A hierarchical decision support system for production planning (with case study)

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH

ELSEVIER

European Journal of Operational Research 104 (1998) 403-422

Theory and Methodology

A hierarchical decision support system for production planning (with case study) Linet Ozdamar *, M. Ali Bozyel, S. Ilker Birbil Department of Systems Engineering, Yeditepe University, lstanbul, Turkey Received 1 May 1996; accepted 1 December 1996

Abstract

We propose a Hierarchical Decision Support System (HDSS) for production planning which enables production planners to utilize complex and structured planning algorithms interactively with no difficulty. The suggested system represents a higher level planning tool than MRP: namely, it encompasses aggregate planning, family and end item planning levels. The HDSS is integrated with MRP through the Master Production Schedule (at the end item level) which is transferred to MRP. The feasibility at all planning levels is preserved through database manipulations which enable communication among different planning hierarchies. The key features of the proposed system are the ease of data manipulation and the highly interactive nature of the system provided by the user-interface. The dialogue management system hides the theoretical background of the model base consisting of multi-optional aggregate planning models and disaggregation algorithms used at the family and end item planning levels. © 1998 Elsevier Science B.V. Keywords: Hierarchical production planning; MRP; Decision support system

1. Introduction

Production planning is a complicated task which requires cooperation among multiple functional units in an organization. Planning is the consequence of a hierarchy of decisions dealing with different issues in the manufacturing environment. A classical approach to handle this multi-level decision-making process is Hierarchical Production Planning (HPP). HPP partitions the larger decision-making domain

* Corresponding author. Correspondence address: Linet 0zdamar, Gayrettepe EmeHi Subay Evleri 23/5, Istanbul, Turkey. Email: [email protected].

into hierarchical levels in agreement with the organizational structure of companies (Schneeweil~, 1995). A rigorous mathematical analysis of HPP is found in the pioneering work of Hax and Meal (1975) and Gabbay (1975). Theoretical work on the topic has followed (Bitran et al., 1981; Bitran and Hax, 1981; Axsater and J6nsson, 1984; Hax and Candea, 1984; Erschler et al., 1986; Pienkosz and Toczylowski, 1993; 0 z d a m a r et al., 1996b). The first level of decisions in HPP involve aggregate decisions at the product type level such as the product mix in each planning period, inventory accumulation decisions, and work force level decisions. Product families with similar production costs and demand seasonality are grouped into a product type.

0377-2217/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0377-2217(97)00016-7

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The next level of the hierarchy is the product family planning level. A product family consists of groups of end items sharing the same set-up costs. The aggregate production plan for the product type is disaggregated into more detailed product family plans which are in turn partitioned into production plans for end items. Consistency among the production plans at lower levels is achieved by linking mechanisms existing between each subsystem. The solution of a higher level subsystem represents a constraint to be imposed on the next level subsystem and thus, decisions at each level constitute a chain. Numerous HPP applications, such as the tile industry (Liberatore and Miller, 1985), steel manufacturing (Bowers and Jarvis, 1992; Lin and Moodie, 1989; Mackulak et al., 1980), metal can manufacturing (0zdamar et al., 1996a), rolling mills (Gelders and Steelandt, 1980), shoe production (Caravilla and de Sousa, 1995), motor industry (Tsubone and Sugawara, 1987), milk powder manufacturing (Rutten, 1993) are available in the literature and an extensive review is given by Bitran and Tirupati (1993). However, although it represents a viable approach to production planning, HPP is not as widespread among manufacturing companies as desired. Rather, most of the manufacturing companies invest on MRP systems which provide a company-wide information system. MRP represents a hierarchical system with two major levels: the Master Production Schedule (MPS) at the end item level, and the disaggregation of the MPS at the component level through the Bill of Materials (BOM) (Andersson et al., 1981). A major criticism of MRP systems is the lack of capacity considerations in the generation of production plans which results in simulating different MPSs repeatedly in order to find a resource feasible plan. Consequently, MRP users require higher level planning systems for developing a MPS which provides an overall feasible plan. Stand-alone MRP packages enable communication among different departments through a common database, but they are not sufficient to cope with the production planning process. Meal et al. (1987) compare the HPP system with MRP and suggest that an ideal planning system should incorporate HPP and MRP systems as complementary entities. A major weakness in HPP and MRP systems is that they are both rigid systems which require re-runs

in case unexpected external or internal events occur (Winter, 1994). Any cause (such as machine breakdowns, changes in finn orders) which endangers the validity of the current production plan leads to the re-generation of the entire plan. In the exceedingly dynamic manufacturing environment of today's competitive world, planning systems need to be interactive so that the production planner can modify the production plan with the least disruption. Furthermore, an automated system does not allow the production planner to impose his/her own preferences on the plan specially when intangible objectives are involved. Consequently, we propose a Hierarchical Decision Support System (HDSS) which integrates HPP and MRP systems while supplying the production planner with considerable freedom in the planning process. Recent research (Forgionne, 1991; Bigdoli, 1993; Te'eni and Ginzberg, 1991) demonstrates that standalone problem-solvers (such as the use of expert systems for a specific problem area) do not produce satisfactory results, since they fail to incorporate human-computer interaction in the decision-making process. We emphasize that the production planner has the best understanding of the problem. HDSS enables the production planner to incorporate all his/her knowledge entirely into the planning process. The planning system is no longer a black box and the production planner is in full control of the system. Furthermore, an interactive computerized planning system such as HDSS is adaptable to the changing environment through integrated data and model management systems. HDSS includes a powerful mathematical base which supports the decision-making process at every level. The production planner (end-user) does not require any mathematical/modeling background to use the system. Previously developed Decision Support Systems in the area of production planning support the operational planning level (Viviers, 1983; Speranza and Woerlee, 1991; Moreira and Oliveira, 1991) and therefore, HDSS combined with MRP fills in the gap between higher and lower levels of planning. In the following sections, the modules of HDSS are described and a case study is presented using the data provided by a company which manufactures agricultural machinery. Through the case study, we

L. Ozdamar et al. / European Journal of Operational Research 104 (1998) 403-422

405

demonstrate both the planning flexibility provided by HDSS and the overall consistency of the planning system.

to remain in the feasible region by the warning messages and corrective actions provided by the model base in case he/she makes mistakes during the decision-making process.

2. The model base of the hierarchical decision support system (HDSS)

2.1. Planning at the product type level

The model base consists of a four-level hierarchy involving aggregate planning (product type planning level), family disaggregation, end item disaggregation and MPS. At the aggregate planning level the production planner may select any planning horizon length covering demand forecasts up to a certain degree of accuracy. The basic time unit suggested by HDSS for aggregate planning is the month, but any user defined time unit can be handled. At the family and end item planning levels, the production plans are generated for the current time period. At the MPS level, monthly end item production quantities are disaggregated into weekly quantities. When confirmed by the end-user, the MPS is exported to the MRP database. At each level of planning, HDSS supports the user for generating capacity-feasible production plans, so that a capacity-feasible MPS is exported to MRP at the last phase. At the aggregate planning level, capacity restrictions are explicitly considered in the model. At the family planning level, capacityfeasibility is maintained by informing the user on the capacity violations in the bottleneck department caused by confirmed lot sizes. Additionally, HDSS prevents the user from moving on to lower planning levels if an infeasible plan has been confirmed. Consequently, when the last stage of planning is reached the user is assured that the final MPS is capacity-feasible. At each planning level the model base supports the decision-maker with both procedural and descriptive structures. The mathematical models used at the aggregate product type level, the heuristic algorithms proposed at the product family and end item disaggregation levels, and the constructive heuristic for the MPS are the procedural structures of the model base. Descriptive tools perform the computations for calculating the consequences of any course of action taken by the end-user and convey them through the dialogue management system. The end-user is forced

Procedural structures. At the aggregate planning level, HDSS provides modeling options to the production planner and constructs the desired model automatically by including all the options confirmed by the end-user. The model base communicates with the data management system to access the necessary data required by the main body of the model and its options. The dialogue management system warns the end-user about any faulty/missing data before the automatic generation of the model. The end-user only needs to know the verbal description of each option when confirming it, so that the consequences of an option are foreseen before the model is generated. The main body of the model includes a linear objective function minimizing total costs (inventory/production costs) and capacity and inventory balance constraints. Modeling options can be listed as follows:

1. 2. 3. 4. 5. 6.

overtime production capacity, subcontracting production capacity, backorders, hiring and firing of work force, safety stocks, permitted levels of under utilization in departments, 7. ending constraints on backorders and inventories. Any combination of modeling options may be confirmed by the end-user. In Table 1, the most general version of the aggregate model is conveyed, with optional portions indicated in italic. In the inventory balance equation (Eq. (6)), the overall consistency of different planning levels is achieved by netting the product type demand in the aggregate plan. Similarly, family demands are also netted at the family planning level. Net demand is calculated as follows: di, = E

E max{0, d e m , , , , - invife. ,_,},

fei eef

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Table 1 The general aggregate model Min Y~,~i(hitlit + citXit + critW/t + cbit Bit + csitSit + coitOit + chitHit + cfit Fit ) subjectto:

kiXit <_ (Wit + O i t ) . A kiXit>(1-pu)Wi, Oit
(x)

t=l ..... H;i=l...l,

t=l ..... H;i= t=l ..... H;i=

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(1)

t = 1. . . . . H; i = 1. . . . . 1,

(3)

1...1,

(4)

1.../,

t=l ..... H;i=

Sit+Xit-lit+li,_l+Bit-Bit_

l=dit

(5)

1...1, t=l ..... H;i=

1...I,

(6)

lit>SSit

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(7)

lil t = El i

i = 1 ... 1,

(8)

B it = O

i = l . . . l.

(9)

Parameters and variables of the aggregate model Decision variables:

1. Bit

xi, Oit

v¢,, n,t F. Sit Parameters: A hit cit cbit c s it

coit cri t chit cf it ki dit SSit H po pu PSit El i

inventory quantity of product type i at the end of period t backorder quantity of product type i at the end of period t production quantity of product type i in period t overtime production hours available in period t for type i regular time production hours available in period t for type i (may also be defined as a 0 parameter if hiring/laying off options are not confirmed) man-hours hired in period t for type i man-hours laid off in period t for type i subcontracted production quantity of product type i in period t

capacity allowance percentage (used for allowing breakdowns, set-up times, absenteeism, etc.) unit holding cost for product type i in period t unit production (materials + overhead) cost for product type i in period t unit backorder cost for product type i in period t unit subcontracting cost for product type i in period t overtime cost per manhour in period t for type i regular time cost per manhour in period t for type i cost of hiring one manhour in period t for type i cost of laying off one manhour in period t for type i unit processing time for product type i (hours/unit) net demand for product type i in period t safety stock quantity for product type i in period t length of the planning horizon percentage of overtime hours permitted. percentage of under utilization permitted. maximum amount of subcontracting permitted for type i in period t (provided by suppliers) desired level of inventory for type i at the end of the planning horizon.

407

L. (gzdamar et a l./European Journal of Operational Research 104 (1998) 403-422

where t is the current planning period, i is the type index, f is the family index, e is the end item index, dem if~, is the demand of the eth end item (belonging to the product family f ) in period t and inv~f,.,_ is the inventory of item e in period t - 1. In the capacity restriction constraints (Eq. (1)) each product type is assumed to use the capacity of a specific aggregate department. An aggregate department represents the group of departments in which the product type is fabricated. According to Eq. (1) two different product types cannot share the capacity of the same aggregate department. However, if different product types share the same capacity, the capacity constraint can be modified accordingly. The process time per unit type is calculated by taking the weighted average of family process times with respect to annual family demand forecasts. A similar reasoning can be utilized for calculating production, inventory and backorder costs at the product type level. The subcontracting option is treated particularly by HDSS if it is confirmed. If a subcontracted quality exists in the aggregate plan generated by HDSS (or the end-user) in the current planning

period, a Subcontracting Details window is activated. The Subcontracting Details window demonstrates the inventories of the end items belonging to the product types for which subcontracted quantities are indicated in the aggregate plan in the current period. The end-user is required to specify the subcontracted amounts for each end item, before the family and end item disaggregation levels are activated. The total subcontracted amount for each type is always preserved as indicated by the aggregate production plan. The end item subcontracted amounts are then added to the end item inventories of the previous month so that the type quantity to be produced within the factory is distributed correctly among different families and end items. Descriptive structures. Descriptive structures in aggregate planning include decision-aid tools such as calculating the consequences of the modifications made on the production plan and corrective actions conveyed by the dialogue management system in case a faulty course of action is taken up by the end-user in modifying the plan. The presentation o f the production plan. T h e optimal production plan is conveyed to the end-user in a

~eneral' /~ggcegate Planning Disaggregatton

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tabular form, so that h e / s h e can easily observe the resource allocation and inventory levels over the whole planning horizon. In the aggregate plan in Fig. 1, the following information takes place for each period and each product type in the planning horizon: the production quantity, the (gross) demanded quantity, the inventory/backorder levels, the manhours required to produce the quantity specified by the plan, the subcontracted amount, the amount of overtime and the work force level at each period. Hence, the whole picture is captured and summarized in a spreadsheet-like table so that the end-user's modifications on the plan are facilitated. The end-user is free to modify the production plan as long as h e / s h e does not take an infeasible course of action. Modifications on the production plan and corrective actions. The end-user is allowed to change the values of four decision variables: the production quantities, the subcontracted quantities, the allocated regular time and overtime work force levels. The consequences of the modified production and subcontracted quantities are the u p d a t e d inventory/backorder levels and their corresponding costs. The decision tools ensure that the user does not exceed the supplier's monthly quota while modifying the subcontracted amount. Modifications in the production quantities result in changed total required manhours. The surplus or missing amount of manhours required by the subtracted/added production quantities are indicated to the end-user through the

dialogue management system. The user is forced to update the overtime manhours allocated in that period a n d / o r the regular work force level if the hiring/firing options exist in the model. The end-user may also modify the work force levels, not as a consequence of production quantity modifications, but simply to impose a preferred work force level policy. The decision-aid tools imbedded in HDSS compute the costs of only feasible plans immediately after a modification is confirmed. In case a modification causes infeasibility, the user is restrained from moving to lower hierarchies of planning before a completely feasible aggregate plan is obtained. 2.2. Planning at the product family level Procedural structures. The objective of the family disaggregation model is that of minimizing annual set-up costs under the constraints that the total quantity allocated to all families is equal to the product type quantity specified in the aggregate plan in the current period and that the family quantities are within intervals specified by their lower and upper bounds. The model is given in Table 2. The family disaggregation procedure used in HDSS is the Filling Procedure (FP) proposed by Ozdamar et al. (1996b). FP works approximately as a gradient search where at each iteration the most promising (in terms of the gradient) family is increased by its own specific stepsize defined as the

Table 2 Formulation of the family disaggregation problem Decision variables: Ylft the lot size of family f in type i in period t Parameters: JT. the set of families belonging to product type i whose net demands in the current period are positive (set of triggered families) sir the set-up cost of family f in type i ibif t net demand of family f in type i in period t ubif t net demand of family f in type i during the remaining periods of the planning horizon including the current period

Minimize ~ f ~ JX,,"(siftubift)/Yif, 5ject to

~'f ~

JTitYift = Xit ,

lbift < Yifl < abift,

f E JTit.

L. Ozdamar et al. / European Journal of Operational Research 104 (1998) 403-422

difference between the upper and lower bound divided by a user defined number of steps. So, the stepsize, and hence, the maximum number of iterations to be carried out by the FP procedure (number of steps × number of families) is a controllable parameter. In previous work, t)zdamar et al. (1996b) demonstrate that solutions deviate 0.09% on the average from the optimum given a step number of 100. The procedure FP is briefly described in Appendix A. The procedure initially sets all family production quantities to their lower bounds if no backorders are imposed by the aggregate plan in the current period. Otherwise, family quantities are set to zero. Then, the lot size of the family with the maximal gradient is increased by its stepsize on the conditions that its production quantity remains within its upper bound and the aggregate product type quantity which is not yet distributed among families is not exceeded. Next, the gradients of all families are recalculated at their current production levels and the family with the maximum gradient is selected again for increasing its lot size. The procedure is repeated until the product type quantity is entirely

General Aggregate Rannlng

409

distributed. The FP procedure is a linear time heuristic, which eliminates some of the infeasibilities resuiting from the Bitran and Hax (1981) family disaggregation algorithm and produces near optimal results with a fine-tuned step number. Descriptive structures. Although the family disaggregation model in Table 2 does not include any capacity considerations (capacity issues are dealt with at the aggregate level), HDSS provides the end-user with a capacity check which compares the required process and set-up times with the capacity of each department (the departments are not aggregate now) and informs him/her on the capacity utilization level of the bottleneck department. The capacity check is a required feature, because the end-user may not exactly know the amount of the aggregate capacity h e / s h e should allow for set-up times (the capacity allowance percentage A), and also, the process time indicated for the product type is just a weighted average of the process times of families with respect to demand forecasts and therefore, an approximate measure. Modifications on the family disaggregation plan and corrective actions. The end-user can freely edit

Dlsaggregation

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the production quantities allocated to product families as long as the consistency link between the aggregate production quantity and the sum of the family lot sizes is preserved. HDSS forces the enduser to remain in the feasible region, by not allowing h i m / h e r to move to the item disaggregation phase in case the consistency link is lost or capacity infeasibility exists. If not satisfied with the disaggregated family lot sizes, the end user may move back to the aggregate planning window in order to modify the aggregate plan and re-disaggregate the updated product type quantity among its families (see Fig. 2). Such moves are permitted even if the production plans at all levels (aggregate, family, and end item) have been previously confirmed. HDSS extracts previous inventories from the database and it is possible to start the planning process from scratch in case any unexpected internal and external events take place. 2.3. P l a n n i n g a t t h e e n d i t e m l e v e l P r o c e d u r a l s t r u c t u r e s . T h e model at the end item disaggregation phase (given in Table 3) involves an objective which aims at balancing the unfulfilled demand percentage of each end item (in the same family) in the cover period, T*. The cover period T* is the earliest future period when the allocated family production quantity does not satisfy the net family demand accumulated from the current period T up to period T*. The objective minimizes the

differences among unsatisfied demand percentages of end items in period T *. By the definition of T *, it is guaranteed that all end item inventories are depleted at the same period (at period T * ), so that family set-ups are not executed too often for a few end items which have slightly positive net demands. Hence, the objective achieves two desired consequences: Equal Run Out Time (EROT) for all end items; and backorder risks distributed equally among end items in case forecast errors exist or firm orders are changed. The constraints in the model satisfy the consistency link between the family and end item disaggregation stages and guarantee that each end item is allocated a production quantity covering at least the net demand in the future periods up to period T * - 1 , so that all end items have to be produced in the same period. A procedure which solves the problem in Table 3 is proposed here and it is called the Min-Risk EROT procedure. First, T* - 1, the number of months that a family production quantity covers the net cumulative family demand is identified. Initially, every end item is allocated a production quantity equal to the sum of its net demand up to period T * - 1. In case there still exists a family production quantity (SP) to be distributed among end items, it is distributed in proportion to the ratio of the net item demand to the net family demand in period T*. The Min-Risk EROT procedure depletes the inventories of all end items simultaneously in period T* and also, since

Table 3 Formulation of the end item disaggregation problem Decision variables: Zifet

production quantity of end item e in family f in type i in period t

Parameters: Bife Ai/e

the cumulative net demand of the eth end item from period t up to the period T * - 1 the cumulative net demand of the eth end item from period t up to the period T * Min {max{((zif~,- Bi/~)/Aq~) - (( zi/j, - Bi/j)/Aifj)}} all pairs of items e,j in family f with All . > O, Aif j > 0 end

subject to

~eE fZifet = Yi/t, Zifet >_~n i l e

for all e Ef.

L. (gzdamaret al. / European Journal of Operational Research 104 (1998) 403-422

allocated a production quantity of 1200 units which is to be distributed among the three end items. The planning horizon is 3 periods. Relevant data including gross demand and beginning inventories are given in Table 4. The execution of the Min-Risk E R O T procedure is as follows. Since the family production quantity to be distributed falls between the cumulative net family demands up to the first and second periods (200 < 1200 < 1400), T* is identified as the second period. Therefore, the lot size of each end item is initially set to its net demand in the first period: Zxfl I = 5 0 0 ; Zxy21 = 0; zxf31 = 300. The remaining family quantity to be distributed is calculated as: SP = 1 2 0 0 800 = 400. SP is then distributed among the end items such that unfulfilled demand percentage is the same for all end items with positive demand:

the left over production quantity is distributed according to demand percentages in period T * , the difference among unfulfilled demand percentages of end items becomes zero. Notice that there can never be inconsistency among the family and end item disaggregated plans in terms of ending inventories since the net family demand is calculated by summing the net end item demands. The same consistency exists between the product type and family planning levels.

The rain-risk E R O T procedure: Step 1.

Identify T*, the earliest future month that the following condition holds:

Y'fL t net family demandi/b > Yift-

Step 2.

411

If T * :~ t, then calculate: zxj21 = 500 + 4 0 0 ( 2 0 0 / 6 0 0 ) = 633;

zis~t = •r'--tl net item demandifeb, Zxr22 = 0 + 4 0 0 ( 0 / 6 0 0 ) = 0;

for all e ~ family f .

Else,

Z i f e t = (net item demandifet/net family demand,ft)y~f t, where t is the current period. Step 3. If ~"eEfZiJet < Yift, then SP = Yift -~'e ~ fZifet; and calculate:

z~j23 = 300 + 4 0 0 ( 4 0 0 / 6 0 0 ) = 567. The unsatisfied demand percentage for both the first and third end items in period 2 is % 33. Descriptive structures. Similar to higher planning levels, the end-user is allowed to modify the allocated end item production quantities by preserving the consistency link between the family and end item planning levels. Capacity checks are not required at this level, since end items in the same family are assumed to have the same process times approximately. Again, if the end-user is not satisfied with

Zifet = Zi[et "t" SP(net item demandiyer.

/ n e t family demandif r. ).

An example. Suppose that a family f belonging to product type x has three end items in its group. Among other families in type x, family f has been Table 4 Data for the example Gross demand Item 1 Item 2 Item 3 Net demand Item 1 Item 2 Item 3 Net family demand

Period 1 (current p e r i o d ) 800 550 720 Period 1 500 0 300 800

Allocated family productionquantity 1200

Period2 200 220 400

Period 3 (T) 350 540 250

Period 2 (T *) 200 0 400

Period3 350 500 250

600

1100

Inventoryat the beginning of Period 1 300 810 420 Total net demand 1050 500 950

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Fig. 3. The end itemplanningwindow. the end item production plan, h e / s h e can modify the family disaggregation plan (whose window is already open on the screen) and re-disaggregate the end items accordingly (see Fig. 3).

2.4. Generating the M P S P r o c e d u r a l structures. Once the production plans at all levels are confirmed, the monthly end item

Fig. 4. Hierarchicalprioritiesdeterminedby the user.

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.pl~t)ss

~1

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Fig. 5. The MPS window. production quantities are partitioned into a MPS with a weekly time bucket. The time buckets may be designed according to the requirements of the enduser. To sequence the end item production runs, the end-user is required to provide hierarchical priorities

such that the highest priority end item of the highest priority family of the highest priority product type is produced initially in the first week. In other words, product types, their families and the end items are prioritized in a hierarchical fashion (see Fig. 4)

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Fig. 6. The informationflow amongthe elementsof HDSS.

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according to the end-user's preferences which may be based on the due dates of firm orders. Once a family production run begins, all its end items are produced consecutively (with no preemption) in order of priority so that each family incurs a single set-up cost in one period. The end items are produced sequentially until the capacity of the bottleneck department (identified at the family disaggregation level) is consumed week after week. The feasibility of the whole plan is confirmed at the MPS level when all end items are successfully manufactured in the quantities presumed jointly by HDSS and the end-user without violating the capacity of the bottleneck department. If feasible, the MPS is exported to the MRP package. Descriptive structures. The end-user may change both the quantities and the sequence of the end item production runs. (The MPS window is given in Fig. 5.) The consequences of these modifications are provided to the end-user in terms of capacity consumption and the resulting end item inventories. The end-user is not permitted to modify the available capacity level at the bottleneck department, though h e / s h e may change weekly capacities which sum up to the available capacity according to his/her requirements.

2.5. lnformation flow in HDSS In Fig. 6, the information flow among the different elements of HDSS is summarized. At each level, information is manipulated by the data management system of HDSS and consists of the appropriate level of detail. For instance, inventories and demand are netted cumulatively as the level of the hierarchy increases and converted into their detailed form at the lower planning levels. All other data (costs, process times, etc.) undergo a similar process as the end-user moves to and fro among different planning levels in his/her search of the preferred overall plan.

3. Case study Company profile. The case study involves a Turkish company manufacturing agricultural diesel engines established in 1956. The company is one of the 73 companies of a cooperative organization that was

founded by over 1.5 million sugar beet farmers. The company has a license agreement with a German company since 1965. The company holds 55% of the Turkish market share. They also export their products to Tunis, Sudan, Lebanon, Jordan, Iraq, Saudi Arabia, Iran, Greece, Netherlands, and Germany. Sixty percent of their endorsement is constituted by exports worth over 2 million dollars/year. Product mix. The company manufactures 1 to 4 cylinder air cooled diesel engines with powers varying between 7 and 77 HP (applicable to agriculture, industry and marine), motor pumps and various kinds of agricultural equipment. Motor pumps are pumps coupled with engines. Besides the sales of engines and motor pumps, the company also sells pumps individually. The engines/motor pumps and stand-alone pumps are grouped into two different types. One of the reasons is that the engines and the pumps do not share the capacity of the same departments. The pumps are manufactured in a single specialized department and the engines have a complex routing over multiple departments excluding the pump department. The engines and the motor pumps are grouped together into the same type, because in respect of material and labor costs (engines are manufactured in seven major departments), the engine part of the motor pump is much more essential than the pump part and therefore, the production plan for the pumps is adjusted according to the plan generated for the engines/motor pumps product type. The pumps are assembled to engines as indicated by the production plan for the motor pumps and they are classified as a dependent product type. Consequently, the product type differentiation is based on the requirements of the manufacturing process and costs rather than only on demand seasonality. From this point on, we rename the 'engine/motor pump' type as 'engine' type for simplicity of presentation. Families in the engine type are grouped with respect to different cylinder bore dimensions and families in the pump type are characterized by their application areas. Considerable set-up time is required in case of changeovers. Three different dimensions of cylinder bores exist and they are coded as E89 (single cylinder), El08 (single cylinder) and Z108 (double cylinders). Pump families are coded as

L Ozdamar et al./European Journal of Operational Research 104 (1998) 403-422

OK (self priming pumps), YK (raining pumps), and SK (flow irrigation pumps). End items in the pump type are distinguished according to their suction and discharge diameters. Some of the end items (uncoupled engines) in the engine type are differentiated according to the manner in which the engines are started (hand start, electric start, hand start-marine). All motor pumps are electric started and their end items are distinguished according to the family of the pump they are assembled to. Since we base our case on the sales data of the company in the previous year, the product mix includes only the end items whose sales quantity is positive and excludes the remaining end items which still occupy the product mix of the company. Demand pattern. Both product types have seasonal demand and peak seasons do not exactly overlap. The engine type has its peak season between the months of April and August; on the other hand, the pump type has two peak seasons, the first one in April and May and the second one during August and September. The family E89 constitutes most (80%) of the engine sales whereas the pump families OK and YK make up 85% of the pump type sales. The percentage of motor pump sales is approximately 55% of engine sales. The sales of pumps alone constitute 25% of total sales. Manufacturing environment. An engine is composed of about 500 different parts, and the total number of different parts used in the factory is 4000-5000; 2000 of these parts are fabricated within the factory. The major elements of an engine are the crank arm, the crank rod, the engine block, the cylinder and the cylinder head, the gears and the flywheel. A group technology approach has been adopted by the company to ease order tracking and minimize transfer and set-up times. Therefore, the factory is divided into specialized cells, each of w h i c h constitutes a partially a u t o m a t e d fabrication/assembly line. Product families in the engine type have complicated routings which involve to and fro movements among existing departments. Hence, the manufacturing process represents a large job-shop with cellular design. Capacity restrictions. The company recruits 255 personnel, 200 of which are workers. Between the years of 1983 and 1994, productivity has been improved by reducing the work force by 80%. The

415

factory works 8 hours per shift six days a week. An additional 8 hours' shift is allowed daily as overtime. During peak seasons it may be possible to add an extra night shift, but this kind of capacity expansion is undesirable due to quality problems arising from overworked/lower skilled labour and higher wage rates. Since the manufacturing system represents a large job-shop and each department is active simultaneously, at each planning period, the regular time capacity for each product type is assumed to be 8 hours daily for both product types. Regular (overtime) capacity associated with each product type is differentiated, since the two product types do not share the same capacity. At the family planning level, capacity requirements on the departments in which the engines are manufactured are calculated in detail by considering individual process and set-up times of product families in each department. Then, the bottleneck department is identified and the user is informed on the capacity consumption in the bottleneck department.

4. Implementation HDSS is implemented to develop an annual production plan for the manufacturing company under consideration. Monthly sales forecasts are assumed to be equivalent to the sales data of the previous year. A 12 month's production plan is generated on a rolling horizon basis. However, the length of the planning horizon is reduced by one period each time. The aim is to eliminate the effects of added demand information on the generated plans. So, the overall consistency of the plan including the aggregate, family and end item planning levels is investigated by assuming a frozen planning horizon and perfect knowledge of future sales figures. The company assumes a planning policy which does not permit backorders and subcontracting. Furthermore, the regular work force is fixed (W/t is a parameter) in the aggregate model due to management's wish to eliminate night shifts during the peak season. Consequently, the mathematical formulation for the aggregate plan becomes as indicated in Table 5. In the inventory balance equation of the pumps type, demand is increased by multiplying the engine

416

L. Ozdamar et al. / European Journal of Operational Research 104 (1998) 403-422

Table 5 The mathematical formulation for aggregate planning Minimize

F.tEi(hitl . + citXit + coitOit )

klXlt<(Wit+Olt)'0.9

subject to:

k2X2t<(W2t+02,)'0.9 Oit
t=l

12,

.....

(10)

t = 1. . . . . 12,

t = 1..... 12;i= !,2,

XD--Ilt+ID_ I=dlt

(11)

t = 1..... 12,

(12)

X2t-12t+I2t_l=d2t+rl2tXlt t = l ..... 12.

production quantity with the ratio o f motor pump demand to total engine demand (r12 t) so that sufficient pumps are manufactured to meet the pump requirements o f the motor pumps. Notice that the engines product type (type 1) is the independent type and the pumps type (type 2) is the dependent type in the third equation, r12 t is calculated each period by considering the ratio of the net demand of motor pumps to the net demand of the engine type. r12 t lies in the range [0.35-0.87] over the 12 months' planning horizon. Two aggregate departments exist: the pump manufacturing department for the pump type and a single aggregate 'engine' department (representing seven major departments) for the engine type. Since each family in both product types has different individual process and set-up times in each actual department, in order to specify k I and k 2, the weighted average

of the family process times is calculated for each type with respect to the percentage o f demand of each family in that type. Here, k~ is calculated as 1.2 h / u n i t and k 2 is calculated as 1.7 h / u n i t . The 'engine' department has the same regular time capacity as the ' p u m p ' department, 8 h / d a y , 6 d a y s / w e e k . A capacity allowance of 10% ( A = 90%) is provided for set-up times. The production cost includes material costs only (28.8 and 2.3 millions Turkish Liras (TL) for the first and second types, respectively), since labor costs are calculated as a consequence o f the production plan. Holding costs for both types are assumed to be 5% o f the material costs. The regular time and overtime hourly wages are 380000 T L / h and 570000 T L / h , respectively. The initial aggregate plan generated at the beginning o f the planning horizon is given in Table 6. The

Table 6 The initial aggregate plan Type 1 Production Gross demand Inventory (65) Overtime

January February March April 59 85 39 0

Type 2 Production 139 Gross demand 30 Inventory (29) 109 Overtime 60 rl2 t 0.5

273 250 56 152

May

June

July

August September October November December Total

293 300 49 176

293 325 17 176

293 310 0 176

150 150 0 4

147 125 61 16

147 175 33 0

105 105 0 0

188 45 201 159 0.35

207 207 207 207 207 117 138 50 100 180 30 30 60 88 240 205 88 11 0 0 0 176 176 176 176 176 22 59 0.8 0.52 0.49 0.87 0.64 0.38 0.48

117 117 0 0

142 142 0 0

203 203 0 68

2222 2287 255 768

104 42 10 0 0.44

104 36 11 0 0.47

117 22 1 22 0.52

1942 713 875 1202

L. Ozdamaret al. / European Journal of Operational Research 104 (1998) 403-422

plan is obtained by an LP package after netting the wype demands, i.e., type demands are calculated as the sum of net end item demands. The coupling percentages r~2 t are included in Table 6 for making the calculations of pump type inventory levels clear. In Table 6 the numbers indicated in brackets in the first column (inventory row) demonstrate the inventories at the start of the planning horizon. Table 7 illustrates family production quantities and inventory levels obtained by disaggregating the type production quantities each month. Disaggregation is carried out by netting family demands according to the end item inventory levels resulting from the previous period's disaggregation. The overtime and extra shift hours required by the bottleneck department (usually the crank arm/rod department among the engine manufacturing departments) are also indicated along with the cost of the plan. Here, the cost of an extra shift hour is assumed to be the same as the cost of an overtime hour, but in the real case, there are additional costs of increased scrap and slower production pace due to the learning effects. in each planning period the aggregate type production quantities are disaggregated first into product family quantities, then into end item production quantities. In the family disaggregation phase set-up costs are calculated by summing the total set-up time of each family in every relevant department and multiplying the sum by the regular time hourly wage. In the disaggregation of the engine type's production quantity net demands are used in the calculation of lower and upper bounds. The calculation of the lower and upper bounds of the pump type's families is only possible after the engine type's production quantity is disaggregated up to its end items and confirmed by the user. The reason is that the production quantities of the end items of the engine type's end items are used in the lower and upper bound calculations of the pump type's families. Since coupling exists between the two product types, the lower and upper bounds of the dependent pump families are increased by the production amounts of the engine type's related end items as indicated by the disaggregated plan for the engine type. In other words, the engine type's production quantity is disaggregated among its families and end items first. Then, the end item production quantities of the motor pumps are added to the net demand of

417

the related pump families to result in updated lower bounds. The upper bounds of the dependent pump families further include the expected future demands of the motor pump end items. Mathematically, lbi/, = ~ max{0, dem i f e t - invife, r-I) e~f + E E Zkmpt" m~k p~m

Here, Zkmpt is the production quantity of the pth end item in the current period t (which has the same pump features as the pump family f in the pump type (type i)) belonging to the motor pump family m of the engine type (type k). Similarly,

I

)

ubifi = ~ max 0, )'-'. d e m i y e b - invile.t_ 1 e~f ~ bet "[- E E Zkrapt reek peru

+ ~ ~ max 0, ~ demkmpb rn~k p~m ~ b=t+ l --inVkmpt I •

Notice that in the upper bound calculations of the pump families, the motor pump end item demands are netted using the current period's inventory, since both the production and inventory quantities of motor pump end items are already confirmed. Thus, the family disaggregation procedure is carried out for each product type in consistence with the hierarchy of dependency between the product types. A similar reasoning is used while disaggregating the pump family quantities among their end items. End item demands are augmented by motor pump end item production quantities and future demand forecasts. In Table 7, we observe that in April, only the second pump family (SK) is triggered and its upper bound (about 55 units) does not allow the disaggregation of the type production quantity (206 units). Consequently, the DM is forced to distribute the type production quantity among non-triggered families in proportion to the family upper bounds. In June, a backorder of 8 pumps takes place in the YK pump family. (The latter cannot be observed in the table

OK, YK 59 0 80 139 112

0 95 95 0

Triggered families OK SK YK Total production Total inventory

Engine dept. Pump dept. Total overtime Extra prod. capacity

Inventory costs Overtime costs Cost of extra prod. capacity Total costs

473,515 1,443,810 51,870 1,969,195

Cost of proposed plan (thousands TL)

Overtime

Type 2

All 43 5 10 58 38

January

Triggered families E89 El08 ZI08 Total production Total inventory

Type 1

Production quantifies

Proposed plan

43 188 231 0

YK 0 0 187 ! 87 214

All 100 25 22 147 58

February

30 213 243 21

OK, YK 83 0 124 207 235

E89 159 0 0 159 43

March

Table 7 The details of the proposed rolled disaggregated plans

184 341 0

1 57

DM (SK) 0 54 152 206 212

All 221 25 14 260 53

April

197 223 420 36

OK 207 0 0 207 98

All 246 21 26 293 48

May

189 206 395 14

YK 0 0 207 207 19

E89, El08 285 8 0 293 14

June

190 210 400 18

OK,YK 43 0 164 207 8

All 280 7 6 293 0

July

28 43 71 0

OK, YK 38 7 66 111 3

All 122 12 18 152 0

August

0 87 87 0

All 37 0 98 135 4

All 77 8 20 105 0

September

0 59 59 0

All 35 17 52 104 14

All 88 11 18 117 0

October

9 31 40 0

All 27 7 70 104 18

All 93 29 10 142 0

100 51 151 0

All 25 14 73 112 0

All 163 16 24 203 0

943 1590 2533 91

1926 937

2222 254

November December Total

bo

J

a-

~n

~'

~, @

""

~"

F,

L. (~zdamar et al. / European Journal of Operational Research 104 (1998) 403-422 Table 8 Summary of performance in consistency measures Initial aggregate plan

Rolled disaggregated plans

Type 1 Total production quantity Sum of inventories Amount of backorders Work hours in excess of maximum overtime limit

2222 255 0 0

2222 254 0 5

Type 2 Total production quantity Sum of inventories Amount of backorders Work hours in excess of maximum overtime limit

i 942 875 0 0

1926 937 8 84

419

b e c a u s e f a m i l y i n v e n t o r y l e v e l s l a c k e n d i t e m details.) T h e D M c o u l d h a v e c o r r e c t e d the latter situat i o n b y t r a n s f e r r i n g 8 u n i t s f r o m t h e lot size o f S K p u m p f a m i l y to the lot size o f Y K p u m p f a m i l y in April. In c a s e s u c h a c o r r e c t i o n is m a d e , t h e D M w o u l d h a v e to u p d a t e the p l a n s o f the m o n t h s between April and June. However, the DM would not s p e n d m u c h e f f o r t in u p d a t i n g t h o s e p l a n s , b e c a u s e at all p l a n n i n g l e v e l s t h e i m b e d d e d a l g o r i t h m s prov i d e the c o r r e s p o n d i n g p l a n s a n d all t h e D M h a s to d o is to s i m p l y e d i t t h e lot sizes o f t h e t a r g e t families. F o r t h e p u r p o s e o f t h e c a s e study, d e m a n d forecasts are a s s u m e d to h a v e n o errors. In the real case, u n e x p e c t e d o r d e r s will i n e v i t a b l y d i s r u p t the p l a n s m a d e already. H o w e v e r , the D M c a n easily u p d a t e

Table 9 The details of the production policy of the planning department Production policy of the finn

Production quantities

Janualaj February March April May June July August September October November

December Total

Type 1 E89 El08 ZI08 Totalproduction Total inventory

83 0 7 90 60

171 19 7 197 130

211 174 5 20 8 22 224 216 180 150

201 30 17 248 100

239 10 8 257 30

255 13 9 277 0

122 12 18 152 0

77 8 20 105 0

88 11 18 117 0

93 29 10 142 0

163 16 24 203 0

2222 650

Type 2 OK SK YK Total production Total inventory

10 0 17 27 0

21 1 123 145 60

43 68 0 29 183 192 226 289 100 160

126 11 40 177 58

61 7 156 224 0

57 5 202 264 0

44 6 66 116 0

34 2 98 134 0

33 14 47 94 0

24 10 66 100 0

33 15 82 130 0

1926 378

0 0 0 0

97 118 215 0

109 242 351 50

145 161 306 0

149 237 386 45

164 306 470 114

28 53 81 0

0 84 84 0

0 !1 11 0

9 22 31 0

100 82 182 0

907 1656 2563 357

Ouertime Motor dept. Pump dept. Total overtime Extra prod. capacity

Cost of plan (in thousands TL) Inventory Costs 979,470 Overtime Costs 1,460,910 Costs of Extra 203,490 Capacity Total Costs 2,643,870

106 340 446 148

420

L. Ozdamar et al. /European Journal of Operational Research 104 (1998) 403-422

the plan for the current month by editing type demands and family demand percentages, the available capacity levels (reduced due to already processed orders) and by importing current inventory levels from the MRP database. Thereafter, HDSS will support the DM in his search for at least a feasible solution, if not optimal. The lower and upper bound modifications carried out on the dependent families and end items of the pump type render a feasible plan over the whole planning horizon. The end items which are supported most by these modifications are the two most demanded pump end items OK 100-200 and YK 65-225 (required by two motor pump end items of the engine family E89). Although an approximate percentage measure is carried out for coupling the pump type with the engine type at the aggregate level, the pump end items almost never run into backorders through the latter modifications. Furthermore, the type production and inventory quantities (summed over end items) of the rolled plans match approximately with the quantities obtained in the initial aggregate plan each month. Some of the discrepancies between these quantities are due to rounding off/truncating the production/inventory quantities into whole numbers. The results of HDSS are represented by real numbers since family and end item demand forecasts are provided in percentages of the type demand quantity. The family disaggregation procedure attempts to reduce the number of set-ups as much as possible within the production quantity limit imposed by the aggregate plan. Consistency of the rolled plans can be measured by the amount of backorders at the end item planning level (not previewed at the aggregate level), the difference between the total aggregate inventory obtained in the initial plan and the inventory summed over all end items in the rolled plans, the difference between the total production quantity obtained in the initial plan and the sum of the production quantities obtained in the roiled plans and the working hours in excess of the actual overtime limit without allowance for set-up times (implied by the rolled plans which include detailed capacity calculations with set-up times). In Table 8 these measures are summarized. The production policy of the planning department is conveyed in Table 9 so that the disaggregated production plan is evaluated against some back-

ground. The production planning department explains that they accumulate some inventory before the peak season in order to minimize extra night shifts and that they emphasize inventories for the engine type. They have settled on specific family inventory levels using their previous experience in order to prevent backorders during the peak season. Indeed, when the gross demand of the previous year is considered, no backorders occur in their planning policy. The overall overtime hours are also very close to the proposed plan's, but due to the lack of the smoothing effect provided by an optimized plan, the planning policy of the firm involves more extra shift hours. Since neither computerized support nor expert personnel dedicated to medium-range planning are available in the firm, the planning department cannot avoid extra night shifts during some months as well as optimize the inventory levels. When compared with the proposed plan in Table 7 it is observed that the production planning department's inventory level decisions add a considerable sum to annual costs.

5. Conclusion

We have developed a Decision Support System for Hierarchical Production Planning (HDSS) in order to facilitate the production planning task for end-users by providing an easy-to-use tool which involves powerful planning procedures at all planning levels. The end-user can work out the plan interactively with the DSS tool while benefiting from the algorithmic components of the system. HDSS can be integrated with existing MRP software since it has been developed with a fourth generation client/server programming tool enabling information flow among different computer platforms. HDSS leads to capacity-feasible material acquisition and manufacturing plans since it provides capacity-feasible Master Production Schedules. HDSS is used in developing the production plans for a company manufacturing agricultural engines. An interesting issue in the planning task is that two different product types are partially coupled together. It is demonstrated that HDSS deals with such complications by simple modifications made via database manipulations.

L. Ozdamar et al./ European Journal of Operational Research 104 (1998) 403-422

Appendix A. The family disaggregation aigorithm: The falling procedure

Step 1. Step 2. Step 3.

Identify the set of families with positive net demand in period t, JTit. Determine each family's lbift, ub,j t and t$iy (step size) for all f ~ JTi,. Calculate Yift for all f ~ JTi,:

where s~f is the set-up cost of family f. Step 4. If Ibq, < Y~jt < ub,ft, for all f ~ JT,, then STOP. Else, go to Step 5. Step 5. Check for natural infeasibility, i.e., check if ~-'f e JTitlbift > Xit"

If the condition above holds, then set Yift ~ 0 for f ~ JTit. Else, set Yilt ~ lbift for f ~ JTi, and reduce Xit" Xit : Xit - ~ f ~=JTi, Yift"

Step 6.

Identify JC : { f ~ JT~, : y,f, + 6~t < ub~ft and ~ift ~ Xit}"

Step 7.

If JC = QS, then go to Step 8. Else, go to Step 7. Sort f ~ JTit in descending order of V/f and select the family at the top of the list and set

Yift ~ Yi[t + ~if ; Xit : Xit - ~if,

where sit'ubift ~t = - Yift

Step 8.

sifubift Yift + 1

Go to Step 6. If X~, > 0, then go to Step 8.1. Else, STOP. Step 8.1. Identify JU = {f ~ JT~, : Yi~t < ubift}; Sort f ~ JT in descending order of I7//. Step 8.2. Select the family at the top of the list and set

Yltt = Yift ; Yif, = man{ Ylf, + Xit, ubift};

Xit = Xit - ( r i d - Ylft); JLI

=

JU - {f}.

If X, > 0, then repeat Step 8.2. Else, STOP.

421

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