A Hierarchical Production Planning System

Transcription

1 A Hierarchical Production Planning System MATTHEW]. LIBERATORE TAN MILLER College of CommeKe and Finance ViUanova Uniitersitif Villanova, l^nsiflvania American Oleait Tile Company 1000 Cannon Avenue Lansdale, Pennsylvania Hierarchical integration of production planning, scheduling, and inventory control is required to coordinate organizational levels responsible for developing and executing plans. A hierarchical planning system has been developed for American Olean Tile Company and is being implemented. Since several system components were already in place, development costs to date include five months of an analyst's time and timesharing charges of about $10,000. Improved coordination and communication between manufacturing and marketing, the development of new sales forecasting procedures, and reduced distribution costs of $400, ,000 per year are the principal benefits. P roduction planning can be seen as a hierarchy of managerial decisionmaking activities. The hierarchy ranges from strategic planning through tactical planning to operations control [Anthony 1965]. In formulating strategy, the firm decides on its objectives, such as profitability, growth, and market and technological position. In analyzing its environment, the firm determines whether existing or new products will better enable it to achieve its objectives during the planning period. Manufacturing policies are established to help close some of the gaps between projected and desired performance. These may call for changes in the capacity, location, and configuration of the firm's physical facilities. What fi- Ciipvrighl C^ 1^85. The Inslitute ii( Management Sciences /85/1504/0001 $01 25 rhis paper was retereed. INVENTDRY/PRODUCnON APPLICATK.WS INDUSrRIES - CERAMIC- INTERFACES 15: 4 July-August 1985 (pp. Ml)

2 LIBERATORE, MILLER nancial, human, and material resources are available to operating management over the planning horizon are also defined. These upper management decisions form a framework for tactical (mediumterm) production planning, which allocates capacity to product lines and establishes the sources of product supply for the various levels in the distribution chain (warehouses, sales centers, and so forth). This tactical plan must be put into operation by determining a short-term production schedule for each manufacturing facility. The firm's hierarchical production planning and scheduling activities must be integrated to insure coordination between the various organization levels responsible for developing and executing plans [Gelders and Van Wassenhove 1982]. Also the hierarchy of managerial decisions must be consistent to avoid excessive suboptimization, recognizing that it is usually impossible to construct one all-encompassing model for analyzing decisions at all levels. Such a hierarchical production planning system has been developed at American Olean Tile Company (AO) because of AO management's interest in using computerbased decision aids to integrate (1) The development of the annual production plan and source of supply, (2) Short-term production scheduling activities at each of the plants, and (3) Inventory control procedures at the sales distribution points (SDP). An annual production-planning and sourcing model has been successfully implemented, and a short-term computerized scheduling model is being field tested. The master production schedule is based on forecasts from a computerized inventory control system at the SDPs, as well as on firm, scheduled orders. Our modeling approach generally follows the framework developed by Hax and Meal [1975]. However, our product aggregation-disaggregation scheme is quite simplistic, while our approach to Production planning can be seen as a hierarchy of managerial decision-making activities. short-term scheduling is based on a mixed-integer-programming model. The literature contains few reports on the practice of hierarchical planning and integration. Notable exceptions include the implementation of Hax and Meal [1975], case studies in a rolling mill [Gelders and Van Steelandt 1980] and a medium-sized chemical firm [Gelders and Van Wassenhove 1982], and an integrated production, distribution, and inventory planning system for a large chemical fertilizer company [Glover et al. 1979]. The need for additional descriptions of industrial applications in designing coordination schemes and integrated systems has been suggested [Gelders and Van Wassenhove 1982]. Company Background The American Olean Tile Company, founded in 1923 as the Franklin Tile Company, manufactures a wide variety of ceramic tile products. These products range from tile produced for walls (indoor and outdoor applications) and for floors (both light residential and heavy commercial). INTERFACES 15:4

3 AMERICAN OLEAN to tiles produced for elaborate mural designs. AO currently operates eight factories located across the US from New York to California that supply approximately 120 sales distribution points, a combination of marketing sales territories and company-owned warehouses. These factories utilize several different production processes, all of which begin with a crushing and milling procedure, and which eventually lead to the firing of the tile in large kilns. AO produces three basic lines of tile products: (1) glazed tile, (2) ceramic mosaics, and (3) quarry tile. The quarry division operates four factories at three locations (Quakertown, Pennsylvania; Lewisport, Kentucky two plants; and Roseville, California), while the glazed and ceramic mosaic divisions have two and one manufacturing sites, respectively. In recent years, AO's distribution network has expanded quite rapidly, and this trend continues today. The growth of this network prompted AO's management to initiate a modeling program designed to assist manual planning of production and distribution. The modeling began with the quarry division, which has the largest distribution network of the three divisions (Figure 1). In implementing the annual production planning model, the need for coordinating it with short-term production scheduling at the plants and inventory control at the SDPs became apparent. It became clear that full benefits from proper plant, product, and SDP assignments cannot be obtained when short-term scheduling and inventory control decisions are not aligned with the annual plan or the assumptions underlying it. A hierarchical production planning system was developed to improve the integration of the annual plan, short-term Plant Sal** A Sala* Svryic* Canlan DUIrlbutMi Figure 1: Quarry tile distribution network for American Olean Tile Company. July-August 1985

4 LIBERATORE, MILLER scheduling, and inventory control. Production Planning Framework The design of any product aggregation scheme depends on product structure, and consistency and feasibility are the principal objectives and constraints [Gelders and Van Wassenhove 1982]. The quarry tile product line was aggregated into 10 families, each of which comprises several hundred items or stock-keeping units (SKU's). Because the number of product families is small, demand seasonality is incorporated at the family level in our system. The Hax-Meal approach [1975] groups families into types having similar seasonality patterns. The level of aggregation employed at AO is appropriate to both the nature of the tile product and its manufacturing process. In most general terms, tile can be classified into two product types: flat tile and trim tile. Flat tile constitutes approximately 90 percent of total quarry sales and is produced in approximately seven to 10 basic shapes (for example, 4" x 8" or 6"x6"). Trim tiles are pieces of tile specially shaped to form a border between the surface covered by the flat tile and the surface next to the fiat tile (for example, the border where a floor and a wall intersect). The demand for trim tile is dependent (in a materials requirements plarming sense [Orlicky 1975]) on flat tile demand. Once we have set the production schedule for flat tile, the amount of associated trim production required is determined through a known flat-to-trim selling ratio. Decisions about trim production are derived directly from decisions on flat production, and often the trim associated with a particular flat product is fired concurrently on the same production line. The flat tile production process itself made it logical to further condense SKU's into major product families. In addition to a basic shape and color, flat tile is made in several different surfaces (for example, regular and abrasive), and in several variations of the basic color (for example. Grey and Grey Flash). However, tiles made from one basic flat shape in one color all require very similar raw materials and have virtually identical manufacturing cost and capacity constraints. Therefore, several major flat tile SKU's can be aggregated into one major product family with minimal impact on the accuracy of our model results. The aggregation process resulted in the formation of 10 major product families encompassing over 98 percent of total quarry sales. Figure 2 summarizes the framework for the hierarchical integration of the production planning and scheduling activities for the AO quarry tile division. The planning process begins with an annual, subjective sales forecast for total quarry division sales expressed in square feet of tile. The director of market planning, in consultation with other top management, generates this sales projection based upon a combination of economic trends and specific quarry market developments. This forecast is allocated to each product family and apportioned to the SDP's based on the ratio of their annual total sales to the total of all quarry tile sales during the previous year. Some adjustments are then made by the planning and marketing staffs. Analysis of recent historical demand patterns has revealed that AO's sales mix remains essentially constant in INTERFACES 15:4

5 AMERICAN OLEAN Annual Forcaal by SOP, by Family Firm. Schadulad Ordari Shoii-tarm Farcatt*. by SKU. by SOP, by Plant SDP Invantory Control Sy«t*m Plant/SDP/Famtly Aaatanmant Modal Monthly Producllon Plan by Plant Maatar Production Schadul* by Plant, by Family Forcaal by Plant, by Month, by Family Family Short-tarm Schaduling Moil*!, by Plant SKU Short-tarm Schadula, by Plant Figure 2: Hierarchical production planning and scheduling framework for American Olean Quarry Tile Division. the short run (12-18 months). These forecasts and the current configuration of AO's plants and SDP's, as well as production line and freight costs, are incorporated into a mode! which assigns annual family demand by SDP to plants within available capacity. A monthly production plan is then developed by plant-level production personnel based on these assignments and seasonal inventory targets and demar\d patterns. The monthly production plan, scheduled orders received from larger customers, and short-term demand forecasts generated at each SDP are combined into a master production schedule (MPS) (by family) at each plant. The planning horizon for the MPS is the upcoming quarter, and the length of the planning period is typically one to two weeks. AO currently uses IBM's Inventory Management Program and Control Techniques (IMPACT) for both SDP short-term forecasting and inventory management (see Chase and Aquilano [1981, pp ] for a good summary of IMPACT'S functions and objectives). The SKU demand forecasts are generated by exponential smoothing with trend and seasonality adjustments [Brown 1962; Tersine 1982, pp ]. A standard order point-economic order quantity (] OQ) system is used for inventory control, where customer service is measured as percentage of demand filled from stock on hand July-August 1985

6 LIBERATORE, MILLER [Tersine 1982, pp ]. Forecast errors are measured and tracked using mean absolute deviation (MAD). Process industries tend to schedule capacity first and then materials [Taylor, Seward, and Bolander 1981]. This differs from materials-oriented systems, such as Materials Requirements Planning (MRP), which are used extensively by the fabrication and assembly industries. Our system uses a short-term scheduling model which first determines the assignment of production lines by planning period to meet the MPS, while minimizing the sum It became clear that full benefits... cannot be obtained when short-term scheduling and inventory control decisions are not aligned with the annual plan.... of variable manufacturing, setup, and inventory costs. (This model is currently being field tested. It is the critical link between the divisional annual planning, plant-level production scheduling, and SDP inventory control activities.) Then, based on SKU demand forecasts for each family and derived demand for trim products, a short-term SKU production schedule and the associated materials requirements for each plant are established. The mathematical formulations of the plant, family, and SDP assignment model and the family short-term scheduling model are described in the appendices. Implementation The process of implementing the revised plant, family, and SDP assignment patterns suggested by our modeling results has required at least as much effort as the model development process itself. It became evident during initial field testing that a successful implementation would hinge on the interest and support of two distinct sets of individuals: (1) key production and distribution personnel at corporate headquarters; and (2) field personnel, such as plant managers. Each group expressed a variety of concerns regarding the changes implied by the model's results. However, two factors provided the most compelling arguments for gaining their support. First and most importantly, we emphasized the potential savings resulting from model implementation. Management interest was heightened by the fact that the benefits would be ongoing. Second, the use of a staged process for implementation allowed changes to be made at an acceptable rate. Massive reassignments u^ere not requested at the outset, nor would they have been approved by upper management. For example, the model suggested many changes in source of supply for the SDP's. However, only a few assignments were altered during each stage. This facilitated a smooth transifion and avoided the turmoil and resistance which might otherwise have arisen. In a staged implementation, it is necessary to evaluate each step separately. The affected personnel consider each step on its own merits, not as part of a larger, overall plan. Therefore, the success of each step, and ultimately of the entire plan, depends upon developing self-supporting stages. Each stage must be evaluated for any potential "suboptimization" INTERFACES 15:4 6

7 AMERICAN OLEAN effects. Specifically, the impact of staged revisions on the entire system must be considered before implementation. This process has been completed for the quarry tile division, and a similar process is under way for the glazed division. Its LP is substantially larger, with 440 decision variables and 2440 constraints. Because the family scheduling model is currently being field tested, a detailed discussion of implementation issues is not yet possible. However, current efforts focus on implementation at one of the three locations, while the remaining sites will be converted in a second stage. Costs and Benefits The development costs fall into two basic categories: (1) man-months committed to data and model development, and (2) expenditures for computer software. Because several system components were already in place, the development costs to date are much less than they would be for the complete system. Specifically, IM- PACT and the annual aggregate forecasting process were already in use and were incorporated into the overall framework. The family short-term scheduling model is still under development, making it difficult to estimate a total cost now. Concerning the plant, SDP, and family assignment model, more accurate estimates can be given. Development required approximately five man-months of an analyst's time distributed over a nine-month period. The computer model was developed and stored on a commercial timesharing system at a cost of under $10,000. Software development costs of the shortterm family scheduling model will exceed the $10,000 level, since an efficient mixed integer programming capability is required. An integrated hierarchical system for planning and scheduling production offers many benefits at both the individual component and the system-wide level of an organization. These benefits range from improved coordination and communication between departments to substantially reduced production and distribution costs. As a whole, the system significantly enhances American Olean's ability to position itself more competitively in the marketplace. AO has used the annual assignment model results in developing the production and distribution allocation plan for the quarry division. This plan saves between $400,000 and $750,000 per year. The suggested plan did not substantially alter the capacity loadings at the individual plants. However, it did suggest significant changes in their family mixes. Thus, the model uncovered comparative cost advantages in terms of delivered cost (variable production costs and freight) from each plant. The development of the assignment model required a sales forecast by family for each SDP. Previously, in the absence of these forecasts, the annual production plans of the manufacturing department did not always coincide with the SDP sales plans of the marketing department. The manufacturing department had always based annual production goals upon the marketing department's annual sales forecast. However, without a detailed forecast, production could not be based on the demands of individual sales territories. As an indirect benefit, the process of July-August 1985

8 LIBERATORE, MILLER developing the model stimulated closer coordination between the marketing and manufacturing departments in meeting the needs of the sales territories. AO also derived several other indirect benefits, which are also difficult to quantify. Specifically, this methodology produces a general pattern of lower delivered costs at AO's sales distribution points. This offers top management the marketing option of lowering product prices (or at least minimizing any price increases) while maintaining AO's required profit margins on an item-by-item basis. The annual planning model can help AO management measure the financial impact of adjusting some medium-term manufacturing and distribution strategies. For example, a plant may have stopped making a particular product because the cost of a major raw material has become too high. The model can determine the system-wide change in annual manufacturing and distribution costs if a less costly alternative material can be found. Other examples include determining what cost savings would result from such capital investment decisions as adding new production capacity to a plant, and what financial penalty would accompany controlling the usage rate of a scarce material at a producing location. The annual assignment model also helps to reduce unplanned redistribution costs which occur every year. These "hidden" costs arise when one SDP transships a product to a second SDP which is out of stock. These costs are reduced because assignments are now tied more closely to demand patterns within each SDP's market area. Although the short-run family scheduling model has been developed and solved using actual production, cost, and MPS data for one plant location, we have not yet fully implemented it. We anticipate that its principal impact will be cost savings from improved short-run production plans. For example, even at a plant with a relatively straightforward production process (say, five production lines and five families), the number of potential production combinations over even a short-term planning horizon (for example, four two-week time buckets, or eight weeks) is very large. It is virtually impossible to evaluate manually the total costs associated with even a small subset of potential production schedules. The family scheduling system will be able to make such evaluation easily and should lead to significant cost savings. In addition, this model and the other components of the system will increase labor productivity by freeing many man-weeks previously devoted to manual planning efforts. In summary, the hierarchical production-planning system offers a modeling approach which integrates decision making and communication across corporate and plant level organizations, enabling more consistent medium- and short-term production-planning and scheduling decisions. APPENDIX 1: Plant/Family/SDP Assignment Model The following definitions are used: ^ijpk = square feet of family / produced on line / at plant p and shipped to SDP it. C,jp^ = the unit square footage cost of producing family i on line / INTERFACES 15:4 8

9 AMERICAN OLEAN at plant p and shipping (at truckload rates) to SDP k. D,k = square footage dentand of family i at SDP k. Siip = square footage annual production capacity of product / produced on line / at plant p. Integer assignment variables are not required since annual SDP demand is sometimes in practice split over several locations. Also since AO planned to operate all current plants during the strategic planning horizon {five years), fixed manufacturing costs were excluded from the analysis. The problem can then be stated in a transportation-type linear programming format. Minimize subject to for all possible i, k (family-sdp) combinations (2) for ali possible j, p (lineplant) combinations y.,kp ^ 0, for all i, j, k, p. The multiplier ClIS,,,) is needed in equation (3) to adjust for the different capacity level (or equivaiently, production rates) for each family which can be produced on a given line. The three locations in the quarry tile division have four, six, and two production lines, respectively There are 10 families, which are produced on different subsets of these 12 lines, and the 120 SDP's stock some or all of these families. The problem can be solved on any large-scale linear programming system. In this case, a matrix generator was used to simplify the input and editing process, and the resulting model was run on MPS III. The model has approximately 1660 decision variables and 570 constraints. APPENDIX 2: Family Scheduling Model The AO family scheduling model minimizes the total of variable production, line setup, and inventory holding costs over the short-term planning horizon while meeting the MPS. Production rates by family by production line are constant during each scheduling period. Backlogging of demand is not permitted. The mathematical formulation is a generalization of a single production line model developed for a chemical processing plant [Liberatore 1984]. The model itself is a mixed integer linear program, and the formulation is given below. Where Xii, ~ ^' ^^ product i is produced on production line ; during period t = 0, otherwise. Vij, = 2, if a production changeover to product / on line / occurs during time t = 0, otherwise. Q, = the unit cost of producing product ( on line j. Pi, = the production rate per period of product I on line ;. S,y = the fixed cost to set up product i on line;. D^, = the demand for product / during period t. H, = the end-or-period holding cost for product i. I, = the inventory of product i at the end of period (. L, = the set of all production lines which can be scheduled to produce product i. M, = the set of all products which can be scheduled on production line /. P = the number of products to be scheduled. July-August 1985

10 LIBERATORE, MILLER L = the number of production lines available. N = the number of periods in the t planning horizon. = the time period, expressed in units of one week. The problem can be stated as minimize N P N P t= I ye/,, 1= I l=\ i-l subject to A,>0, /=I,2 P, /= 1,2,...,A', 2 Y «r 1 I I 9 / ^iji ^'J,'-i' t=\,l N, X,,,, V,,,, binary, where /, X^^ given as initial conditions. Finally, ending inventory is defined as A/ = Ao Pij^ijk' 2 A* / k-\ j&l, k=\ i= I,2,...,/>, /= 1,2 N. (5) (6) (7) Equation (5) prevents backlogging of demand, while equation (6) insures that at most one product is scheduled on a given line during each period (an assignmenttype constraint). Equation (7) relates the changeover variable (V,,,) to the production scheduling variables in the current and previous periods (X,^, and X,,,_,, respectively). A changeover to product i on line / occurs during period t and only if X,,, = 1 and X,,,, _, is 0. Thus even if the line was idle during period f-1, we assume that a changeover occurs to i if it is then scheduled during period t. It is easily shown that equation (7) forces V^,, to be 1 or\iy if X,,, = 1 and X,,,,., is 0; in all other cases V,,, must be 0. Thus, V,,, need not be specified as a binary variable. The inventory variables can be eliminated from the formulation, and after grouping terms and simplifying, we obtain minimize 2 2 2[Q + (^-' subject to 2 2 ^y-^i;*>2 A.-Ao. / = 1, 2,... P> t = 1,2,..., N, ^j ijt ' _/ = 1,2 L, t = 1,2,...,7V, (9) (11) /=l,2 P. i^l, (12) X^,, specified as binary; /,o, X,^ given. We define C(2) to be the cardinality of the set Z. It follows that y = where V is the number of distinct product production line scheduling combinations. Therefore, the problem defined by equations (9) (12) is a mixed integer program, with 2NV decision variables, NV of which must be specified as binary, and (P-\-L+V)N constraints. A variety of techniques and approaches has been suggested in the literature (for example, Crowder, Johnson, and Padberg [1983]; Guignard and Spielberg [1981]) which improve the performance of searching algorithms for binary integer programming. To reduce the time required to find an acceptable integer solu- INTERFACES 15:4 10

11 AMERICAN OLEAN tion for the family scheduling model, a series of redundant constraints was added to the problem formulation. These serve to increase the optimal cost of the linear programming (LP) relaxation of the problem and tend to force more variables to assume binary values. The amount of searching time required to find both an initial feasible binary solution and a good solution is drastically reduced. Initial results were dramatic: for one sample problem, the number of branches checked to find an initial feasible solution dropped from 2000 to 15. Depending upon the actual data, some of these redundant constraints may be more effective than others so that additional testing is required before final implementation. References Anthony, Robert N. 1965, Planning and Control Systems: A Framework pr Analysis. Harvard University, Graduate School of Business Administration, Division of Research, Boston, Massachusetts. Brown, Robert G. 1962, Smoothing, Forecasting and Prediction of Time Series, Prentice-Hall, Englewood Cliffs, New Jersey. Chase, Richard B. and Aquilano, Nicholas J. 1981, Production and Operations Management, (third edition), Richard D. Irwin, Homewood, Illinois. Crowder, Harlan; Johnson, Ellis L.; and Padberg, Manfred 1983, "Solving large-scale zero-one linear programming problems," Operations Research, Vol. 31, No. 5 (September-October), pp Gelders, L. F. and Van Steelandt, E V 1980, "Design and implementation of a production planning system in a rolling mill: A case study," AllE Thansactions, Vol. 12, No. 1, pp Gelders, L. E and Van Wassenhove, Luk N. 1982, "Hierarchical integration in production planning: Theory and practice," Journal of Operations Management, Vol. 3, No. 1 (November), pp Glover, Ered; Jones, Gene; Kamey, David; Klingman, Darwin; and Mote, John 1979, "An Integrated production, distribution, and inventory planning system," Interfaces, Vol. 9, No. 5 (November), pp Guignard, Monique and Spielberg, Kurt 1981, "Logical reduction methods in zero-one programming," Operations Research, Vol. 29, No. 1 (January-Eebruary), pp Hax, A. C, and Meal, H. C. 1975, "Hierarchical integration of production planning and scheduling," in Studies in the Management Sciences, M. A. Geisler, editor. Vol. 1, Logistics, North Holland, Amsterdam. Liberatore, Matthew J. 1984, "A dynamic production planning and scheduling algorithm for two products processed on one line," European Journal of Operational Research, Vol. 17, No. 3 (September), pp Orlicky, Joseph 1975, Material Requirements Planning, McGraw-Hill, New York. Taylor, Sam G.; Seward, Samuel M; and Bolander, Steven E 1981, "Why the process industries are different," Production and Inventory Management, Vol. 22, No. 4, pp Tersine, Richard J. 1982, Principals of Inventory and Materials Mana^ment, second edition, Elsevier North Holland, New York. A letter from Linwood A. Kulp, Jr., Director, Distribution Services at American Olean Tile states that: "This model now represents the major annual production planning tool utilized by American Olean's quarry and glazed white body tile divisions. It also forms the basis for distribution decisions. As this modeling system at AO matures, it should yield an estimated savings of over $400,000 annually.... The short-run mixed integer scheduling model discussed in the paper would represent the next component to AO's distribution and production planning system. AO's plant managers have expressed interest in this model. However, as noted, plans for this model remain in the developmental stages at present." July-August

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