problems.in other words it is the method of achieving best outcome (3). Linear programming is a branch of mathematics which concerns solving optimization problems. The problem consists of a linear cost function (also called the objective function) that is to be either minimized or maximized with respect to a certain number of constraints. These constraints are linear inequalities of the used variables in the cost function. Further research on management science led to lots of methodological developments with the most significant using simplex method to solve linear programming problems. This was discovered by George Dantzig in 1947 with the intention to solve the U.S. Air Force planning problems (4). The main concern of Management Science is to solve managerial flaws and aid in designing such models to achieve maximum organizational excellence (5). B. APPLICATIONS OF MANAGEMENT SCIENCE Basically, management science concentrates on the development and application of concepts and models which are useful in elucidating management issues and solving managerial problems. Many operation management decisions aim at utilizing the most effective use of an organization s resources. Hence, linear programming has been successfully applied in operations management fields such as; (i) Transportation: e.g. schedule of school buses to minimize the total distance covered while transporting students i.e. to determine the shortest route (Northwest corner method). (ii) (iii) Banking: e.g. scheduling tellers to minimize total labour cost while needs are met during each hour. Security: e.g. minimizing response time to emergency calls by allocation of police patrol units to areas with high crime rates.

2 875 (iv) Maximizing an organization s profit by selecting a product mix in a factory with best use of machine and labour hour available. (v) Minimizing total production and inventory costs for a firm by developing a production schedule satisfying future demands. (vi) Minimizing total shipping costs from various warehouses to several selling points. (vii) Maximizing revenues by a leasing company by allocation of space to a tenant in a new shopping mall. (ix) Telecommunications e.g. number of calls received, missed or waiting on the queue as well as messages. (x) Identification of an Organization strategy that has been adopted in terms of Information Systems (6) C. PRODUCTION SCHEDULING In order to supply customer needs and hearken to market demand, most factories produce various products.scheduling simply means allocating resources to various tasks (7). Every organization needs production scheduling so as to remain in the competing market and meet the customer needs. Scheduling is a vital tool for both engineering and manufacturing as it could have paramount impact on the productivity of a process. Its aim in manufacturing is to minimize the production time and costs and maximize the efficiency of operation and reduce costs. One of the most important tasks of a manager is production scheduling as a result of a competitive market. Lots of methods have been implemented in solving production scheduling problems, one of which includes linear programming (8). II CASE STUDY A. A GENERAL OVERVIEW OF PZ CUSSONS Founded in 1879 as Paterson Zochonis, PZ Cussons is a principal manufacturer of personal consumer goods and healthcare products. George Paterson and George Zochonis started the company in Sierra Leone as a trading post which enlarged its operations into neighbouring Nigeria before the end of the 19 th century (9). PZ enlarged considerably around the 20 th century with the acquisition of factories and establishment of offices in Kenya and Ghana. The company dominated Guinea commercially before 1958 (10) and acquired Cussons Group in In 1986, its first factory was built in Thailand as offices and factories were acquired in Asia and operations reaching Indonesia in In 2002, a rename from Paterson Zochonis plc.was made to PZ Cussons plc. The table below shows the timeline of PZ Cussons. B. OPERATIONS AND BRANDS OF PZ CUSSONS OPERATIONS PZ Cussons operates in selected markets where they believe they can capitalize on their local knowledge and apply global know how and best practice; finding opportunities and innovating to create market leading products which are delivered to customers through their fast and flexible supply chain. PZ Cussons have their major market operations in Africa (one of the longestestablished and most thriving markets), Europe (consisting interesting mix of categories and markets with continued growth potential), and Asia (an exciting balance of maturing and emerging markets with an excellent opportunity for growth). BRANDS PZ Cussons are the business behind some of the world s best known brands with their success lying in their unique approach in looking for new and better ways to enhance customers lives. They major in five different brands which includes Personal Care, Beauty, Electricals, Food and, and Home Care. Various products are produced under each brand of PZ Cussons. Personal Care: PZ Cussons develop innovative products from well-known international brands like Imperial leather, Cussons baby, and Carex to local brands like Robb and Luksja, Mum & Me, Premier. Beauty: The beauty brands make luxury more accessible every day. The products include St. Tropez, Fudge, Charles Worthington, and Sanctuary Spa. Electricals: PZ trusted brand for 40 years Haier Thermocool combines technology and innovation to solve everyday household challenges, and a joint venture operating in Lagos and Ghana (12). Their products are the refrigerators, freezers, and washing machines. Food and : PZ Cussons improves lives and communities with their unique and delicious food products ranging from African milk drinks and organic baby food to Greek olive oil. These products include Yo, Coast, Nunu, Bliss, Rafferty s garden, Benecol, Horio, Minerva, and Mamador. Home Care: By helping families keep their homes clean and fresh for many years with their market-leading range of home care products, PZ Cussons are the producers of Morning Fresh, Zip, and Radiant. C. THE APPLICATION OF MANAGEMENT SCIENCE FOR PRODUCTION AT PZ CUSSONS At PZ Cussons, production is being planned in the three regions. The business has an impact upon the

3 876 environment, both through manufacturing and logistics operations, hence, it must run in a way to minimize adverse impacts and make positive contribution to meeting global environmental challenges. Therefore, the production is limited by both water allocated and available electricity. For the purpose of this study, production for the past three years shall be examined ( ), and a forecast for the next three years ( ). It is agreed that each region will produce the same proportion of its available land capacity. However, any combination of brands may be produced at any of the regions. The duty of the managers coordinating office is to plan how many resources to devote to each brand at the respective region while satisfying given restrictions. PRODUCTION FOR THE YEAR 2011 The table below highlights the available land and water allocation for the three regions. Region Usable land Electricity (acres) allocation (kw) Africa (1) Asia (2) Europe (3) Table 1: Table showing the available land and electricity allocation for the three regions Below are the given brands to be produced in the three regions, the total land quanto for each brand, the electricity consumption for each brand, and the net return from each brand. Brands Maximum land quanto (acres) Electricity consumption (kw/acre) Net revenue (million ) Personal care Beauty Electricals Food and Home Table 2: Brands to be produced in the three regions in The management has decided that for each region, specific constraints abound. It is said that for African region, allocation for usable land, electricity and maximum land quanto for Personal Care must be at most 20%, at most 47% for Personal Care, Beauty, and Electricals, Personal Care and Beauty must not exceed 32%, and Beauty and Food & must be at most 26%. The objective is to maximize the total revenue for PZ Cussons as a whole. The table below shows the decision variables according to the regions and brands to be produced at each region. Regions Brands Personal care X 11 X 12 X 13 Beauty X 21 X 22 X 23 Electricals X 31 X 32 X 33 Food and X 41 X 42 X 43 Home X 51 X 52 X 53 Table 3: Decision variables according to regions and brands for each region. NOTE: X ij : number of production of brand i in region j. Regions 1, 2, 3 represent Africa, Asia, and Europe respectively Objective function: Max Z = 165(X 11 + X 12 + X 13 ) + 105(X 21 + X 22 + X 23 ) + 115(X 31 + X 32 + X 33 ) + 118(X 41 + X 42 + X 43 ) + 123(X 51 + X 52 + X 53 ) Constraints: (Land constraint); X 11 + X 21 + X 31 + X 41 + X X 12 + X 22 + X 32 + X 42 + X X 13 + X 23 + X 33 + X 43 + X (Electricity constraint); 2X X X X X X X X X X X X X X X (Land quanto constraint); X 11 + X 12 + X X 21 + X 22 + X X 31 + X 32 + X X 41 + X 42 + X X 51 + X 52 + X X ij 0, i, j = 1, 2, 3, 4, 5. The table below shows the calculated percentages for each region according to the management s constraints. Brands Africa Asia Europe Personal Care Beauty Electricals Food and Home Table 4: Calculated percentages for each region according to Managements constraints.

4 877 Hence, by substituting these values above into the objective function; Max Z = 165(X 11 + X 12 + X 13 ) + 105(X 21 + X 22 + X 23 ) + 115(X 31 + X 32 + X 33 ) + 118(X 41 + X 42 + X 43 ) + 123(X 51 + X 52 + X 53 ), we obtain the optimum value as thus: Max Z = 165( ) + 105( ) + 115( ) + 118( ) + 123( ). Max Z = 165(205) + 105(160) + 115(165) + 118(165) + 123(190) Max Z = Max Z = 112,440m PRODUCTION FOR THE YEAR 2012 The table below highlights the available land and water allocation for the three regions. Region Usable land Electricity (acres) allocation (kw) Africa (1) Asia (2) Europe (3) Table 5: Table showing the available land and electricity allocation for the three regions Below are the given brands to be produced in the three regions, the total land quanto for each brand, the electricity consumption for each brand, and the net return from each brand. Brands Maximum land quanto (acres) Electricity consumption (kw/acre) Net revenue (million $) Personal care Beauty Electricals Food and Home Table 6: Brands to be produced in the three regions in The management has decided that for each region, specific constraints abound. It is said that for African region, allocation for usable land, electricity and maximum land quanto for Food and must not exceed 100, both Food & and Beauty must not exceed 23.33%, Food & and Home must be at most 25%, and at most 20% for Personal Care and Home. For Asian region, the allocation for usable land, electricity and maximum land quanto for Food and must be at most 80, at most 36.67% for Food & and Personal Care, at most 25% for Personal Care and Home, and Beauty and Home must not exceed 25% as well. For the European region, allocation for usable land, electricity, and maximum land quanto for Food & must be at most 20, at most 20% for Food & and Electricals, Electricals and Personal Care must not exceed 27.5%, and at most 17.5% for Personal Care and Beauty. The objective is to maximize the total revenue for PZ Cussons as a whole. The table below shows the decision variables according to the regions and brands to be produced at each region. Regions Brands Personal care X 11 X 12 X 13 Beauty X 21 X 22 X 23 Electricals X 31 X 32 X 33 Food and X 41 X 42 X 43 Home X 51 X 52 X 53 Table 7: Decision variables according to regions and brands for each region. NOTE: X ij : number of production of brand i in region j. Regions 1, 2, 3 represent Africa, Asia, and Europe respectively Objective function: Max Z = 270(X 11 + X 12 + X 13 ) + 230(X 21 + X 22 + X 23 ) + 122(X 31 + X 32 + X 33 ) + 135(X 41 + X 42 + X 43 ) + 100(X 51 + X 52 + X 53 ) Constraints: (Land constraint); X 11 + X 21 + X 31 + X 41 + X X 12 + X 22 + X 32 + X 42 + X X 13 + X 23 + X 33 + X 43 + X (Electricity constraint); 3X X X X X X X X X X X X X X X (Land quanto constraint); X 11 + X 12 + X X 21 + X 22 + X X 31 + X 32 + X X 41 + X 42 + X X 51 + X 52 + X X ij 0, i, j = 1, 2, 3, 4, 5. The table below shows the calculated percentages for each region according to the management s constraints.

5 878 Brands Africa Asia Europe Personal Care Beauty Electricals Food and Home Table 8: Calculated percentages for each region according to Managements constraints. By substituting these values above into the objective function; Max Z = 270(X 11 + X 12 + X 13 ) + 230(X 21 + X 22 + X 23 ) + 122(X 31 + X 32 + X 33 ) + 155(X 41 + X 42 + X 43 ) + 100(X 51 + X 52 + X 53 ), we obtain the optimum value as thus: Max Z = 270( ) + 230( ) + 122( ) + 155( ) + 100( ) Max Z = 270(150) + 230(90) + 122(105) + 155(200) + 100(130) Max Z = Max Z = 118,010m PRODUCTION FOR THE YEAR 2013 The table below highlights the available land and water allocation for the three regions. Region Usable land Electricity (acres) allocation (kw) Africa (1) Asia (2) Europe (3) Table 9: Table showing the available land and electricity allocation for the three regions Below are the given brands to be produced in the three regions, the total land quanto for each brand, the electricity consumption for each brand, and the net return from each brand. Brands Maximum land quanto (acres) Electricity consumption (kw/acre) Net revenue (million $) Personal care Beauty Electricals Food and Home Table 10: Brands to be produced in the three regions in The management has decided that for each region, specific constraints abound. It is said that for African region, allocation for usable land, electricity and maximum land quanto for Food and must not exceed 100, both Food & and Beauty must not exceed 23.33%, Food & and Home must be at most 25%, and at most 20% for Personal Care and Home. For Asian region, the allocation for usable land, electricity and maximum land quanto for Food and must be at most 80, at most 36.67% for Food & and Personal Care, at most 25% for Personal Care and Home, and Beauty and Home must not exceed 25% as well. For the European region, allocation for usable land, electricity, and maximum land quanto for Food & must be at most 20, at most 20% for Food & and Electricals, Electricals and Personal Care must not exceed 27.5%, and at most 17.5% for Personal Care and Beauty. The objective is to maximize the total revenue for PZ Cussons as a whole. The table below shows the decision variables according to the regions and brands to be produced at each region. Regions Brands Personal care X 11 X 12 X 13 Beauty X 21 X 22 X 23 Electricals X 31 X 32 X 33 Food and X 41 X 42 X 43 Home X 51 X 52 X 53 Table 11: Decision variables according to regions and brands for each region. NOTE: X ij : number of production of brand i in region j. Regions 1, 2, 3 represent Africa, Asia, and Europe respectively Objective function: Max Z = 185(X 11 + X 12 + X 13 ) + 175(X 21 + X 22 + X 23 ) + 121(X 31 + X 32 + X 33 ) + 85(X 41 + X 42 + X 43 ) + 52(X 51 + X 52 + X 53 ) Constraints: (Land constraint); X 11 + X 21 + X 31 + X 41 + X X 12 + X 22 + X 32 + X 42 + X X 13 + X 23 + X 33 + X 43 + X (Electricity constraint); 3X X X X X X X X X X X X X X X (Land quanto constraint); X 11 + X 12 + X X 21 + X 22 + X X 31 + X 32 + X

6 879 X 41 + X 42 + X X 51 + X 52 + X X ij 0, i, j = 1, 2, 3, 4, 5. The table below shows the calculated percentages for each region according to the management s constraints. Brands Africa Asia Europe Personal Care Beauty Electricals Food and Home Table 12: Calculated percentages for each region according to Managements constraints. By substituting these values above into the objective function; Max Z = 185(X 11 + X 12 + X 13 ) + 175(X 21 + X 22 + X 23 ) + 121(X 31 + X 32 + X 33 ) + 85(X 41 + X 42 + X 43 ) + 52(X 51 + X 52 + X 53 ), we obtain the optimum value as thus: Max Z = 185( ) + 175( ) + 121( ) + 85( ) + 52( ) Max Z = 185(275) + 175(165) + 121(160) + 85(180) + 52(200) Max Z = Max Z = 124,810m III DECISION MAKING AND FORECASTING AT PZ CUSSONS In a situation whereby there are many alternatives of choices to be made, it is not advisable for managers to make decisions based on their qualitative knowledge; hence a qualitative approach is necessary for effective decision making. PZ Cussons utilizes the LINGO programming in their decision making. This is as a result of many products being produced from various brands, and being distributed in various continents having many countries. It is thus impossible for PZ Cussons to make calculations manually in order to make production decision for each product of each brand. The LINGO program helps PZ Cussons to know the profit each product yields, the slack and surplus generated by each product, the region which produces more profit and that which produces less. It also helps them to know how much increase or decrease in profit will be incurred if one unit is added or deducted from the production of a particular product of each brand (14). PZ Cussons uses LINGO program to determine the quantity of product of a particular brand to be produced in each region to maximize their profit. To forecast for the next three years for PZ Cussons, we examined the relationship between the sets of previous data. The table below shows the previous output of PZ Cussons. Year (X) Output X 2 Y 2 XY (Y) TOTAL Table 13: Table showing the previous outputs (Y) of PZ Cussons Y = a + bx, n = 3; a = X 2 Y X XY / n X 2 ( X) 2 a = (14 x 355.2) (6 x 722.8) / (3 x 14) 6 2 a = ( ) / (42 36) a = 636 / 6 a = 106 b = n XY X Y / n X 2 ( X) 2 b = (3 x 722.8) (6 x 355.2) / (3 x 14) 6 2 b = ( ) / (42 36) b = 37.2 / 6 b = 6.2 Thus, Y = x Hence, for 2014, x = 4. Substituting this into the equation above, Y = (4) Y = Y = This implies that for the year 2014, PZ Cussons is likely to have an output of 130,800m For 2015, x = 5. Substituting this into the equation, Y = (5) Y = Y = 137 This implies that a forecast for the year 2015 for PZ Cussons is 137,000m For the year 2016, x = 6 Y = (6) Y = Y = This means that a forecast for PZ Cussons for the year 2016 yields and output of 143,200m IV CONCLUSION Decision making in large companies such as PZ Cussons could be very challenging, thus they implement an optimization modeling software such as LINGO (15). But take for instance a company producing two products and distributing to three locations, decisions can be

7 880 made manually by calculating the profit generated from each product and each region. REFERENCES [1] Why and Which Manufacturing Matters?Brookings Institution, February [2] Stafford Beer (1967), Management Science: The Business use of Operations Research. [3] J. E. Beasley, editor. Advances in Linear and Integer Programming. Oxford Science, 1996, Collection of surveys. [4] Mark A. Schulze Linear Programming for Optimization, Perceptive Scientific Instruments, Inc [5] What Is Management Science? Lancaster University, 2008 Retrieve 5 June [6] Production and Operations Management, the Official Journal of the Production and Operations Management Society. [7] HojjatAdeli, AsimKarim- Construction of Scheduling, Cost Optimisation and Management, 2003, P54. [8] SoheilSadi-Nezhad, Samira Borhani Darian Production Scheduling for Products on Different Machines with Setup Costs and Times. [9] PZ Cussons: Our History. [10] Thomas O'Toole, Historical Dictionary of Guinea, Scarecrow Press, 1978, p. 55. [11] Hall, W Weak dollar slows down PZ Cussons Financial Times. [12]Reuters: PZ Cussons boosted by Strong Trading in Nigeria, Jul [13]Lixin Tang, Jiyin Liu, AiyingRong,Zihou Yang. Theory and Methodology, A Mathematical Programming Model For Scheduling Steelmaking- Continuous Casting Production. [14] J. Neuwirth, A Production Scheduling System At The Stahl Linz Gmbh, In: D.K. Baik (Ed.), International Conference on Computerized Production Control in Steel Plant, Korea, 1993, pp. 342±350. [15] K. Hamada, T. Baba, K. Sato, M. Yufu, Hybridizing A Genetic Algorithm With Algorithm With Rule-Based Reasoning For Production Planning, IEEE Expert 10 (1995) 60±67.