a multilevel decision-making system with multiple resources for controlling cotton harvesting

• . . . , , :

ELSEVIER Int. J. Production Economics 46-47 (1996) 55 63

international journal of

product!on economics

A multilevel decision-making system with multiple resources for controlling cotton harvesting

Dimitri Golenko-Ginzburg*, Zilla Sinuany-Stern, Vladimir Kats

Department qf lndustrial Engineering and Management. Ben-Gurion University ~)f the Neget,, Beer-Sheva 84105, Israel

Abstract

A number of our recent papers have demonstrated the advantage of using multilevel production control models, especially for flexible manufacturing systems. The results obtained may be applied to various man-machine systems, e.g., building systems, mining, forestry, agriculture, etc., where control actions are carried out by decision-makers on different levels since the plants are not fully automatic.

The best results can be achieved for hierarchical production systems, e.g.. company-section-production units, where each level faces stochastic optimization problems.

In this paper, we consider the problem of reallocating multiple resources among production units while all previous models include only one type of interchangeable resource• For control problems with several resources, all the optimization problems become more difficult. The results obtained are used for creating a hierarchical decision-making system for controlling cotton harvesting. Three levels are considered - the team level, the farm level and the district level. Two types of resources are considered: mechanical harvesters and workers. On the team level, the team's foreman periodically reallocates the resources among cotton fields. The farm level is faced with stochastic optimization problems of rcallocating resources among the teams. The district level is faced with similar reallocation problems, including problems of determining minimal additional resource amounts that. on the average, guarantee completion of cotton harvesting by the due date. A numerical example is presented. Various application areas are considered.

Keywords: Cotton harvesting; Resource reallocation; Multilevel control model; Stochastic optimization; Multiple resources

1. Introduction

A number of recent papers have d e m o n s t r a t e d the a d v a n t a g e of using mult i level p roduc t ion control models , especial ly for flexible manufac tu r ing

* Corresponding author.

systems [see, e.g. Refs. [1--10]). G o l e n k o - G i n z b u r g and S inuany-Ste rn [5] present a h ierarchical pro- duc t ion system where the ou tpu t can be measured only at preset cont ro l po in ts as it is imposs ib le or cost ly to measure it cont inuous ly . Three levels are c o n s i d e r e d - c o m p a n y - s e c t i o n - p r o d u c t i o n unit -- each level faces s tochast ic op t imiza t ion problems. Each unit p roduces a given target a m o u n t by

0925-5273/96/$15.00 Copyright 57 1996 Elsevier Science B.V. All rights reserved SSDI 0 9 2 5 - 5 2 7 3 ( 9 5 7 0 0 0 5 6 - 9

56 D. Golenko-Ginzburg et aL ~Int. J. Production Economics 46-47 (1996) 55-63

a given due date (common to all units) and has several possible speeds that are subject to disturbances. On the unit level at each control point, decision-making centers on determining both the next control point and the speed at which to proceed up to that point. The section and the company levels are faced with problems of either reallocating resources among the section's units or reassigning the remaining target amounts among them. The results obtained may be applied to various man- machine systems, e.g., building systems, mining, forestry, agriculture, etc., where control actions are carried out by decision-makers on different levels since the plants are not fully automated.

We here present a multilevel control model that is a further extension of those developed in recent years. The main difference is that different types of resources will be considered, while all previous models have included only one type of interchangeable resource. Control models with multiple resources occur in various areas, e.g., in controlling harvesting, which is carried out by individual workers together with different types of harvesters, in mining, where at least two different types of resources (trucks and loaders) are used, etc. For control problems with multiple resources, all the optimization problems become more difficult.

In this paper we develop a decision support system for controlling cotton harvesting. Three levels are considered: team level---, farm level ~ district level. This model is new and it is essentially different from those developed in recent years. The main difference is that two different types of resources (mechanical harvesters and workers) will be considered while all previous models include only one type of interchangeable resource. For two types of resources, all the optimization problems become much more difficult.

The team level is not faced with determining control points, since in cotton harvesting inspection is carried out periodically. Decision-making centers on determining only the speed at which to proceed with the harvesting. The second level is faced with stochastic optimization problems of reallocating resources among the teams so that the faster ones will help the slower ones. The district level is also faced with optimization problems, i.e., reallocating resources among the farms and deter-

mining minimal additional resource amounts that, on the average, guarantee completion of cotton harvesting by the due date. The objective function is to maximize the probability of completing the overall target by the due date.

The multilevel control system will be used in Uzbekistan, the Commonwealth of Independent States. In that country, the problem of controlling the process of cotton harvesting is one of the most important.

The structure of the paper is as follows: in Sec- tion 2 we develop theoretical grounds for controlling multilevel production systems with multiple resources. In Section 3 we present the system's description, while in Section 4 we consider optimization models on different levels. Section 5 pres- ents a numerical example. Sections 6 and 7 consider various application areas.

2. Two-level control model with multiple resources

2.1. The system

A section comprises n units that produce similar products. Each unit within the manufacturing process utilizes different resources. Resources may be reallocated among the units (e.g., manpower) to speed the production. There are several possible speeds to produce the product that are subject to random disturbances. It is assumed, too, that each speed depends linearly on the resource capacities.

2.2. Notations

vf

n

T p v (t)

Rfk

s

Vjk ( R 1 k . . . . . Rsk) m

the production plan (target amount) of unit k; 1 ~< k ~< n; the number of units; the due date common to all units; the actual output of unit k ob- served at time t, 0 < t ~< TP; the resource capacity of the f th type of unit k, 1 ~<f~< s; number of different types of resource; the j th speed of unit k, l < j ~< m; number of possible speeds;

D. Golenko-Ginzburg et al. lint. J. Production Economics 46 47 (1996) 55 63 57

~k(R lk . . . . , R~k)

rain max R f k , R f k

Rf

tki

Sk i ~ j

the average of speed 1)jk (Rlk . . . . . Rsk); it is assumed that relation

f j k (R lk . . . . ,Rsk) = ~ C j f k ' R f k f=~

holds (values C~Sk pregiven);

lower and upper boundaries of value Rfk; total available resource of type f a t the section's disposal, 1 ~<f~< s; the ith inspection point (control point) of unit k; the index of the speed chosen by unit k at moment tki.

2.3. Unit-level problems

On the unit level, all the units first work indepen- dently and are controlled separately. At each control point tki, given the actual amount already produced, V{(tu), decision-making centers on determining both the new control point, tk.i+ 1, and the index j -- Ski of the new speed Vjk, to proceed with up to that point. Thus the decision variables are tk.i+ 1 and Ski. In case V ~ - V S k (tki)> (T p -- tki)'fmk(Rxk . . . . . R~k), i.e., if it is anticipated that the production output will not be on target, an emergency is called and the second level is faced with optimization problems. The corresponding algorithms at the unit level are outlined in [3-5, 9].

2.4. Section-level problem of resource reallocation

If it is anticipated that one of the units will not be on target, i.e., will not complete manufacturing on time, an emergency is called and the section level is faced with the problem of reallocating resources among the units, so that the faster ones will help the slower ones. Golenko-Ginzburg and Sinuany-Stern [5] have formulated the resource reallocation problem for the general case. For the case of multiple resources, the problem can be modified as follows:

At moment t determine optimal values, Rfk, 1 ~< k ~< n, 1 ~<f~< s, to maximize the minimum for

the probabilities of each unit completing manufacturing on time:

M a x [ M ~ + Xk(Rlk ' . . . . ,R~k, T p - t ) }

>~ Vf l (1)

subject to

R smlk" <. Rfk <~ R f~?,x (2)

~ Rig = Ry, (3) k = l

(4, f = l

where Xk(Rlk . . . . ,Rsk, T ; -- t) denotes the future output to be manufactured in period I T p - t] and is a random variable conditioned on our future decisions.

Restriction (4) means that, on the average, each unit k completes manufacturing on time when applying maximal speed frog from t till T P, i.e., even the slowest unit is guaranteed on the average to meet the deadline on the due date.

Note that restriction (4) is imbedded in the model on condition that the two-level production system is governed by a higher hierarchical level. If problem (1)-(4) cannot be solved, i.e., no feasible solution can be obtained, an emergency is called and the higher hierarchical level has to undergo optimal resource reallocation among the subordinated sections. If the two-level system under consideration is a closed one and does not enter any other multilevel production system, restriction (4) has to be either removed or relaxed, since there may not be sufficient resources at the section level to meet this constraint.

Problem (1)(4) is a stochastic optimization problem with a variable number of constraints. Furthermore, the distribution of the speeds in un- known. The problem is too difficult to be solved in the general case. We suggest a heuristic solution as follows:

Let us introduce for each unit the term that we will henceforth call "the unit's ability". It can be calculated at any time moment t and is equal to the

58 D. Golenko-Ginzburg et aL lint. J. Production Economics 46-47 (1996) 55 63

ratio of two values: - the average accumulated output within the re-

maining time T p - t, given that only maximal speed V,,k will actually be used throughout: ~,,mk( r p -- t);

- the remaining output that needs to be manufactured: V f - V[(t) .

It can be well-recognized that the slowest unit s ability determines the possibility for the whole section to accomplish manufacturing on time. The basic idea of the heuristic solution is to substitute a probabilistic objective (1) for a deterministic one

MaX[MinV=k(TP-t) ~

[ 1 = Max Min I=1 ~ - V-~(O~ (1") {Rjk } k k - - k ~,'!

and to solve a deterministic optimization problem: to maximize (1") subject to (2-4). Objective (1") may be modified to

n . ( 1 . * ) i=1 ~ - Vk( t )

Substituting

Cmlk ' (T p -- t) V~ - V {(t) -- qfk

we obtain the objective

Ma.I n }, , isaco sta.t. {R~} k f= 1

A substitution

K i n l ~ qlk'RYkl = Z f = l

modifies problem (1)-(4) to another one:

Max Z (5) {RI~}

subject to (2)-(3) and

Z/> 1, (6)

Z <~ ~ q y k ' R I k , 1 <~ k <~ n. (7) f = l

This problem can be solved by using linear programming. If the problem has no solution, we apply the next hierarchical level [3-5].

It can be well-recognized that removing constraint (4) results in removing constraint (6) of the modified problem (2), (3), (5)-(7). If the optimal value of objective (5) is less than one, i.e., certain units cannot meet their due date on the average, then the highest speed Vm has to be introduced for those units up to the due date without intermediate control points.

3. D e s c r i p t i o n o f t h e s y s t e m

The structure of the cotton harvesting system is as follows. A district usually comprises 3(~50 farms (sections) while a cotton farm may include 15 20 teams (units). A cotton team usually gathers harvest on several (6-10) cotton fields. At the end of the day (shift), each team weighs the amount of cotton gathered during the day, i.e., the process of harvesting is inspected periodically.

A cotton team: - is required to harvest a given target amount of

cotton by a given due date common to all teams in the district;

- utilizes two different types of resources: workers Rig and harvesters REk;

- has several possible speeds that are subject to random disturbances. The team's speed depends both on the number of workers and harvesters and on the intensity of harvesting, e.g., working more hours per shift, etc. In Uzbekistan the season of cotton harvesting

can be subdivided into three periods, namely: Period 1: the earliest period when the lower cot-

ton bolls ripen and may be picked by workers only (the beginning of the harvesting);

Period 2: the mass harvesting period when both workers and harvesters may be used; but harvesters are dominant (the mass harvesting);

D. Golenko-Ginzburg et al. ~Int. J. Production Economics' 46 47 (1996) 55 63 59

Period 3: the final harvesting period for late ripening cotton bolls; both harvesters and workers may be used (the final harvesting).

These periods are taken into consideration for the system to be created.

A worker who works with the maximal speed, gathers cotton (on the average): - 0.08 t/'day (shift) within the first period; - 0.2 t/day within the second period; - 0.1 t/day within the final period.

The maximal harvester speed is as follows: - 8 l/day (shift) within the second period; - 6 t/day within the final period.

It can be well-recognized that for the Uzbekistan region, relations

g m k ( R l k , R 2 k ) =

{ 0.08R~a tons/day for the first period,

(0.2R~k + 8R2k) t/day for the second period,

(0.1Rig + 6R2k) t/day for the final period

hold. In cotton harvesting, in our model, the team's

foreman does not use any optimization technique either to reallocate harvesters and workers among the fields or to determine the proper speed to work with. Here, the foreman's decision-making must be based on his practical experience and should be carried out repeatedly (usually several times per shift). Since, every day, each cotton team weighs the amount of cotton gathered within that day, we do not need to determine control timing to inspect the progress of cotton harvesting. The problem is to ensure daily that harvesting is not deviating from the target, due to random disturbances from the environment, such as rain, illness among personnel, breakdowns of harvesters, etc. We will consider cotton harvesting not deviating from the target at moment t if, when applying the maximal speed from that point on, there is enough time to meet the deadline on the average. Such daily control is carried out as follows:

On day t check if

1/~ -- V~(t) <~ V.,k(Rlk, R2k)(T p - t), (81

where

g m k ( R l k , R 2 R ) ( T p - - t) =

f O.08Rla(TI - t) + (0.2Rig + 8 R 2 k ) ( T 2 - Tj) +(O.1RIa+6R2a)(TP-T2) if r~(To, T1),

(0.2R1k + 8R2k)(T2 - t ) + (0.1Rig + 6R2k)

x ( T " - T2) i f r ~ ( T 1 , T2) ,

(0.1Rig + 6R2k)(T v t) if t f f ( T 2, T").

(9)

If relation (8) holds, cotton harvesting proceeds. Otherwise, it means that the cotton team is unable to meet the deadline on time on the average even when applying the maximal speed, i.e., when utiliz- ing their harvesters and workers with the maximal intensity. In order to complete harvesting on time, the team needs additional resources. Thus, if V~' - - V {'(t) > V m k ( R l k , R 2 k ) ( T p - t) holds, an e m e r -

g e n c y is declared and the team's foreman applies to the cotton farm level for additional resources. To sum up, first, all cotton teams work indepen- dently using their own resources and are controlled separately. In the case of an emergency, decision- making is carried out at the cotton farm level.

4. Optimizat ion problems on different levels

If it is anticipated that one of the cotton teams will not be on target, i.e., will not complete harvesting on time, an emergency is called and the farm level is faced with the problem of reallocating workers and harvesters among the teams, so that the faster one will help the slower one. To solve this problem linear programming (1"), (2), (3), (5) (7) may be used. Here s = 2, R~ is the number of workers in the farm, R 2 is the number of harvesters in the farm.

If an optimal solution of the problem can be obtained, cotton harvesting proceeds. Otherwise another optimization problem has to be solved:

Determine

Min R1 = R*, (lO)

Min R 2 = R ~,

60 D. Golenko-Ginzburg et al. ~Int. J. Production Economics 4 ~ 4 7 (1996) 55-63

which deliver an optimal solution to the problem (1"), (2), (3), (5)-(7), R~ = R*, R2 = R*. Note that there is a trade-offbetween values R~ and R2 when solving a two-criteria optimization problem (10). Various methods to solve this problem can be used, e.g., substituting (10) for

Min {Rlk,REk} (D,R1 + DzR2), (11)

D1 and Dz being the costs per day of using a worker and a harvester, respectively. Additional resources ARx = R ~ ' - R a and A R 2 = R * - R 2 are calculated. An emergency is declared and decision- making is later carried out at the district level.

Let us introduce additional terms at the district level:

R~ number of workers on the dth farm, 1 <~d<~w;

Rn2 number of harvesters on the dth farm; w number of farms in the district; Q~ total number of workers (at the district's dis-

posal); Q2 total number of harvesters (at the district's

disposal). If the district has, or may obtain, additional

workers and harvesters, the requested amounts ARI and AR2 are passed on to the farm. Otherwise a problem is solved:

Determine 2w values R d and Rd2 , 1 ~ d ~< w, to minimize

or

{Ra~'Rd2} d = l

subject to

{ ~ R d ~ Q 1 , d=l

Ra2 <~ Q2, d=l

(12)

(13) [D1R~ + D 2 R ~ ] )

(14)

on condition that each couple (R~, Rd2) develops a solution to the problem (1"), (2), (3), (5)-(7) at the farm level, R1 = R d, R2 = R~. If problem (12)-(14) can be solved, the district reallocates its resources among the farms, and cotton harvesting proceeds. Otherwise additional amounts

AQx = ~ R d -Q1 , d=l w

A Q 2 = ~ Rd2--Qz , d=l

are calculated on the basis of the problem similar to the problem (10) or (11), and the district applies for resources to the higher hierarchical level.

Thus, in the case of emergency, the process of harvesting is first optimized on line from bot tom to top until at one of the upper levels resources are reallocated to assure that the subordinated "top- to-bot tom" elements of the system will meet their deadlines. Afterwards, the corrected resources are again reallocated among the elements of the next subordinated level, etc., up to the team level.

5. Numerical example

A cotton farm comprises three cotton teams with two types of resources: workers and harvesters. The parameters of each cotton team are as follows:

Team 1 Team 2 Team 3

V~ = 1200 t VP2 = 1500 t Vg = 1450t Ral = 40 R12 = 50 R13 = 45 R z l = 2 R 2 2 = 3 R 2 3 = 3 RT~ n = 10, Rlm~" = 10, RT~ n = 10, RT~ 'x = 100 Rlm~ x = 120 R ~ x = 110 Rn~ n = 1, Rzmi~ n - - 1, Rerr~ n = 1,

RT~ x = 6 R2~ x = 8 R2~ x = 8

Cmll = 0.1 t; c,,az = 0.1 t; Cml 3 = 0, I t; C,,2~ = 6 t Cr, ZZ = 6 t Cm23 = 6 t

The due date for all teams is T p = 80. At moment t = 60 (final period) it is anticipated that both teams 1 and 3 cannot, on the average, meet their deadlines on time even when applying their maximal speeds within the remaining period T p - t.

D. Golenko-Ginzburg et al. /Int. J. Production Economics 46 47 (1996) 55-63 61

The corresponding values V {(t) are as follows:

V{(60) = 800 t; V{(60) = 1250 t;

VY3(60) = 950 t.

The cotton farm management decided to reallo- care R~ = 135 workers and R 2 = 8 harvesters among the three cotton teams in order to help the slowest teams (teams 1 and 3) to accomplish harvesting on time. Values qyk are ql~ = 0.005, q21 = 0.3, q21 = 0.008, q22 = 0.48, q23 = 0.004, q23 = 0.24.

The optimization problem (1"), (2), (3), (5)-{7) is as follows: determine new values Rl l , R2~, R1z, R22, Rt3, R23 to maximize the objective

M a x Z subject to (15)

Z ~> 1, (16)

Z ~< 0.005Rll + 0.3R21, (17)

Z ~< 0.008R12 + 0.48R22 , (18)

Z ~< 0.004Rx3 + 0.24R23, (19)

RI1 + R12 + R13 = 135, (20)

R21 + R22 + R23 : 8, (21)

10 ~< Rl l ~< 100, (22)

10 ~< R12 ~< 120, (23)

10 ~< R13 ~< 110, (24)

1 ~< R21 ~< 6, (25)

1 ~ R22 ~< 8, (26)

1 ~< R22 ~< 8. (27)

Note that all optimal values Rik are integer num- bers.

Using the classical G o m o r y method for solving problems of integer programming results in obtain- ing the following solution:

Z = 1.068, Rl l = 34, R21 = 3, Raz = 74, R22 = 1, R13 = 27, R23 = 4. Thus, teams 1 and 3 obtain more harvesters on the account of team 2. Since Z > 1, this solution assures that all cotton teams meet their deadlines on line when applying their maximal harvesting speeds in the time period [60, 80].

6. Application areas in cotton harvesting

The multilevel decision-making control system centers on optimal resource maneuvering. Thus, this system will be especially useful for cotton- growing areas with restricted resources (manpower as well as harvesters), e.g., in Uzbekistan for the Djizak region, the Syr-Daria region, etc. For those regions, using a decision-making support system may recover 8-10% of the harvest amount. This results in approximately 120 00(L150000 tons of cotton.

In 1993-1994, extensive experimentations were undertaken on several cotton farms in Uzbekistan to test the fitness of the developed two-level control model. The best results were achieved on a collective farm "Galaba" in the Tashkent district, with a cotton sown area of 3800 hectares. The average distance from the cotton fields to the cleaning factory is 18.5 Kin, while the crop capacity is 3.4 + 4.0t/hectare. In the course of the model's installation, the farm's management came across some principal difficulties. First, all the cotton harvesters are used with trailers; the number of trailers varies from 1 to 15. Second, to develop a proper system, the management has to control separately the work of the harvesters and the transportation of raw cotton from the fields to the cleaning factory. In order to minimize the harvesting expenses, it is necessary to solve the problem of opti- mizing the amount of trailers for one harvester. Thus, the management was faced with developing a simulation model comprising all the above outlined parameters, in order to determine their optimal values, namely: the volume of one trailer, the number of trailers per harvester, the number of trailers used to form the so-called "cotton trains" that deliver raw cotton to the cleaning factory, etc. Such a simulation model, including the above outlined control techniques in cotton harvesting, was used in 1994 within the planning horizon (approximately two months from August to October) in order to minimize the harvesting expenses per hectare. The developed simulation model enables both optimal resource reallocation among cotton teams (within the harvesting period 7 reallocations have been undertaken) and optimal cotton transportation. Several parameters are imbedded in

62 D. Golenko-Ginzburg et al./lnt. J. Production Economics 46-47 (1996) 55 63

- the - the - the

that model: - the weather forecasting, - the number of harvesters,

types of soil, collective farm's productivity, harvesting period, etc.

By using the model, the management decided to raise the number of trailers per harvester to six, with the trailer's volume not less than 220 Kg. This led to a decrease in the harvesting expenses by 9%, to $92 per hectare. Despite non-favorable climatic conditions in autumn 1994, the collective farm met its due date on time.

In metallurgy, hot strip mills, various steam-ham- mers and other machines can be reallocated among metallurgical sections to meet the company's deadline on time.

8. F u t u r e re search

In the future, the developed control system for cotton harvesting has to be extended to five levels, namely, team ~ farm ~ district ~ region ~ Re- public Uzbekistan. Additional research has to be undertaken to consider cost objectives to maximize the net profit.

7. A p p l i c a t i o n to o ther a r e a s

The developed multilevel control model covers a broad spectrum of production systems, namely, the "semi-automated" systems [5]. The output of these systems can be measured only at predeter- mined inspection (control) points, since it is costly or impossible to measure the output continuously. Such systems can be controlled only via decision- making at the control points. Most semi-automated systems utilize multiple non-consumable resources (manpower, machines, etc.) which remain unchanged within the planning horizon. For such systems, control actions under emergency conditions usually result in optimal resource reallocation among production units so as to prevent the system from deviating from its target. Several important examples are presented here.

In mining, ore of various grades is produced from several pits. Both the production rate and the grade of ore produced can be predicted approximately but will vary in practice. To achieve a certain amount of ore of a specified grade by a given date, the management has to periodically reallocate personnel, trucks and loaders among grade pits.

In building construction, workers, cranes, scrapers, etc. are usually reallocated among building pro- jects at the lower level. Both objectives to maximize the expected net profit as well as to maximize the possibility of meeting the total target on time can he used for controlling those hierarchical systems.

A c k n o w l e d g e m e n t s

The authors are very thankful to the former and present Rectors of Ben-Gurion University, Profes- sors Dov Bahat and Nahum Finger, who authori- zed and supported this research.

The research has been partially supported by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev.

The authors wish to thank Professor A.V. Ser- bulov (Uzbekistan) for some helpful comments. The authors express their thanks to the anonymous referees for their usefull corrections and amend- ments.

R e f e r e n c e s

[1] Bitran, G., Haas, E. and Hax, A., 1981. Hierarchical production planning: a single stage system, Oper. Res., 29(4): 717 743.

[2] Bitran, G., Haas, E. and Hax, A., 1982. Hierarchical production planning: a two stage system, Oper, Res., 30(2): 232 251.

[3] Golenko-Ginzburg, D., 1990. A two-level production control model with target amount rescheduling, J. Oper. Res. Soc., 41(11): 1021-1028.

[-4] Golenko-Ginzburg, D. and Sims, J., 1990. Controlling a Two-Level Multi-Product System. Presented at the 1990 Pacific Conference on Manufacturing, Sydney-Melbourne, December 17-21, 1990, Vol. I, pp. 228 242.

[5] Golenko-Ginzburg, D. and Sinuany-Stern, Z., 1993. Hier- archical control of semiautomated production systems, Prod. Planning Control, 4(4): 361 370.

D, Golenko-Ginzburg et al./lnt. J. Production Economics 46 47 (1996) 55 -63 63

[6] Lefkowitz, I., 1982. Hierarchical control in large-scale in- dustrial systems, Large Scale Systems, In: Y.Y. Haimes, led.), North-Holland, Amsterdam.

[7] Sawik, T., 1991. Hierarchical Production Planning and Scheduling in a Flexible Manufacturing System. Presented at the 1 lth EURO Congress, RWTH Aachen.

[8] Sinuany-Stern, Z., Golenko-Ginzburg, D. and Keren, B., 1989. A Static Adaptive Approach for Solving a Dynamic Problem of Production Control. in: D. Murray-Smith.

J. Stephenson, and R. Zobel, (Eds.}, Proc. 3rd European Simulation Congress, Edinburgh, pp. 508 511.

[9] Sinuany-Stern, Z. and Golenko-Ginzburg, D., 199(I. Phys- ical simulation of a two stage control algorithm for FMS, Comput. Indust. Eng., 18(4i: 535 545.

[10] Sinuany-Stern, Z., Golenko-Ginzburg, D. and Keren, B.. 1993. On-Line Production Control Using lhe EVPI Approach Eur. J. Oper. Res., 67:344 357.

a multilevel decision-making system with multiple resources for controlling cotton harvesting

Documents