Scheduling in the precast concrete industry using the simulation modelling approach

Building and Enwronmenr,

Pergamon

Vol. 30, No. 2, pp. 197-207, 1995 Ekvier Science Ltd Printed m Great Britain 0360-1323/95 $9.50+0.00

0360-1323(94)00039-S

Scheduling in the Precast Concrete Industry Using the Simulation Modelling Approach N. N. DAWOOD* The precast industry is a supplier of building materials COthe construction industry. It is capital intensive and the instability of construction demand makes investment in the industry a high risk undertaking. As a result, a highly structured and ef$cient scheduling system is required to maximise the utilisation of resources and minimise the waste associated with them. The main objective of this paper is to develop a scheduling model, using the job shop scheduling approach, in order to help production managers to make better planning decisions, and to explore alternative options. The model is a computerised factory simulator which comprises scheduling rules and the factory’s attributes. These rules have been developed in this research to mimic the decision making process of a production scheduler. A number of experiments were conducted using the model as a test bench COevaluate the performance of the scheduling rules under different measures ofperjormance andfactory conditions. The work also examined the effect of sales fluctuations on the performance of the model. It was concluded that it is feasible and beneficial to model the industry using the simulation modelling approach in which there is no scheduling rule superior to others under any factory conditions.

1. INTRODUCTION

mating the process of planning and predicting the effect of several managerial strategies before production commences. The objective of this paper is to develop a computer based scheduling system for the precast industry using the ‘job shop’ scheduling technique. The job scheduling technique has been extensively developed by academics and used by practitioners in different industries and has proven to be a useful and cost saving exercise. The reminder of this paper discusses briefly the theory of job shop scheduling and details the scheduling model which has been developed in this research.

MUCH of the U.K.‘s precast industry is classified as Make-To-Stock (MTS) type manufacturing, where hundreds of different standard products are produced and stocked. The prime reasons for holding stock are the seasonality and fluctuations of the construction market in which the precast industry is a prime supplier. The amount of money invested in this sector of the industry is huge and in order to get the desired return on such investment a more systematic and objective scheduling system is needed. While the business of this sector is referred to as MTS, its production operations are of the Make-To-Order (MTO) or ‘job shop’ type. That is, production plant and machinery are multi-task and very flexible and can be adapted to process several types of products and this is the nature of MT0 business. Traditionally, MTS and MT0 are reviewed as separate entities and their planning processes contrast sharply (see [l]). This might be the case for certain industries but is not true for the precast industry. In a survey of current production planning practices in the U.K., the author concluded that the current scheduling practices are fairly basic and depend greatly on subjective, experiential approaches. Such practices have contributed to inaccurate planning performance which may result in carrying of excessive stock or running-out of stock for key products. This has promoted the idea of developing a computerised scheduling model for auto-

2. JOB SHOP SCHEDULING : A REVIEW Baker [2] defined job shop scheduling as “the allocation of resources over time to perform a collection of tasks”. Once the jobs to be produced have been determined, it is necessary to decide when each of the job operations should be achieved. Eilon [3] describes job shop scheduling as a queuing problem. It is made up of a huge network of queues and priority is used to select the next job for the running machine. The following conclusions have been extracted from previous literature on production scheduling (see [4-61). l

* Division of Civil Engineering and Building, School of Science and Technology, The University of Teesside, Middlesbrough TSl 3BA, U.K.

l

197

There are three main approaches to job shop scheduling. These are : (1) the optimal approach, (2) the heuristic dispatching approach and (3) the artificial intelligence system approach (AI). These approaches contrast sharply in terms of their ability to model a real production environment. The optimal approach, which utilises mathematical

N. N. Dawood

198

equations to model job shops, has not been received well by practitioners due to its complexity and theoretical nature. It is often applied to single machine shops. The optimal approach makes certain assumptions (for example, machines do not break down, job operations never overlap and a job is never interrupted once it has started), which have tnade it remote from reality. Most of the research in the precast industry is concentrated on the applications of mathematical models to scheduling and long range planning in make-to-order manufacturing systems (see [7,8]). The heuristic dispatching approach receives much attention from academic researchers and practitioners due to its flexibility and ability to mimic real job shops. This approach uses priority loading rules to select the next job when there is a conflict between usage resources. The simulation technique is often utilised in the heuristic approach and used to model demands and production facilities for a given situation. It has been proven that there is no single scheduling rule superior to any other under all job and factory characteristics. In practice, manufacturing industry favours rules that take into accountjobs’ due dates and customer interest. The AI approach is a way of simulating a human scheduler by learning and changing the scheduling rules from one time to another to satisfy a number of criteria. This approach is still far from maturity and needs more development and examination (see [I]).

introduced in Section 6 of this paper to illustrate the potential of the model. The demand forecast represents sales forecasting for each group of products for 12 months ahead and it is prepared by managers using forecasting models. Terminology used in the paper for the purpose of specifying the entities of the production planning model is given in the Appendix.

In the present paper it has been hypothesised that production in the precast industry can be modelled as a job shop for scheduling the work to be done. A computerised simulation model is developed to mimic the production operations in the industry and several product and plant selection rules have been developed and incorporated in the model.

3.2.1. Theproduct selection rules. These rules determine which product is to be produced prior to others. Three distinct rules have been developed to satisfy the criteria discussed below. It should be mentioned that these product selection rules are not the only loading rules possible and the reason for choosing just three rules is to illustrate the use and potential of the model. The product selection rules developed in this research are described in the following.

3. THE SIMULATION MODEL : SPECIFICATIONS AND PROCESSES The objective of this section is to introduce the specifications of the model, the scheduling process and the measures which are used to evaluate the performance of the model. Figure I shows the specification of the model and the interaction between information input, the scheduling process and information output. 3.1. Information input The information input is presented sources :

by the following

(a) plant attributes information ; (b) product attributes information ; (c) daily shift patterns for the scheduling (d) demand forecast ; (e) dispatch information.

period ;

The plant and product attributes convey the characteristics of the factory being simulated and can differ from one factory to another. Tables 1 and 2 give examples of plant and product attributes. These attributes are used as a factory example in the experimental work which is

3.2. The scheduling process In the model, the forward scheduling technique is used. This technique is commonly used in job shops where customers place their orders on a ‘needed-as-soon-aspossible’ basis. Forward scheduling determines start and finish times for the next priority product by inserting it into the earliest available slot. The scheduling process embodies three distinct heuristic rules. (a) Product selection rules. (b) Plant selection rules. (c) Allocation rules. The product selection rules determine which product is to be produced prior to others where there is a choice between several products. The plant selection rules determine which plant is to be used for the selected product. Finally the allocation rules handle the allocation of shifts to a particular plant and determine when the next event will occur. The following sections discuss the above heuristic rules.

(a) Stock couer minimum cost (SCA4C) rule. This rule sorts products with respect to their stock cover. The one with the lowest stock cover would have priority over others. In certain situations where two products might have similar stock cover, the product with lower inventory cost would have priority over the other. Under this rule, stock cover for each product should be maintained and balanced (i.e. having the same stock cover for all products) as a first choice and minimizing the cost of stock as a second choice. The logic expression for this rule is IF stock cover for product A > stock cover for product B THEN product B is prior to product A ELSE IF stock cover for product A = stock cover for product B AND cost of carrying stock for product A > = cost of carrying stock for product B THEN product B is prior to product A ELSE product A 1s prior to product B Stock cover is calculated

in the model as follows :

Scheduling

IDemand Allocation

199

in the Precast Concrete Industry

of shifts and

Schedules

are evaluated

w

Plants to the rumling products and produce

Cost of inefficiency Cost of changovers Cost of lost sales

Fig. 1. Specification of the model.

Table 1. Plant attributes used to test the model (current setup : PRl) Products that can run Attributes of plant A PRl PR2 PR3 PR4 PR5 PR6 PR7 PR8 PR9 Attributes of plant B PRl PR2 PR3 PR4 PRS PR6 PR7 PR8 PR9 Attributes of plant C PRI PR2 PR3 PR4 PR5 PR6 PR7 PR8 PR9

Production units/shift

Efficiency (%)

Change-over cost (L)

64 64 38 75 75 75 75 63 35

70 70 70 100 100 100 100 100 70

92 92 54 75 75 15 75 63 50

100

100

100 100 100 100 100 100 100 100

100 100 100 100 100 100 100 100

92 92 54 53 53 53 53 44 50

100 100 100 70 70 70 70 70 100

100 100 100 100 100

100 100

100 100

100 100 100 100 100

100 100 100 100

stock cover for product A at time (t) = curing time x (number of units available in the stock yard at time (t) + number of units under curing at time (t))/rolling accumulated demand for curing time (t to t+4) where number of units available in the stock is ‘dispatchable stock’, number of units under curing is ‘yet to be dispatchable stock’, and curing time (maturity strength) is the minimum time required from production to delivery and it is equal to four weeks in the model. When stock cover for any given product is four weeks, then demand for the period (t) to (t+4) can be satisfied without delays, indicating minimum stock level. If stock cover is greater than four weeks then more than minimum stock is available to satisfy demand. When stock cover is less than four weeks then less than minimum stock is available and demand is not fully satisfied. The same equation is used for the other loading rules discussed below. (b) Minimum stock cover maximum demand (MSCMD) rule. This rule sorts products with respect to their minimum stock cover. The minimum stock cover should be equal to four weeks for any product. The product with four weeks cover or less would have priority over others. In the case of two products having more than minimum stock cover, then the product with higher demand would have priority over the other. Under this rule, minimum stock cover for each product should be maintained as a first choice and maximising run length as a second choice. The logic expression for this rule is

200

N. N. Dawood Table 2. Product

Products

Link between other products

Plant required

A A A A A A A A A

PRl PR2 PR3 PR4 PR5 PR6 PR7 PR8 PR9

or or or or or or or or or

B or B or B or B or B or B or B or B or B or

attributes

C C C C C C C C C

THEN product A is prior to product

B ELSE IF stock cover for product A < 4 weeks AND IF stock cover for product B > = 4 weeks THEN product A is prior to product B ELSE IF stock cover for product A i 4 AND IF stock cover for product B < 4 AND IF volume for product A > = volume for product product A is prior to product B ELSE IF stock cover for product A > = 4 weeks AND IF stock cover for product B < 4 weeks THEN product B is prior to product A

B THEN

(c) Stock cover maximum demand (SCMD) rule. This rule is similar to the SCMC rule. The main difference concerns the secondary option. When two products have similar stock cover, then the product with high demand would have priority over the other. The logic expression for this rule is IF stock cover for product A > stock cover for product THEN product B is prior to product A ELSE IF stock cover for product A = stock cover for product AND IF volume for product A > = volume for product B THEN product A is prior to product B ELSE product A is prior to product B

B

B

3.2.2. An example to illustrate the use of the loading rules. The following example explains the use of product selection rules in the model. Given the information in Table 3 about products PRl-PR9, the task is to sort 3. Information

from the experimental different products

Curing time (weeks)

None None None None None None None None None

IF stock cover for product A > = 4 weeks AND IF stock cover for product B > = 4 weeks AND IF volume for product A > = volume for product B

Table

used to test the model

work

Product

Demand for four weeks ahead

cost of product (&)

PRl PR2 PR3 PR4 PR5 PR6 PR7 PR8 PR9

270 49 101 30 386 211 325 139 68

43 96 29 49 23 24 36 48 56

about

nine

Stock cover (weeks) 9 9 9 10 10 11 9 5 8

cost (f)

Profit G)

43 96 29 49 23 24 36 49 56

7 19 5 6 3 3 9 7 10

products into the form of a queue for each product selection rule. According to the three product selection rules, products PRlLPR9 in Table 3 should be queued as shown in Table 4. Under the SCMC rule, priority is given to maintaining and balancing stock cover for each product. That is, trying to keep stock cover for all products nearly the same. In the case of two products having the same stock cover, priority will be given to the product with lower stock cost. This minimises the cost associated with keeping expensive stock. The SCMD rule is similar to the SCMC rule, except when the products have the same stock cover, the priority then will be given to the product with higher volume demand. This would help to prevent high volume products from running out of stock, especially if sales fluctuate greatly. Under the MSCMD rule, priority is given to just maintaining minimum stock cover, i.e. maintaining enough stock to satisfy demand. The extra available capacity, after maintaining minimum stock cover, is used for producing high volume demand only. This rule minimises the risk associated with running out of stock for high volume demand products on the assumption that such products are fundamental to the business of the factory and necessitate maximum running length. The main setbacks associated with the MSCMD rule are as follows : increased risk of running out of stock for small volume demand products (especially in a highly fluctuating market), having just kept minimum stock cover ; high stock carrying cost could be associated with this rule when high volume products are expensive to produce and consequently expensive to keep in stock.

Table 4. Queues of products using the three product selection rules Schedule SCMC PR8 PR9 PR3 PR7 PRl PR2 PR5 PR4 PR6

chosen MSCMD PR5 PR7 PRl PR6 PR8 PR3 PR9 PR2 PR4

SCMD PR8 PR9 PR3 PR7 PRl PR2 PR5 PR4 PR6

Scheduling

in the Precast Concrete Industry

3.2.3. Plant selection rules. Plant selection rules are combinations of heuristic and artificial intelligence rules. The model chooses a product from a given queue and goes through the available plant in order, choosing a plant with respect to the following rules : IF shifts are available to run the plant AND Case 1 IF the plant is able to produce the product AND Case 2 IF the plant is able to produce the product at 100% efficiency AND Case 3 IF the current set-up is compatible with the product THENCase 4 Allocate the available shifts to the plant and run the product Rule a ELSE go to the next plant and repeat Rule a ELSE IF none of the plants is found to match Rule a THEN start again from the first plant and relax just case 3 OR IF set-up cost is less than inefficient cost THEN relax just case 4 and allocate the available shifts Rule b ELSE IF set-up cost is more than inefficient cost THEN relax just case 4 and allocate the available shifts Rule c ELSE IF none of the plants is found to match Rules b and c THEN start from the first plant and relax case 3 and 4 Rule d

IF rule d does not match any plant THEN GO to the next product in the queue and repeat Rules a, b, c and d Rulee ELSE IF shifts are not available for certain plants THEN do not include in the checking process Rule f IF shifts are not available for all plants THEN Update time and check the end of the planning

time

Rule g

It can be seen that the plant selection rules are developed using logic and expertise rules. The criteria behind the logic rules could be seen as : (a) if shifts are available to run a given plant ; (b) if a plant can produce a given product ; (c) if a plant can produce a product at 100% efficiency with compatible set-up. On the other hand, the expertise rules are those which control the choice of plant when shifts and plant are available. In certain cases there might be a choice between whether to run the product on inefficient plant with a compatible set-up or to run it on efficient but not compatible plant, in which case the choice could be quite different from one situation to another. That is, when the set-up cost is very expensive compared to the inefficient production then the choice could be to minimise changeovers and inefficient production. However, in the case of high cost associated with inefficiency compared with change-over cost, the choice could be to prevent inefficient production and to allow change-overs. Rules b, c and d above are examples of the expertise rules. 3.24. The allocation rules. These rules handle the process of allocating shifts to plant once a plant is found and determine when the next event will occur. Having identified which product is to be produced and which plant is to process the product, the allocation rules decide the number of shifts to be allocated for a particular day and check events and updating time. 3.3. Description of the scheduling process The main operations of the scheduling processes follows :

201

(a) reading information ; (b) initializing time ; (c) reading dispatches ; (d) reading demand ; (e) calculation of stock cover ; (f) the allocation process ; (g) checking ‘end of week’ ; (h) storing information ; (i) checking the end of the scheduling

period.

For the purpose of simplifying the process of scheduling and to make it more acceptable in practice, certain assumptions have been made. These are as follows :

(4 plant is operating independently

and each plant represents a production line in the simulated factory ; (b) there is no relation between products and each product is treated independently ; the number of shifts for each plant is finite and swap(cl ping shifts between plant is not allowed ; (4 time is updated when all shifts in a given day are utilized or all demand is produced ; (e>no product is allowed to run on two plants on the same day and no product is allowed to share plant with other products in a given day ; (f) stock yard capacity is unlimited ; (g) no plant is allowed to stay idle when shifts are available ; 09 practical minimum run length should be applied for all plant in the model ; that is, when practical minimum run length is one day, for example, then all plant items are permitted to change over every day if required ; (i) dispatches of products occur at the beginning of each week. ‘Turbo Pascal’ language has been used for the development of the software for implementing the model. The details of the scheduling process are not given in this paper due to space limitations but are available from the author on request.

3.4. Measures of performance In order to evaluate the impact of several planning strategies on production and stock, different measures of performance have been developed. These measures should facilitate the choice of these planning strategies under several demands and factory characteristics. All the measures of performance focus on cost, as the overriding objective of the model is to produce low cost production plans through the selection of the best planning strategy. It should be noted that the calculation involved in the measures is simplified and an approximation of current practices.

3.4.1. Cost of stock. with stock holding for period. The following the total cost of stock

This represents the cost associated each product during the planning formulae are used for calculating in the stock yard :

are as total cost of stock for PR(n) for the planning

period (m) :

N. N. Dawood

202 ,=

total cost of change-over

“l

1 stock level for PR(n) at time (t) x cost(n) I= I total cost of stock for all products

for the period

(m) :

PR=n c total cost of stock for PR(n) PR=I for the planning

period (m),

where t : 1 to m = planning period (weekly or monthly) ; stock level for PR(n) is the number of units under curing or ready to be dispatched at time (t) ; cost(n) = cost of carrying one unit of products PR(n) for time(z); cost(n) = (overhead + material cost + labour cost) x cost of capital ; and n = number of products in the stock yard. The cost of stock is the cost of money which management has to invest during the planning period on stock and not the actual production cost. The calculation of the cost associated with stock holding can play a major factor in maintaining a company’s cash-flow and consequently controlling financial plans. Also, the calculation of stock holding for each product can give important information to planners in deciding the allowable period in which a product is allowed to remain in the stock yard. It must be recognized that establishing the exact cost of stock holding is an accounting exercise rather than a planning task. 3.4.2. Cost of inef$ciency. This measure represents the cost of running products on inefficient plant. The following formulae are used for this purpose. Cost of producing PR(n) inefficiently on a plant for period(m) :

,=m ,c, (1 -E(n)) cost of producing

x N(lOO%E)

where E(n) = efficiency of producing PR(n) on a parvaries from 10 to 100%; and ticular plant N(lOO%E) = number of units which a particular plant can produce PR(n) as if it was 100% efficient for a given shift ; and P(PRn) = profit margin associated with marketing PR(n), and it can be a percentage of product cost. The total inefficiency cost is then PR=n C cost of producing PR=I for the planning

period (m).

The cost of inefficiency can play a major role in allocating demands and gives management an in-depth view of the inefficiency of the production plant. 3.4.3. Cost of change-avers. This measure represents the cost associated with plant change-overs during the course of planning. A plant’s change-over occurs when a product is allocated to a plant which must be set up before it can be run. The following formulae are used for this purpose : change-over

cost for plant(n)

r=m 1 number of change-overs ,= s

cost for plant (n) for period (m).

In certain situations where change-overs are very expensive, management is advised to maximize run-length on plant. 3.4.4. Cost of lost sales. This measure represents the cost associated with losing sales due to unavailability of certain products in the stock yard. The formulae used for calculating this measure are : cost of lost sales of PR(n) during period m :

,=m c number of lost sales for PR(n) in time (t) ,=I x cost of producing

one unit x P(PRn)

total cost of lost sales :

PR=n 1 cost of losing sales of PR(n) during the period (m). PR=I The above four measures sheet models.

were developed

4. DESIGN OF THE EXPERIMENTAL

using spread-

WORK

In the above section, the scheduling model has been introduced and discussed. This section introduces and discusses the experimental work which has been carried out using the model. The main objectives of the experiments are as follows :

x

one unit of PR(n) at time (t) x P(PRn),

PR(n) inefficiently

plant =n 1 change-overs plant=I

:

: in time (t)

x average cost of change-overs

(a) to investigate the performance and potential of the product selection rules under several demand patterns and measures of performance; (b) to study the effect of sales fluctuations on the performance of the loading rules ; (c) to study the effect of the ‘practical minimum run length’ of a plant on the performance of the model. In order to achieve these objectives, several test runs have been carried out. The parameters, which have been varied from one run to another, are: product selection rule, demand, sales pattern and minimum practical run length. Each run has been evaluated using the four measures of performance. The following section introduces the parameters of the experimental work. 4.1. The simulated factory The simulated factory example used in the experiments has been obtained from one of the leading precasting companies in the U.K. and is composed of the following.

(1) Three production

plants: A, B and C. Table 1 shows the attributes of each plant in the factory. (2) Five shifts per week are available to each plant for 48 weeks (12 months). (3) Nine products, PRl to PR9. Table 2 shows the attributes of the products. (4) Demand period is 12 months. Table 5 gives the demand for the nine products.

Scheduling

in the Precast Concrete Industry

203

Table 5. Seasonal demand pattern Month

PRI

Jan Feb Mar Apr May Jun Jul Aug Sept Ott Nov Dee

42 132 168 168 336 672 810 1215 1458 1216 810 586

PR2 23 61 31 31 62 124 149 224 268 224 149 56

PR3 70 122 62 62 142 241 298 447 536 447 298 29

PR4 25 41 21 21 42 83 100 150 180 150 100

28

(5) Curing time is (6) Cost of capital

four weeks for all products. (interest rate) is 5% per month. (7) All products can be made on all plant; however, the following efficiencies apply : Plant 1 : only 70% efficient on products PRl, PR2, PR3 and PR9 ; Plant 2 : only 70% efficient on products PR4, PR5, PR6, PR7 and PRK PIant 3 : 100% efficient on all products. Table 1 gives the attributes for each plant. (8) Output per shift at 100% efficiency for all plant is given below (units/shift) : PR2: 92; PR1:92; PR3 : 54; PR4: 75; PR5: 75; PR6: 75; PR7: 75; PR8: 63; PR9 : 56. 4.2. Sales pattern Sales pattern is the dispatching of products to customers. In fairly certain market conditions sales pattern is similar to demand pattern. However, this would be a very rare case in the precast industry. In practice, sales can be affected by both internal factors (characterised by policy decisions, pricing, competence of sales managers, etc.) and external factors (characterised by interest rate: money available in the construction sector and weather) which can cause unpredicted sales fluctuation occurring from one period to another. In order to model such fluctuations, four cases are developed to represent sales for each demand pattern, and are used in the experimental work. These cases are : (a) case 1 : 0% fluctuation (b) case 2 : - 25 to + 25% (c) case 3 : - I5 to + 35% (cl) case 4 : - 35 to + 15%

from demand ; fluctuation from demand ; fluctuation from demand ; f uctuation from demand.

Case 1 represents a situation where sales are not affected by market conditions or any other factors and demand forecasting is very accurate. Case 2 represents a situation where the overall sales level is unchanged and the sales are affected by such factors as weather, price policy, competitors and presence of sales managers. These factors could have a short term effect on sales. Case 3 represents a situation where the overall sales level is higher than the demand, due to, say, increased spending on the construction activities, low interest rates and others. Finally, case 4 represents a situation where the overall sales level is lower than the demand due to, say,

PR5

PR6

PRI

75 517 261 261 523 1046 1260 1890 2268 1890 1260 600

50 108 155 155 311 623 750 1125 1350 1125 750 548

94 199 199 398 797 960 1440 1728 1440 960 736

50

high interest rates, shortages and so on. The mathematical equation the above cases is : sales in week(x) number

= [demand

generator

PR8

PR9

150 267 135 135 270 540 650 975 1170 975 650 435

37 73 37 37 75 149 180 270 324 270 180 54

of construction

activities

used to generate

sales for

in week (x) x random

from Y to Z] + demand

in week (x),

where l

l

Y and Z are the fluctuation ranges of above ; the random number generator is drawn normal distribution. Ten sales patterns for and 4 have been generated so that different of the randomness can be examined.

the cases from the cases 2,3, situations

It should be mentioned that the range of fluctuation in cases 2,3 and 4 can depend on the type of products and their sensitivity towards market conditions, weather, prices and other considerations. In this paper it has been assumed that the normal distribution is the best way to model the error in forecasts.

4.3. Practical run length The practical run length is the number of days or weeks or months in which a plant is allowed to run to produce a particular product without allowing any change-overs. For example if the practical run length is one day then the model will allow one product to run for one day (one shift) before it might allocate the same product or a different product on the next day. In the case of allocating another product then a change-over should occur. On the other hand if the practical run length is one week then a plant will run for one week (five shifts) to produce the same product before another product is allowed to run. In the experimental work, one week practical run length is selected.

5. DISCUSSION

OF THE RESULTS

The results of running the model using the sine wave demand pattern and weekly change-overs are presented in Table 6 and Figs 2-5. The results for each range of ffuctuation are discussed below.

204

N. N. Dawood Table 6. Results of running the model (sine wave demand, weekly change-over) SCMC rule

Cost of stock (f) Cost of inefficiency (f) Cost of change-overs (f) Cost of lost sales (E) Total cost (5)

- 25 to + 25% fluctuations

- 15to + 35% fluctuations

- 35 to + 15% fluctuations

100% accuracy

Min. of 10 patterns

Max. of 10 patterns

Min. of 10 patterns

Max. of 10 patterns

Min. of 10 patterns

Max. of 10 patterns

55759 6619 10 100 7583 80061

54 282 6177 9500 3527 73 486

57 399 10 884 10200 14448 92931

49914 5729 9000 30 765 95 408

52 558 12 585 10 100 40 248 115491

61 152 6675 9600 0 77 421

65 566 13117 10000 392 89 075

MSCMD rule - 25 to + 25% fluctuations

Cost of stock (f) Cost of inefficiency (f) Cost of change-overs (f) Cost of lost sales (E) Total cost (E)

- 15 to + 35% fluctuations

- 35 to + 15% fluctuations

100% accuracy

Min. of 10 patterns

Max. of 10 patterns

Min. of IO patterns

Max. of 10 patterns

Min. of 10 patterns

Max. of 10 patterns

56 980 4567 6300 8165 76012

54157 5293 6000 5410 70 860

59 757 8493 7100 1291 I 88 261

49914 5129 9000 30 765 95 408

52 558 12 585 10 100 40 248 115491

58 076 5039 6000 0 69115

65 607 10573 7100 1488 84768

SCMD rule - 25 to + 25% fluctuations

Cost of stock (f) Cost of inefficiency (5) Cost of change-overs (f) Cost of lost sales (E) Total cost (E)

- 15 to + 35% fluctuations

- 35 to + 15% fluctuations

100% accuracy

Min. of 10 patterns

Max. of IO patterns

Min. of IO patterns

Max. of 10 patterns

Min. of 10 patterns

Max. of 10 patterns

54 736 11281 9500 7703 83 220

53 942 6284 9200 3501 72 927

58 069 13301 10 300 12787 94 457

49 805 6794 9000 25 743 91 342

52 887

62 275 5978 9400 0 77 653

65 607 9964 10 300 407 86 278

I 1669 9800 39 780 114136

5.1. 100% accurate sales Using the sine wave demand and 100% accurate sales (sales = demand forecasts), the three product selection rules have resulted in a high stock cost (65-75% of the total cost) (see Table 6). The reason for this is the nature of the seasonal sales compared to the availability of the shifts during the planning period. The model has stocked products in the low season when capacity exceeds demand (first cycle of the sine wave) and prepared them for the high season when demand exceeds capacity (second cycle of the sine wave). The SCMC and SCMD rules have achieved fractionally less stock cost compared to the MSCMD rule (see Fig. 2). The results suggest that the SCMC and SCMD rules balance the stock cover for all products, and the maximum proportion of stock volume for any product is less than 18% of the total stock volume at any time of the planning period. This minimizes the risk of running out of stock (through balancing stock covers for the products) in a period of highly fluctuated sales. In the case of the MSCMD rule, high demand volume products are allowed to stay running in the model after achieving minimum stock cover for all other products. As the results suggest, products 1, 5 and 7 have a very high proportion (40-50%) of the total stock. Other products show lo-15% of the total stock.

Measuresof performance

0

Fig. 2. Results of the planning scheduling model,

sine wave

demand.

The disadvantages of the MSCMD rule are : (a) high volume products might be very expensive to stock and consequently high stock cost could be associated with this rule; and (b) the risk of running out of stock for small volume products, having kept their stock cover to the minimum. However, the advantage of this rule is in minimizing plant change-overs by allowing a single product to run on a specific plant for a long time. As can be seen in Table 6, the MSCMD rule has resulted in a low change-over cost compared to the other rules. The

Scheduling

in the Precast Concrete Industry

$120.000 $100,000 $80.000

n Cost

$60,000

Cost

s40.000

of change -avers of inefficiency

520.000 SO 1 codes: I

2

3

4

5

100% ACC”,OC”. 2.3Ml”cl”dt&Y0, 10.-25*to25% met.4.5 MOX

Fig. 3. Results

of running

‘or

10. -35%

the model under

6 Mill

and

Max

7 0‘

10. -15%

10 35%

fluct;

6.7,

+o 15%

the SCMC rule using sine wave demand fluctuations.

and three types of

of lost sales of change -avers of inefflclency of stock

3

2

1

Codes: 1.100%

Accumcy:

Fig. 4. Results

2.3

Min

of running

and

4

5

Max of 10. -25% +a 25% fluct. Moxfo, 10. -35% +o 15%

d.5

6 Mm

and

Max

7 of 10. -15%

lo 35%

fluct:

6.7:

the model under the MSCMD rule using sine wave demand fluctuations.

and three types of

120,000 100,000 $80.000

n

$60.000

Cost of change-avers Cost

of inefflciency

s40.000 $20,000 SO 1

Coder;

1~100%

3

2 Accuracy.

Fig. 5. Results

2.3’

Min

of running

on*

5

4

Max of IO. -25% to 25% flucf: Max lo, IO. -35% to 15%

the model

under

OS

the SCMD

6 Min

and

Max

7 of IO. -15% to 35% fluct.

6.7.

rule using sine wave demand and three types of

fluctuations.

MSCMD rule has also resulted in very low inefficiency cost (35% better than the SCMC rule and less than half of the cost of SCMD) where high volume products have occupied efficient plant. The MSCMD rule has resulted in a relatively high value of lost sales cost compared to other rules because of the nature of keeping just minimum stock cover for certain products. This causes the model to run out of dispatchable stock for certain products quite easily, especially when the model approaches the end of the planning period. It should be mentioned that sales could be lost in spite of having minimum stock cover due to the unavailability of dispatchable stock and most of the stock volume is l3 weeks old. In practice, certain orders could be delayed

for l-2 weeks if the quantity is available but yet to be cured. In general, lost sales are caused by having a restrictive delivery and a long curing time. In conclusion, all the rules have resulted in a high proportion of stock cost. The rules have also resulted in 5-15% proportion of inefficiency cost. With respect to overall costs, the MSCMD has resulted in a better performance (5-10%) than the other rules. However, this rule might not produce the same results if high volume products were expensive to stock.

5.2. -25 to +25% saIes_fZuctuation The model was allowed to generate 10 fluctuated sales patterns and test them in separate runs. The results of the

206

N. N. Dawood

runs are presented by taking the maximum and minimum values of each measure from the 10 sales patterns. This should indicate the minimum and maximum effect of a fluctuating sales pattern. This was done for all the results obtained from fluctuated sales. Looking at Table 6 and Figs 3-5, the costs of stock for the three rules are affected by minimum - 3 to maximum + 5% compared with the ‘100% accurate’ sales forecasting. The cost of changeovers and inefficiency is affected by minimum -5 to maximum + 10% from the 100% accurate sales case. With respect to the cost of inefficiency, the results have shown that the SCMD rule has greatly been affected by the fluctuation and gives costs from - 100 to + 15% from the 100% accurate sales. The rules have resulted in a very high cost of lost sales due to the sales fluctuations, varying between minimum -50 to maximum 100% from the ‘100% accurate’ sales. In general the MSCMD rule has resulted in less overall cost compared to other rules in both the minimum and maximum effects. From the above results, it can be concluded that the effect of having sales fluctuation can increase the cost of lost sales and cost of inefficiency due to unpredictable sales. For example, an increase of sales by lS-25% in a particular week for a particular product could affect the availability of dispatchable stock and sales could be lost, especially in the high season. It should be mentioned that fluctuations in sales affect to a higher degree the availability of stock of high volume products. The results also indicate that -25 to +25% fluctuation could have a very low effect on the cost of stock, because, although the sales fluctuate, the overall level and trend remains constant. Low stock in one week due to high sales for particular product could be compensated by high stock in the next week due to low sales.

5.3. - 15 to + 35% sales,fktuation The consequence of having - 15 to + 35% sales fluctuation mainly affects cost of stock, cost of inefficiency and cost of lost sales (see Table 6 and Figs 3-5). The cost of stock has decreased for all rules by minimum + 1715% to maximum +25-20% from the 100% accurate sales case for all rules. The cost of lost sales has increased by at least +400 to maximum 500% from the 100% accurate sales case. The reason for the relatively low stock cost and high lost sales is the general increase of the sales level compared to the demand forecasting. The volume of sales has increased by at least 10% and consequently some of the sales are lost due to the unavailability of dispatchable stock and limited capacity. The cost of stock has decreased because of the early departure of dispatchable stock compared to the 100% accurate sales. The MSCMD rule has resulted in less overall cost compared to the others because of the low change-overs and low inefficiency cost. On the other hand, the SCMD rule has resulted in marginally better cost than other rules. It should be mentioned that under the - 15 to + 35% fluctuation, the management have certain problems to address. Management should detect such changes of sales level and decide how the level of available shifts for cer-

tain periods can be increased so that lost sales can be minimized. It should be mentioned that the cost of change-overs is slightly affected by such sales fluctuation as the case of - 25 to + 25% fluctuation. 5.4. - 35 to + 15% salesfluctuation The consequence of having -35 to + 15% sales fluctuation affects the costs of stock, lost sales and inefficiency as in the previous section. The cost of stock for all the rules has increased by minimum +3-20% to maximum + 16-20% from the 100% accurate sales case. The cost of lost sales has decreased to zero in the case of minimum effect (see Table 6 and Figs 3-5). That is, lost sales are kept to a minimum under such a fluctuation pattern. The high cost of stock and very low cost of lost sales are caused by having a low sales level compared to the demand level. Sales have dropped by at least lo%, consequently the volume of dispatchable stock has decreased. This has left stock to be accumulated from one week to another, while the model was utilizing all available shifts. This also explains why the cost of lost sales is kept to a minimum. In general the MSCMD rule has resulted in a low overall cost compared to the SCMC and SCMD rules due to the low cost of change-overs. It should be mentioned that management under such fluctuation faces another problem. The difficulty here is the high cost associated with stock and the low level of sales. The management can choose between the following alternatives : (a) slowing down production outputs by decreasing the number of shifts available for a given period ; and (b) changing pricing policy to attract customers and increase the share of the market. In order to develop the model further more applicable to different fluctuations, cedures and intelligent rules are required.

and make it control pro-

5.5. Summary of the results The results have revealed that sales fluctuations affect the performance of the model. The main influencing factor is the changing of sales level. In the case of -25 to + 25% sales fluctuation, where sales level is not changed, the model under all the rules and weekly change-overs has resulted in minimum -3 to maximum +3% fluctuation in the cost of stock from the 100% accurate sales case. This indicates that the model is absorbing sales fluctuations and, for example, low stock in one week due to high sales could be compensated for by high stock in the next week due to low sales. The cost of lost sales is highly affected by the - 25 to + 25% sales fluctuation. In the case of - 15 to + 35% sales fluctuation, where sales level has increased by at least lo%, the results have shown that the cost of stock has decreased by minimum - 12 to maximum -8% and cost of lost sales has increased many times from the 100% accurate sales case. The scenario is quite different under the - 35 to + 15% sales fluctuation, where sales level has decreased at least 10%. The stock cost has decreased by minimum 13 to

Scheduling in the Precast Concrete Industry maximum 18% from the 100% accurate sales case. The cost of lost sales has greatly decreased. From these results, it can be concluded that fluctuation in sales (especially when sales level is changing from demand level) affects the performance of the model and causes high overall cost. In order to minimise the impact of sales fluctuation, the model can be developed to accommodate certain sales monitoring procedures and adopt certain decisions. In the case of any increase or decrease of sales level, such decisions are: (a) increasing or decreasing production capacity to suit certain fluctuations for a given period, (b) changing pricing policy and (c) changing production technology and altering curing time. This leads to the development of intelligent rules which accommodate the market situations more objectively. The results also have indicated that certain factors which are related to product and plant characteristics can affect the performance of the model. These are as follows : l

l

l

l

volume and cost of products: high volume products might be very expensive to keep and consequently high stock cost could be associated with the MSCMD rule ; cost of change-overs: in certain situations and especially in the case of daily change-overs, the cost of change-overs can play a key role in deciding which rule is to be selected ; profit margin : profit margin affects the cost of lost sales and inefficiency. In the case of a high profit margin, the cost of inefficient production or lost sales would have a high impact on the overall cost and consequently affect the performance of the rules ; and curing time: the results obtained from running the model are based on four weeks curing time ; if, say, the curing time was to be changed to two weeks by using special cement or changing the water/cement ratio or introducing steam curing, the cost of stock and lost

207

sales would be expected to decrease ; however, such saving in the cost might not increase the profit because of the extra cost associated with changing curing time from four weeks to two weeks. 6. CONCLUSIONS The objective of this paper was to develop a scheduling model for the precast industry using the heuristic job scheduling approach. A computer based factory simulator has been developed and used to test a number of product and plant selection rules under several measures of performance and factory characteristics. The product and plant selection rules were developed in this research to suit the requirement of the precast industry. The paper has concluded that the model is generating automatically reasonable plans using different loading rules and this is regarded as the first step towards automation in production planning and scheduling. From analysis of the results of the experimental work it was concluded that no product selection rule is superior to others under all measures of performance. That is, certain rules have shown very good performance under certain measures and poor performance under others. In this sense, all rules can be utilised in practice and managers should be able to select the rule which can suit their business. The MSCMD rule has resulted in less changeovers cost compared to other rules under the sine wave demand. This means that this rule achieves fewer changeovers because of the possibility of running high volume products for long times, having achieved the minimum stock

cover

for other

The paper

examined

the performance - 15 to + 35% affect

products. the effect

of the model

of sales and

and

- 3.5 to + 15%

the performance

of the model

of sales

trend

in both

fluctuations

it is concluded fluctuations

on that

severely

due to the changing

cases.

REFERENCES 1. L. C. Henery and B. G. Kingsman, A decision support system for job release in make-to-order companies. International Journal of Operation and Production Management 11(6), 6- 16 (199 1). 2. K. R. Baker, Introduction to Sequencing and Scheduling. John Wiley, New York (1984). 3. S. Eilon, Production scheduling, in Operation Research (Edited by K. B. Haley), pp. 237-266, NorthHolland, Amsterdam (1979). 4. N. N. Dawood, Scheduling in the precast concrete industry. MPhil. thesis, University of Nottingham, U.K. (1988). 5. K. R. Baker, Sequencing rules and due-date assignments in a job shop. Management Science 30, 10931103 (1984). 6. J. H. Blackstone, D. T. Phillips and G. L. Hogg, A state-of-the-art survey of dispatching rules for manufacturing job shop operations. International Journal of Production Research Management (1982). 7. A. Warszawski, Production planning in prefabrication plant. Building and Environment 19, 139-147 (1984). 8. A. Warszawski and E. Ishai, Long range planning of prefabrication industry in a national economy. Building and Environment 17,47-54 (1982).

APPENDIX Plant is an independent production line within a factory. Each plant includes a mixer, moulds, a press and operatives. A factory can have any number of plants with similar or different specifications. The plant can produce different types of products but one at a time. Change-over of plant from one product to another has a time implication (about four hours) as well as a cost implication. In the model, it is assumed that the time needed for the change-over is out of working hours (i.e. can be performed

at weekends or night-time). However, if the model is operating three shifts, seven days a week, then the model will lose production of one shift. Efficiency is the capability of a plant to reach its theoretical design output rate. This is expressed in percentage terms. For example, 100% efficiency means that a plant is matching its theoretical output rate and it is 100% utilised, 70% efficiency means that a plant is achieving just 70% of its theoretical output and 30% of the output is left without utilisation due to technical, organisational or demand reasons.