Integration of Production Sequencing and Outbound Logistics in the Automotive Industry

Yi Luo

Department of Industrial and Systems Engineering, Mississippi State University,

P.O. Box 9542, Mississippi State, MS, 39762.

Mingzhou Jin*

Department of Industrial and Systems Engineering, Mississippi State University,

P.O. Box 9542, Mississippi State, MS, 39762, mjin@ise.msstate.edu, Tel: +1 662 325 3923, Fax: +1 662

325 7618

Sandra D. Eksioglu

Department of Industrial and Systems Engineering, Mississippi State University,

P.O. Box 9542, Mississippi State, MS, 39762.

* Corresponding author

Integration of Production Sequencing and Outbound Logistics in the Automotive Industry

Abstract

This paper addresses the mixed model assembly line sequencing and outbound logistics planning

problems in the automotive industry at the operational level. The decision-making procedures in practice

consider these two problems sequentially. This study proposes an integrated scheme coordinating both

decisions. We provide mixed integer programming models for production sequencing, logistics planning,

and the integrated scheme. The integrated model is simplified based on an understanding of the properties

of an optimal solution for the sequencing problem and the assumption that there is one closed bottleneck

workstation. The numerical experiments demonstrate the benefit of the integration by comparing it with

two sequential schemes, the Production-First-Scheme and the Logistics-First-Scheme.

Key Words: Integration, Production planning and control, Logistics, Sequencing, Optimization

1. Introduction

The Just-in-time (JIT) philosophy originated from the work of Taiichi Ohno at Toyota Motor Company

and was introduced into the United States about 20 years ago (Askin and Goldberg 2002). The JIT

philosophy has been adopted by most automakers all over the world. In a JIT system, inventory is

considered a big cost contributor. Thus, one of the major objectives of manufacturers is to reduce the

inventory level to “zero” (Monden 1998). This objective puts manufacturing requirements in the center of

production planning.

The automotive industry has shown an increased interest on lead time reduction in the recent years.

Shorter lead times: (a) increase responsiveness to market changes, (b) reduce pipeline inventory, and (c)

improve customer satisfaction (Eskigun et al. 2005). The total lead time depends on: the time between

receiving an order from the customers or dealers and launching the production of this order, the

manufacturing lead time, and the time to ship the final product to customers. With the JIT systems’

emphasis on balancing the mixed model assembly lines, especially on reducing the variation of the

consumption rate of the parts (Kubiak 1993), the required parts reach the assembly line in time without

hurting the overall lead time. In addition, the manufacturing lead time is relatively fixed, allowing little

room for further improvement. Based on a prior project with a major US automaker, the authors believe

large improvement potential lies on outbound logistics lead time. However, it is a common practice in the

automotive industry to have a production planning that considers very few logistics requirements

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(Spencer et al. 1993), though logistics/distribution related costs are not taken into account, though they

comprise about 15-30 % of the final product cost (Abernathy et al. 1999).

This paper is motivated by a prior project conducted for a major automotive manufacturer located in the

United States. The company is implementing the JIT philosophy. The production planning is first

prepared based on forecasted or actual demand; next the inbound and outbound logistics are planned; the

planning information is broadcasted to the transportation service providers (railway and/or truck

companies); and finally, the outbound transportation plans are determined by the transportation service

providers. In the current sequential operational planning structure, production planning is prioritized. This

sequential structure, while seems to satisfy the production managers, has raised a number of questions

from the logistics managers. The logistics managers are concerned about the long waiting times to deliver

vehicles. Vehicles wait in the staging area up to 48 hours for truck delivery and anywhere from 1 to 5

days for rail delivery. These long waiting times are mainly result of restrictions in loading. The logistics

group does not wish to send less-than-full-railcar (or less-than-full-truck) shipments because of the cost

structure for rail or truck transportation. Because of additional costs and lead time required in

intermediate ramps for loading and unloading operations, there is little incentive to use the same railcar to

ship vehicles with different destination ramps. The logistics managers believe that the primary cause of

these long waiting times is the mismatch that exists between the production schedule and the distribution

practice. This paper studies the impact of integrating production sequencing and outbound logistics

planning. There are a number of papers in the literature that deal with the integration between production

and logistics decisions at the strategic level, such as site locations and transportation mode selections.

However, very little has been done to integrate production and logistics problems at the operational level

for daily decisions.

The remaining of the paper is organized as follows. Section 2 gives a literature review. Section 3 provides

the production model, the outbound logistics model, and the integrated model. Section 4 presents

numerical experiment results to compare the integrated model with two sequential schemes, the

Production-First-Scheme and the Logistics-First-Scheme. Section 5 concludes the paper.

2. Literature Review

This research analyzes a mixed model production sequencing problem and a distribution problem faced

by automotive manufacturers. In addition, it introduces a model that integrates both problems. This

section presents a review of literature for each of the above mentioned problems.

2

The mixed model assembly line problem finds good applications in JIT systems (Ventura and

Radhakrishnan 2002). In such assembly environments, workers are expected to be more versatile and

have better skills than those working in traditional systems (Bukchin et al. 2002). Paced assembly lines

with closed workstations and fixed-rate launching are the most common types of assembly lines in the US

automotive industry (Matanachai and Yano 2001). The sequence of launching the products to the line is

determined by the actual (short range) demand pattern and customer orders (make-to-order policy)

(Bukchin et al. 2002).

The production model presented in Section 4.1 discusses the sequencing problem of a mixed model

assembly line. In fact, the sequencing of vehicles to the mixed model assembly line depends on the goals

or purposes of controlling (Monden 1998). Yano and Rachamadugu (1991) address the problem of

sequencing jobs on a paced assembly line to minimize the total amount of utility work. Bolat (1997)

maximizes the total amount of work completed by decomposing the sequencing problem into two set of

jobs: identical and repeating jobs. Matanachai and Yano (2001) propose a new line balancing approach

for a mixed model assembly line by considering short-term workload stability. Vilarinho and Simaria

(2002) develop a two-stage procedure that minimizes the number of workstations along the line during

the cycle time and balances the workload between and within workstations. Zhao et al. (2004) assign the

tasks to workstations so as to minimize the total overload time. The assignment considers the daily

assembling sequence of the models, the tasks of each model, the precedence relations among the tasks

and the operations parameters of the assembly line. In practice, most automakers use simple dispatching

rules (Monden 1998), such as continuation control and interval control, without considering sophisticated

optimization tools.

Routing decisions are treated in the literature under general manufacturing settings as well. Chandra and

Fisher (1994) are among the first to study integrated production-distribution planning problems. They

investigate the effect of coordinating production and distribution on a single-plant, multi-commodity,

multi-period scenario. Their computational study shows that the coordinated approach can yield up to 20

percent in cost savings. Fumro and Vercellis (1999) propose an optimization model that integrates

production and distribution decisions. The model coordinates decisions such as capacity management,

inventory allocation, and vehicle routing. Lei et al. (2005) discuss the integrated production, inventory

and distribution routing problem that involves heterogeneous transporters with non-instantaneous

traveling times and multiple customer demand centers with inventory capacities. All models mentioned

above consider neither production scheduling nor transportation loading factor. We believe that

3

coordinating production scheduling and delivery planning at the operational level can significantly reduce

supply chain lead time and costs, as pointed by Hall and Potts (2003).

There exists a vast literature on models that integrate production and inventory or inventory and

distribution decisions in a supply chain. Most papers that study integration are mainly focused on

strategic designs of supply chains. For example, Cohen and Lee (1988) present a comprehensive model

framework for linking the decisions about production and distribution in a supply chain. Dogan and

Goetschalckx (1999) study a production-distribution allocation problem using a mixed integer

programming formulation. Kaminsky and Simchi-Levi (2003) develop a two-stage model to design a

manufacturing supply chain including capacitated production in stages and a fixed cost for transporting

the product between stages. Chauhan et al. (2004) consider the problem of the strategic design of a supply

chain where new production/distribution has to be launched in the existing network because of a new

market opportunity. More recently, Eskigun et al. (2005) study supply chain design problems that

minimize the total of fixed facility location and transportation costs. Shen et al. (2005) consider a multi-

commodity supply chain design problem that determines the facility locations and the assignment of

customers to facilities so that the total costs are minimized.

3. Problem Statement and Basic Models

This paper considers the production sequencing and outbound logistics problems over a T-day planning

horizon (t = 1,…,T). The automaker produces n different models (i = 1,…,n). Because of concerns about

the loading factor in railway and highway transportation, we group the dealers whose vehicles can be

shipped together from the staging area. Here, the loading factor is the ratio of actual shipment amount

over shipment capacity of a truck or railcar. Assume there are totally M groups (m = 1,…,M). Em denotes

the transportation batch size of vehicles for group m. For example, a bi-level railcar can hold about 10

vehicles while an auto transport truck can hold about 8 mid-size vehicles. A typical distribution network

for finished vehicles of a major automaker in the US has 20~40 rail ramps. We let Dimt denote the number

of model i that should be shipped to dealer group m on day t to meet demand on time. A transportation

batch (a railcar or a truck) to dealer group m costs Fm. This cost is mainly determined by distance and

demand volume. When a vehicle of model i cannot be shipped on time, a unit shortage cost Ui is incurred

per vehicle per day. Hi denotes the unit inventory holding cost per day for model i. This cost is incurred

when vehicles wait in the staging area for shipment. Though shipping in multiples of Em vehicles to dealer

group m per day minimizes the transportation cost, less-than-truck-load (LTL) or less-than-railcar-load

shipping may save inventory and shortage costs.

4

The assembly lines in the automotive industry usually have a constant speed (Matanachai and Yano

2001). We let Cy denote the cycle time and let K (k = 1,…,K) denote the total number of the vehicles

produced in the planning horizon. The cycle time is typically chosen to provide the desired annual output

rate (Matanachai and Yano 2001). Under the assumption of the constant-pace line, the total production on

each day is constant and assumed to be Ca, which is assumed to be no larger than the maximum daily

production capacity of the line. The bottleneck workstations are the most important in an assembly line.

Similar to the models proposed by Dar-El et al. (1999), we consider one closed workstation as the

bottleneck workstation in the mixed model assembly line. The processing time of model i in the

bottleneck workstation is denoted by ri. The length of the bottleneck workstation is assumed to be L.

The following is the list of the decision variables used in the models:

Yik: takes 1 if the kth vehicle in the production sequence corresponds to model i; and 0 otherwise,

Bk: the starting position (measured in time units) of the kth vehicle in the bottleneck workstation,

Ok: the amount of utility work in the bottleneck workstation required by the kth vehicle,

Qit: the number of model i vehicles produced on day t,

Iimt: the inventory level of model i vehicles for dealer group m in the staging area at the end of day t,

Pimt: the number of model i vehicles produced on day t for dealer group m,

Wmt: the number of batches (railcars or trucks) shipped to dealer group m on day t,

Simt: the number of model i vehicles delivered to dealer group m on day t,

Limt: the shortage of the model i vehicles for dealer group m on day t.

3.1. Production Problem

The production problem considers an assembly line with fixed-rated launch and closed workstations. The

operators move downstream on the line to perform their tasks and then return upstream to meet the next

vehicle. We assume that the operators start their operations as early as possible and the upstream walking

time to the next vehicle is negligible (Scholl 1999). In case that the required work on a vehicle cannot be

completed at the end of the workstation, utility work is used at a cost of G per time unit. The utility work

caused by an imbalanced sequence is considered as the only production cost in our analysis. If the

operators reach the upstream boundary of the station before the next vehicle arrives, idle time occurs. The

production sequence over all T days on the assembly line is determined by the following mixed integer

programming model MP:

5

MP: Min

Subject to: k=1,2,…,K; (1)

i=1,2,…,n; (2)

k=1,2,…,K; (3)

k=1,2,…,K-1; (4)

(5)

(6)

Constraint set (1) and Constraint set (2) in model MP ensure that each vehicle is assigned to exactly one

position in the sequence. Utility work for each vehicle is determined by using constraint set (3).

Constraint set (4) represents the evolvement of the starting positions for processing vehicles in the

bottleneck workstation. The production problem assumes the starting position of the first vehicle to be 0

(constraint (5)).

3.2. Outbound Logistics Problem

The outbound logistics model minimizes the total of inventory, shortage and transportation costs of the

finished vehicles. Backorders are not allowed at the end of the horizon (i.e. for

i=1,2,...,n). The outbound logistics model ML is as follows:

ML: Min

Subject to: i=1,2,…,n; m=1,2…,M; t=1,2,…,T; (7)

m=1,2…,M; t=1,2,…,T; (8)

t=1,2,…,T; (9)

6

i=1,2,…,n; m=1,2,…,M; t=1,2,…,T; (10)

i=1,2,…,n; m=1,2,…,M; (11)

; integer; (12)

Constraint set (7) considers the inventory evolvement over time. Constraint set (8) captures the fixed cost

for a railcar or truck. Constraint set (9) indicates that the daily production amount is a constant that is

determined by the conveyor speed. Constraint set (10) is used to calculate the shortage amount. Constraint

set (11) ensures zero shortage at the end of the planning horizon.

3.3. Integrated Production and Outbound Logistics Model

In this section we present an integrated model that combines production and outbound logistics decisions.

The objective is to minimize the total operational costs that consist of the cost of utility work in

production, inventory holding cost, shortage cost, and transportation cost. The integrated model is built

based on the same assumptions that we stated in both production and outbound logistics problems. Please

note that the total number of model i vehicles produced on day t in the production model should be equal

to the total number of model i vehicles produced on day t for all dealer groups in the outbound logistics

model. The two models can be connected by the constraint set (13) to form the integrated model IT:

IT: Min

Subject to: Constraints (1), (2), (3), (4), (5), (7), (8), (9), (10) and (11)

i=1,2,…,n; t=1,2,…,T; (13)

integer; ; (14)

The integrated model presented above coordinates production sequencing and outbound logistics planning

with the objective to minimize the total operational costs. The numerical experiments indicated that it is

not efficient to use commercial optimization packages (e.g. ILOG CPLEX) to solve the integrated model.

In order to solve real-world problems, we develop a modified integrated production and outbound

logistics model in the next section. The modified model is then used to investigate the benefit from

integrating production and distribution decisions.

4. Modified Integrated Production and Outbound Logistics Model

7

Assume that model i* has the longest processing time ( ) and model i’ has the shortest

processing time ( ) in the bottleneck workstation. If the cycle time of the assembly

line Cy satisfies the inequality , then the starting position of the next vehicle will

increase when we sequence a model i*. When the starting position of the vehicle is lager than L-ri*, utility

work occurs if a model i* is scheduled. Scholl (1999) claims that the two objectives of “minimizing the

total utility work” and “minimizing the total idle time” are equivalent. Therefore, we assume the length of

the workstation is long enough to avoid idle time if model i’ is scheduled when the starting position is

lager than L-ri*. In other words, the bottleneck workstation length satisfies L . Based on

the assumptions stated above, we propose the following sequencing rule:

Proposition 1: For a given Qit (the number of model i produced on day t), the optimal sequence on day t

can be obtained by sequencing a model with the possibly largest processing time without causing utility

work in all vehicles waiting for sequencing at the current position. If all waiting vehicles cause utility

work, choose the one with the smallest processing time. The sequencing rule yields the minimum utility

work:

. (15)

Please check the appendix for a formal proof of proposition 1. By incorporating equations (15) in

formulation MI, we obtain the following modified integrated model MI:

MI: Min

Subject to: Constraints (7), (8), (9), (10), and (11);

t=1,2,…,T; (15)

i=1,2,…,n; t=1,2,…,T; (16)

t=1,2,…,T; (17)

;

. (18)

8

Constraint set (16) is used to obtain Qit. Constraint set (17) indicates that the number of the vehicles

produced per day is equal to the average daily demand over T days.

5. Numerical Experiments

In order to evaluate the benefit from the integration, we compare the performance of the modified

integrated model MI with two sequential decision making schemes: the Logistics-First-Scheme (LFS) and

the Production-First-Scheme (PFS). In the LFS, the outbound logistics model ML is solved first to obtain

the daily production amount for each model (Qit). The production sequencing problem is then solved for

each day to obtain the total utility work, which is calculated by using inequality (15). In the PFS, a master

sequence is first identified solving the production model MP for all T days. The daily production

quantities are calculated by using and then used as parameters in the outbound

logistics model to obtain a transportation plan that minimizes the total logistics costs based on the

determined production plan.

Our numerical experiments use the data that we collected from the project with the major US automaker

with small modifications. The following is a detailed list of the data:

Four models (n = 4), twenty dealer groups (M = 20), three days (T = 3), and one major bottleneck

workstation in the assembly line.

The transportation costs per truck (or railcar) for dealer groups are: F1=2150, F2=1700, F3=2200,

F4=2090, F5=1500, F6=2000, F7=2050, F8=2300, F9=1660, F10=2020, F11=2115, F12=1680, F13=2020,

F14=2080, F15=1800, F16=1950, F17=2190, F18=2180, F19=1765, and F20=2350.

Other costs include: unit inventory holding cost H=$30, unit shortage cost U=$20, unit utility work

cost G=$25, and transportation batch size Em=10.

We assume the cycle time is Cy =60 seconds and the workstation length is L=100 seconds.

The processing times for the four models in the bottleneck station are r1 = 45, r2 = 78, r3 = 70, and r4

= 58 seconds.

Daily demands per vehicle type of dealer groups are randomly generated by a uniform distribution

defined on the interval [0, 20]. A total of 10 instances are generated. The modified integrated model MI

and the sequential decision schemes of the LFS and PFS are all solved using ILOG CPLEX 9.0 on a

Pentium-4 PC with a CPU at 2.80GHz and 512 MB of RAM. Table 1 summarizes the solutions and

computational times for the MI, LFS, and PFS.

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Table 1 shows that the modified integrated model can be solved by commercial optimization solvers in

reasonable time. Based on the results, the total operational costs of the modified integrated model is on

average 2.75% smaller compared to the LFS and 2.49% smaller compared to the PFS. Production and

logistics costs in the automotive industry are very high. Thus, although the percentage savings seem

small, the corresponding absolute cost savings are huge. The annual savings from the integration are

estimated to be in millions of dollars. Paired T-test shows both savings are statistically significant with a

confidence level at 99.5%.

Ins

Modified Integrated Scheme LFS PFS

Log. Cost

Prod. Total Cost

Time (s)

Log. Cost

Prod. Total Cost

Time Log. Cost

Prod. Total Cost

Time

Cost Cost (s) Cost (s)

1 496,375 2,250 498,625 764 496,325 12,875 509,200 726 502,750 2,175 504,925 458

2 503,820 8,925 512,745 680 503,760 19,225 522,985 570 515,800 8,850 524,650 390

3 505,640 9,750 515,390 610 505,580 18,975 524,555 540 512,890 9,700 522,590 480

4 499,115 52,850 551,965 287 499,035 85,550 584,585 312 509,725 52,850 562,575 212

5 538,810 3,150 541,960 710 538,770 21,300 560,070 476 560,480 3,050 563,530 254

6 499,085 10,575 509,660 998 499,035 17,200 516,235 754 509,725 10,500 520,225 534

7 498,785 3,950 502,735 651 498,735 13,300 512,035 875 520,295 3,900 524,195 768

8 499,410 5,700 505,110 589 499,360 24,375 523,735 302 510,990 5,675 516,665 212

9 498,835 75 498,910 77.66 498,805 18,525 517,330 291 518,605 0 518,605 62

10 498,250 7,725 505,975 421 498,220 21,750 519,970 347 509,450 7,675 517,125 276

Table 1: Numerical Experiment Results for One Planning Horizon Based on Real-word Data

In practice, the decision making process follows a rolling horizon concept. The plan is determined for the

next T days but only implemented for the next day. Another T-day problem is solved again on the next

day with new information. We simulate this process for one month (30 days) for all three schemes with

ten different seeds of random numbers. Because of the computational time, we consider only the first five

dealer groups (i.e. M=5). A uniform distribution defined on [0, 3] is used to calculate the initial inventory

of each model for each dealer group. The rest of the data is the same. The results are presented in Table 2.

Ins.

Modified Integrated Scheme LFS PFS

Logistics Cost

Prod. Cost

Total Cost

Comp. Time (hour)

Logistics Cost

Prod. Cost Total Cost

Comp. Time (hour)

Logistics Cost

Prod. Cost

Total Cost

Comp. Time (hour)

1 412,070 67,120 479,190 0.63 410,610 128,520 539,130 0.42 452,120 58,720 510,840 0.152 331,980 52,200 384,180 0.68 329,090 92,320 421,410 0.33 359,060 50,900 409,960 0.123 354,340 57,800 412,140 0.61 353,100 80,100 433,200 0.38 395,920 50,980 446,900 0.234 347,270 61,160 408,430 0.65 345,060 111,140 456,200 0.30 376,820 61,080 437,900 0.315 334,050 49,940 383,990 0.67 331,290 89,040 420,330 0.52 385,180 48,660 433,840 0.156 358,170 71,260 429,430 0.62 352,130 100,380 452,510 0.48 399,980 70,600 470,580 0.187 388,890 64,000 452,890 0.57 377,450 102,160 479,610 0.41 419,600 63,960 483,560 0.22

10

8 388,860 43,800 432,660 0.49 376,230 94,560 470,790 0.48 430,820 43,480 474,300 0.329 317,160 48,080 365,240 0.56 312,570 93,980 406,550 0.53 343,410 45,560 388,970 0.19

10 367,560 80,440 448,000 0.71 366,670 106,460 473,130 0.58 389,560 76,220 465,780 0.18Table 2: Numerical Experiment Results with Rolling Horizon over 30 Days

The costs from the integrated scheme are on average 7.82.2% smaller compared to the LFS and 7.23%

compared to the PFS. Paired T-test shows both savings are statistically significant with a confidence level

at 99.5%. With fewer dealer groups, the integration has more impact on cost saving because of the

smaller chance to have a good sequence in the LFS and to have a good logistics plan in the PFS.

6. Conclusion

This paper addresses the production sequencing and logistics planning decision problems at the

operational level. An integrated scheme is proposed that coordinates these two decisions based on the

industrial needs identified by a prior project. Mathematical programming models for production

sequencing, logistics planning, and the integrated scheme are proposed. These models are used to perform

numerical comparisons and show the benefit of the integration. Because of the size and complexity of the

integrated model, we propose a new modified integrated MIP model based on the assumptions that there

is only one closed bottleneck workstation in the assembly line and the assembly line has a constant pace.

The modified model can be solved for real-world instances to obtain optimal solutions in reasonable time.

Numerical experiments demonstrate significant cost savings by integrating production and distribution

decisions.

A possible future research direction is to consider multiple workstations in the sequencing problem. With

multiple workstations, the optimal sequence cannot be obtained by any simple rules. Heuristics, including

dispatching rules, will be necessary in practice. Then, the impact of the integration needs to be

reinvestigated under these dispatching rules.

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Appendix:

Proof of Proposition 1:

We prove it by two facts:

Fact 1:

Overload and idle time do not both happen in a sequence created by using the sequencing rule.

Fact 2:

The sequencing rule can provide the optimal sequence with minimum utility work.

Proof of fact 1:

Given a sequence created based on the sequencing rule, let the first overload happen to the kth vehicle.

Since no overload happens right after processing the (k-1)th vehicle, the starting position of the kth vehicle

will be Bk L-Cy. Assume that the kth vehicle is model v. Because of the overload, . The

processing times of all vehicles sequenced after the kth one is at least Cy because, based on the sequencing

rule, model v has the smallest processing time compared to the models of the vehicles sequenced after the

kth vehicle (including the kth vehicle). Therefore, rv Cy. As a result, the starting position for all vehicles

sequenced after the kth will be at least L-Cy. In other words, no idle time will happen after the kth vehicle.

Now let investigate the vehicles sequenced before the kth vehicle. The vehicles that are sequenced before

the kth vehicle and have a starting positions earlier than L-rv have a processing time greater than or equal

to rv. Based on the sequencing rule, rv Cy. Therefore, no idle time happens after finishing these vehicles.

For the vehicles that are sequenced before the kth vehicle and starting positions later than L-rv, no idle

time happens after processing them because of the assumption that , where ri* and ri’

are the largest and smallest processing times of all models. Thus, when there is utility work in a sequence

created by using the sequencing rule, there is no idle time in the sequence.

Following a similar logic, we can prove that if there is idle time in a sequence created by using the

sequencing rule, there is no utility work in the sequence.

Proof of fact 2:

In any production schedule, the total required work plus total idle time must equals the total available

time plus the total utility work. For given production amount Qit on day t, total required work at the

12

workstation is equal to . The total available time of the workstation is equal to ( -1) Cy + L.

Since the sequencing rule guarantees that idle time and overload do not happen both, the minimum total

utility work is

= .

13

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