Schedule of supply chain management project based on TOC

Abstract

Firms are being increasingly pressured under the current marketing environment, the uncertainty and risks has greatly influenced the Supply Chain Management project implementation. In this paper, we present a new buffer sizing method that takes into consideration the activity duration risk as well as the multi-resource constraint risk under uncertainty. First of all, the key risk factors are identified and the SCM activity duration risk is effectively assessed by using the Bayesian Network. Secondly, the resource constraint risk is appropriately determined by using the resource flow network. The, a reasonable buffer sizing method is developed for the construction of a stable critical chain scheduling plan. A numerical example and comparative study validate the effectiveness and practicability of the proposed method, which is capable of maintaining the schedule stability with a short project makespan, while ensuring a high on-time completion rate.

Keywords

Supply chain management critical chain management theory of constraints buffer management

1 Introduction

The current marketing environment is changing rapidly with increasingly fierce competition, firms are being increasingly pressured to consider productivity issues in their Supply Chain Management project implementation. The uncertainty and risks involved by these projects, especially for large-scale projects are increasing constantly. The structure and scale of these projects are complicated with each passing day. The competition of scarce resources is intensified gradually, resulting in an increasing number of projects are hard to be completed on schedule. Traditional project plans and adjusting methods can’t satisfy demands of schedule management for these SCM projects [1].

For this reason, Goldratt [2] applied Theory of Constraint (TOC) to the project management field, proposed a Critical Chain Scheduling and Buffer Management (CC/BM) and proposed a set of integrated management theory, including plans, execution and control, which has attracted extensive attentions in the business circles and academic circles [3 –7]. It has already acquired good performance applied to engineering SCM projects [8]. Project makespan and project schedule risks are determined by buffer sizing and monitor methods directly, which become one of the upmost contents in CC/BM [9, 10]. Classical methods that confirm the buffer sizing mainly include the shearing method proposed by Goldratt [2] and the root variance method proposed by Newbold [11]. Afterwards, many scholars have conducted comparative study on these two methods, considered different influence factors comprehensively, such as project network features [12], resource tensity, risk preference of managers, process execution time and starting flexibility, and proposed multiple improved buffer setting methods, [13 –16].

The above-mentioned methods have their own reasonability, but generally speaking, they still have some research limitations, as follows: (1) the improved method based on the root variance method has the foundation of probability theory. Calculation with worse activity variance mainly depends on subjective judgment of project managers on uncertainty of activity duration, but has no pertinence and universality. Thus, it can’t measure different duration risk degree of different activities; (2) Buffer is established from the perspective of uncertainty of duration, but it gives no consideration to the correlation formed by risk influences between activities, while the correlation of activity duration will exert an influence on total duration of projects. A risk is the primary cause for resulting in changing activity duration [17]. When confirming buffer sizing, it is necessary to translate uncertainty into risk management; (3) When existing methods use resource factors to set up buffer, they only analyze it from the perspective of resource utilization, namely they only consider the proportion between quantity demand and available quantity (demand strength), but aim no at the planning network of specific projects to consider resource limited situations caused by distribution relations of every resource.

In the field of SCM projects, the necessity of risk management enjoys popular support and it has acquired certain management experience. Generally speaking, risk consequences can be eliminated or reduced, and projects can be completed on schedule by evaluating occurrence probability of risk factors and influences on project performance and adopting effective countermeasures of risks. The majority of risk management technologies, such as fuzzy method and mixed qualitative/quantitative evaluation, are not applied successfully in practice, because SCM project teams generally pay more attentions to solving current problems, namely completing a task, but having no enough time to consider (let alone execute) specific countermeasures of risks. Under the theoretical framework of CC/BM, it is proved that risk evaluation results should be blended into influences on activity duration. An advanced SCM project scheduling plan under uncertainty is contained by inserting time buffer. Buffer fully embodies the gathering principle of risks and increases stability of project system. Thus, aiming at SCM projects, a Critical Chain Scheduling and Buffer Management (CC/BM) that gives both considerations to activity duration risks and resource constraint risks is proposed in the paper, for the sake of reaching two major targets of project time management, namely to ensure completion on schedule and maintain stable schedule, so as to better manage SCM project schedule risks.

2 Measurement methods for influence of buffer sizing

2.1 Activity duration risk evaluation based on BN

It is well known that risk factors relating to every activity are different, probability of occurring risks is diverse, and its influences on activity duration also is different. Different activities should be equipped with uncertainty and importance with different levels in accordance with the duration risk level. Buffer calculation should give consideration to such a difference. For this reason, literature [18] once proposed the basis— “risk time quantum = risk probability×time consequences” to allocate buffer for software projects. The simple product rule is far from satisfying demands for the realistic environment, including high complexity of modern engineering project network, strong resource dependency and more risk factors. It is urgent for buffer expression based on risks to require for a more reasonable technical tool.

Recently, an increasing number of domestic and overseas scholars have applied Bayesian Network (hereinafter referred to as BN) to risk analysis and risk evaluation of SCM projects, provide reasonable quantitative basis for decisions of managers [19]. A graph model is used by BN to describe a series of variables and causality. Probability theory is used to deal with the uncertainty generated by condition correlation between variables. Thus, it is necessary to blend expert opinions and prior knowledge into existing data to analyze and reason. Moreover, the ability based on change information to update events can greatly reduce complexity of multi-variable statistical problems. All features of BN provide possibility and good interfaces for considering risks to set up buffer.

Differing from previous CC/BM, which originally adopted mean/median of activity duration estimation as the planning duration, completion time $d_{i}^{*}$ of activities i (i = 1, 2, …, N) under ideal operating conditions (risk-free situation) is the basis (it is called as the “ideal duration”) to evaluate influences of risk variables on activity execution time. Activities that are equipped with similar risk structure are called as the “activity group”. The advanced cognition of activity group can greatly provide convenience for risk analysis process, and then construct the schedule risk based on Bayesian Network (SRBN) for every activity group, so as to reflect and solve all kinds of uncertainty and correlation and acquire quantitative results. The specific situation can be divided into two stages.

Bayesian Structure Learning

The target in this stage is to confirm Bayesian Network of every activity group impacted by risks, endow property— activity duration risks for every activity node i, and is described as the degree of exceeding ideal duration for expected activity duration under the risk influences. The stage can be divided into three stages, including “low”, “middle” and “high”, standing for the corresponding risk consequences, when expected activity duration exceeds “0–20% ”, “20–50% ” and “above 50% ” than ideal duration $d_{i}^{*}$ , respectively, namely it is embodied into the delayed degree of ideal activity duration and is marked as $w_{j} \times d_{i}^{*}$ (j = 1, 2, 3), w₁ ∈ (0, 0.2], w₂ ∈ (0.2, 0.5], w₃ ∈ (0.5, 1]. The specific value practice of weight w_j can be confirmed in line with risk environment of projects in entirety, risk preference of project principals/work team quality, and so on.

Other risk nodes are endowed with two states, namely “yes” and “no”. Based on an activity A, risk network diagram that impacts actual execution time of activities in Fig. 1.

Bayesian Parameter Learning

Fig.1

Risk bayesian structure diagram of activity A.

The target of the stage is to provide condition probability of non-root node risk for SRBN in accordance with experience data and expert evaluation, and then evaluate occurrence probability, which is marked as $p_{i}^{j} (j = 1, 2, 3)$ , of three duration risk levels for every activity. Based on the Activity A again, “Critical supply delay” conditional probability for evaluating its non-root node risks is shown in Table 1. Conditional probability evaluation process of property node “activity duration risks” (non-root nodes) is also similar to it. By applying BN software tool MSBNx¹ to input prior probability of root node risks, duration risk probability results $p_{i}^{j}$ of activities can be calculated (refer to Table 2 in Section 4.1).

Table 1

“Critical supply delay” conditional probability example for evaluating risk nodes

Father node (if)		Child node “Critical
“Collaborator variation”		supply delay”
		Yes	No
State	Yes	0.8	0.2
	No	0.1	0.9

Table 2

Activity duration risks and resource risk evaluation results

Activity	Ideal	Risk probability			Plan duration d_i	Duration risk	RRI _i
No. i	duration $d_{i}^{*}$	distribution of			Formula (5)	$(p_{i}^{2} w_{2} + p_{i}^{3} w_{3}) * d_{i}^{*}$	Formula (4)
		activity duration
		$p_{i}^{1}$	$p_{i}^{2}$	$p_{i}^{3}$
1	15	0.30	0.55	0.15	16	4.65	0.39
2	25	0.49	0.27	0.24	28	6.30	0.45
3	30	0.41	0.42	0.17	33	8.10	0.39
4	10	0.52	0.33	0.15	11	2.22	0.53
5	15	0.45	0.25	0.30	17	4.20	0.30
6	15	0.32	0.37	0.31	16	0.51	0.18
7	20	0.7	0.18	0.12	23	2.88	0.34
8	25	0.25	0.45	0.30	27	9.00	0.35
9	20	0.67	0.28	0.05	23	2.84	0.48
10	10	0.65	0.20	0.15	12	1.70	0.38
11	15	0.34	0.43	0.23	16	4.65	0.70

To sum up, BN combines qualitative analysis with quantitative treatment to do visual modeling on causality in risk generation mechanism, unify risk occurrence probability with risk consequences and measure correlation between activities through risk variables. The construction of SRBN and evaluation of duration risk makes managers firstly define key risk factors and key activities with high risk and is beneficial to give key monitoring on project execution process. Secondly, when setting up buffer sizing, activities in varying degree of duration risks are treated differently, so as to formulate a CC/BM schedule plan that is more satisfactory with project practice.

2.2 Measure methods for resource constraint impacting buffer sizing

When giving consideration to influences of resource factors on buffer sizing, existing literatures generally select the resource that has the biggest tensity. The influence coefficient is defined as: $r = max_{k} \frac{\sum_{i} r_{i}^{k} * d_{i}}{R^{k} * T} .$ (1)

Where, $r_{i}^{k}$ stands for quantity demand for renewable resource, R^k is the supply limit of the resource k, d_i is the plan duration of the activity I, and T is the length of the critical chain [12]. Such the definition treats all activities equally without discrimination, when calculating buffer (adjustment coefficient is 1 + r), while in actual application, limit degree of every resource may be different. Demand strength of activities on multiple resources also has differences. These two aspects will impact smooth execution on a critical chain plan and are summarized as “resource constraint risks”. On the one hand, demand strength of activities on resources can be expressed by using resource utilization coefficient: $u_{i}^{k} = \frac{r_{i}^{k}}{R^{k}}$ (2)

On the other hand, in order to measure limit degree of every resource, the paper explores from the perspective of resource allocation and firstly establishes the resource flow network G’ of an initial scheduling plan before inserting into buffer. For this reason, scholars have proposed multiple methods. The specific situation can refer to references [20, 21]. Based on it, the additional constraint generated by identifying any resource flow relation has the total quantity of NUMG’. The quantity of additional constraint relation only caused by the resource k is marked as $N \cup M_{G^{'}}^{k}$ . If pre-constraint quantity of the original project network G is marked as NUM_G, limit degree of the resource k can be described as the proportion of constraint relation based on the resource among total constraint relation of projects G ∪ G′ is shown as follows: $r^{k} = \frac{N \cup M_{G^{'}}^{k}}{N \cup M_{G} + N \cup M_{G^{'}}} = \frac{N \cup M_{G^{'}}^{k}}{N \cup M_{G \cup G^{'}}} .$ (3)

Obviously, $u_{i}^{k}$ is larger, indicating that the activity i may be impacted by the kth resource limitation; $N \cup M_{G^{'}}^{k}$ is larger, indicating that the possibility of forming the resource constraint relation is larger, namely kth resource limitation degree of projects is higher. Then, Resource Risk Index (RRI_i) that defines the activity i is: ${RRI}_{i} = \sum_{k} u_{i}^{k} * r^{k} .$ (4)

RRI_i is larger, indicating that the activity is easy to be delayed for not providing resources in time. Therefore, buffering capacity aiming at the activity should be set up larger. The theory of the definition is reasonable. Based on the project network diagram (refer to Fig. 3) in the following calculating-example analysis, it can be further explained in two situations: ➀ Assuming that available quantity of three resources is [R¹, R², R³] = [7, 7, 7], obtaining N ∪ M_G∪G′ = 29, $[N \cup M_{G^{'}}^{1}, N \cup M_{G^{'}}^{2}, N \cup M_{G^{'}}^{3}] = [17, 10, 9]$ ; ➁ Assuming that available quantity of three resources is [R₁, R₂, R₃] = [7, 7, 18], obtaining N ∪ M_G∪G′ = 23, $[N \cup M_{G^{'}}^{1}, N \cup M_{G^{'}}^{2}, N \cup M_{G^{'}}^{3}] = [16, 11, 0]$ . Obviously, under the first situation, the Resource 3 is not limited to some extent. Under the second situation, the Resource 3 is not limited at all (because the Resource 3 has no any additional resource constraint relation), it will cause resource conflict risks in the project execution process. On the other hand, other measure methods of resource influences proposed by Tukeletal [12] or Zhu Chunchao [14] in other literatures can’t better perform the difference under multi-resource environment.

Fig.2

SCM project network diagram.

Fig.3

SRBN evaluation result of the SCM activity 10.

3 Buffer sizing method

Based on the duration risk evaluation results in Section 1.1 and resource risk measure methods in Section 1.2, a new buffer sizing method is proposed in the paper. First of all, “low” risks are brought into ideal duration to protect directly, making: $d_{i} = (1 + p_{i}^{1} w^{1} * d_{i}^{*}) .$ (5)

d_i is regarded as the activity plan duration (basis/scheduling duration) to construct Baseline Schedule(BS) of a critical chain. The longest chain that determines project duration is the Critical Chain (CC). In the end of CC, Project Buffer (PB) is added. Under the interchange of Non-Critical Chain (assuming as h) and C, Feeding Buffer (FB) is established. The buffer sizing is determined by the sum of expected risks with the “middle” and “high” level on the chain and resource risk coefficient. The calculation is shown as follows: $PB = \sum_{i ∊ C C} (1 + {RRI}_{i}) (p_{i}^{2} w_{2} + p_{i}^{3} w_{3}) * d_{i}^{*} .$ (6) ${FB}_{h} = {\sum_{i ∊ N C C}}_{h} (1 + {RRI}_{i}) (p_{i}^{2} w_{2} + p_{i}^{3} w_{3}) * d_{i}^{*} .$ (7)

The reasons of the above-mentioned buffer sizing are shown as follows: (1) If ideal duration d_i is project basis scheduling, namely even if buffer is inserted, absolute uncertainty in project execution still will result in frequent exceeding of activities. Actual schedule has larger deviation from BS, resulting in tension or confusion of project executers. Meanwhile, if all or the majority of risks are joined into the scheduling duration. This is also unadvisable, because risks and influence consequences are probability events. Thus, it has no need to protect in one hundred percent. For this reason, the paper only brings “low” risks into the ideal duration, while “middle” and “high” risks are gathered into time buffer to protect smooth execution of plans. (2) The practice experience shows that it is really difficult to evaluate time uncertainty by estimating activity duration allocation function or distribution parameter directly [17]. It seems that the estimated buffer may be not correct. Moreover, occurrence probability of risks is estimated in the paper. Influences are fixed to reflect in the activity duration, evaluate risk probability distribution of activity duration, and combine uncertainty of duration with objective risks, instead of being impacted by risks, so as to describe uncertainty more specifically and reliability. (3) RRI_i realizes the specific buffer sizing by aiming at different activities and then aiming at different chains from two perspectives of multi-resource limitation and activity resource utilization rate. It also shows that execution time of different NCC chains may cause resource conflict strength with the CC chain more reasonably. Moreover, influences are blended into the buffer sizing differently.

4 Calculating-example analysis

4.1 Calculating-example introduction

In order to explain the calculation process of buffer sizing under the proposed method, a small-scale SCM Project is selected as a calculating-example in the paper. The paper includes 11 activities and utilizes three renewable resources (employees, machines and materials). Limits of every resource are 7 units, project network, activity duration and resource parameter, as shown in Fig. 2.

First of all, BN is used to confirm the SRBN that every activity group is impacted by risk factors. The identification of basic risk variables can apply brainstorming method, literature review method and Delphi method or adopt ways of negotiating with contractors and visiting risk management database. Based on the activity 10, the Fig. 3 shows the risk Bayesian structure and parameter learning process.

In the step two, it is generated by using the branch and bound method. Meanwhile, it should give consideration to an initial scheduling plan of process constraint and resource constraint. Based on S the resource flow network algorithm proposed by the literature [18] is applied to obtain $N \cup M_{G \cup G^{'}} = 29, [N \cup M_{G^{'}}^{1}, N \cup M_{G^{'}}^{2}, N \cup M_{G^{'}}^{3}] = [17, 10, 9]$ .The limits of three resources are shown as follows: $r^{1} = \frac{17}{29}, r^{2} = \frac{10}{29}, r^{3} = \frac{9}{29}$

Based on the activity 10 again, resource utilization coefficients of three resources are shown as follows: $u_{10}^{1} = \frac{r_{10}^{1}}{R^{1}} = \frac{3}{7}, u_{10}^{2} = \frac{r_{10}^{2}}{R^{2}} = \frac{2}{7}, u_{10}^{3} = \frac{r_{10}^{3}}{R^{3}} = \frac{3}{7},$

Then, according to Formula (4), Resource Risk Coefficient of the activity 10 is shown as follows: $\begin{matrix} {RRI}_{10} \sum_{k} u_{10}^{k} * r^{k} \\ = \frac{3}{7} \times \frac{17}{29} + \frac{2}{7} \times \frac{10}{29} + \frac{3}{7} \times \frac{9}{29} = 0.38 \end{matrix}$

In the paper, [w₁, w₂, w₃] = [0 . 2, 0 . 4, 0 . 6], duration risks and resource risk coefficients of activities are shown in Table 2.

In the step three, the algorithm in the literature [6, 20] is applied to identify CC and NCC and calculate buffer sizing (Formula 6 and 7). The results are shown in the first column of Table 3. The CC/BM basic scheduling plan BS is obtained and as shown in Fig. 4.

Table 3
Buffer sizing and project Makespan of methods

Method Feeding Buffer Project Buffer PB Project Makespan

FB₁ FB₂ FB₃

Proposed method 7 16 6 39 173

Shearing method 8 25 8 53 187

Root variance method 8 20 8 27 161

APRT 9 24 9 35 170

Comparative method 8 20 7 38 172

Method	Feeding Buffer	Project Buffer PB	Project Makespan
Proposed method	7	16	6	39	173
Shearing method	8	25	8	53	187
Root variance method	8	20	8	27	161
APRT	9	24	9	35	170
Comparative method	8	20	7	38	172

Fig.4

The critical chain scheduling method.

4.2 Performance contrastive analysis

In order to display applicability and superiority of the method, we apply MATLAB programming to stimulate simulation experiment and compare with traditional shearing method, root variance method and Adaptive Procedure with Resource Tightness (APRT) proposed by the literature [12] considering resource tightness for performance. These three methods also regard d_i as the scheduling duration, while a half of ideal duration di^* is regarded as the activity safety time to calculate buffer sizing. In order to stand out superiority of the “resource risk coefficient” proposed by the paper, we additionally consider a comparative method one, namely when calculating buffer, the part based on duration risks is consistent with the proposed method. The part based on resource risks adopts resource tightness expression in APRT. Buffer sizing and makespan of project plan calculated by several methods are listed in Table 3 comprehensively.

According the executive strategy of the critical chain plan defined by the literature [6, 22], simulation above 6 scheduling plans is executed for 1000 times (m = 1000). Activity simulation duration is generated at random in line with the risk probability in Table 2 in the form of interval distribution (instead of adopting specific distribution functions), namely in m simulation time value generated by aiming at the activity I, there are 100 $p_{i}^{1} * m$ , which come from uniform distribution of $[d_{i}^{*}, 1.2 d_{i}^{*}]$ , 100 $p_{i}^{2} * m$ come from uniform distribution of $[d_{i}^{*}, 1.5 d_{i}^{*}]$ , and additional 100 $p_{i}^{3} * m$ come from uniform distribution of $[1.2 d_{i}^{*}, 2.25 d_{i}^{*}]$ , so as to fit with influences of risks on specific activity execution time roughly.

The performance evaluation index adopted in the experiment is the project completion time (PCT), Timely Project Completion Probability (TPCP) [3], and Total Deviation Time (TDT).

Where, the size of TDT is defined as:

TDT =∑_i ∥ S_i - s_i ∥, s_i and S_i stand for plan starting time and actual starting time of project activities. The TDT is larger, indicating that project execution relating to changes of BS is larger, resulting in higher execution costs (including punishment costs of project delay, various management costs generated by plan change and coordination costs) [23, 24]. According to plan completion value under various methods in static stage (refer to Table 3), project completion time δ is set up as δ= 165, 170, 175. Performance evaluation index of five buffer sizing methods obtained by simulation execution is shown inTable 4.

Table 4
Performance index obtained by project simulation execution

Methods PCT TDT TPCP

δ= 165 δ= 170 δ= 175

Proposed method 148.44 134.09 0.942 0.972 0.993

Shearing method 146.82 159.87 0.956 0.980 0.993

Root variance method 149.33 149.74 0.929 0.971 0.984

APRT 150.81 156.97 0.916 0.964 0.982

Comparative method one 149.83 150.74 0.928 0.970 0.987

Methods	PCT	TDT	TPCP
Proposed method	148.44	134.09	0.942	0.972	0.993
Shearing method	146.82	159.87	0.956	0.980	0.993
Root variance method	149.33	149.74	0.929	0.971	0.984
APRT	150.81	156.97	0.916	0.964	0.982
Comparative method one	149.83	150.74	0.928	0.970	0.987

It can be observed from Table 3 that the buffer obtained by shearing method is the biggest one, while the buffer obtained by root variance method is the minimum. The buffer sizing obtained the APRT and the proposed method is moderate. It can be observed by further analyzing simulation performance of the Table 4 that when generating CC/BM by executing buffer sizing method in the paper, it is still superior to root variance method and APRT, even if the TPCP and PCT are not the most excellent. What’s more, comparing with other methods, the proposed method can obtain the lowest planned TDT, indicating that the stability of the basic scheduling plan under the method is the best, because the proposed method has already analyzed and fully considered uncertain influences on project schedule caused by duration risks on the activity level in details. Moreover, on the one hand, parts of risks blend planned duration as the direct supplement of activity time estimation. On the other hand, concentrated time buffer is used to absorb the rest uncertainty of probability. Therefore, it can reduce influences of duration risks on the project scheduling plan reasonably, protect smooth execution of the critical chain plan effectively. Furthermore, if we only regard ideal duration as the scheduling duration or adopt shearing method, though it lower mean completion time can be obtained, it should be realized at the cost of higher planned derivation time. In fact, it will cause anxiety for project executers or even cause disorders, result in unnecessary panic, reduce reference values of the basic scheduling plan, and increase storage costs of projects operating costs, and organizational coordination costs in otheraspects.

In addition, on the condition of adopting the descriptive method for the same duration risks, it can be observed from the analysis between the resource risk coefficient (RRIi) proposed in the paper and the resource tightness proposed by the literature [14, 25] (comparative method one) that the proposed method can provide higher completion protection with smaller buffer. The planning stability is more excellent, further verifying that it is necessary and reasonable to apply resource flow network to judge multiple resource limit degrees [26, 27]. Based on the above-mentioned analysis, the proposed method has the optimal integrated performance and is capable of maintaining the schedule stability with a short project makespan, while ensuring a high on-time completion rate.

5 Conclusions

Making a comparison between the critical chain buffer sizing method proposed in the paper and the existing literatures, the originality mainly lies in: (1) applying Bayesian Network to analyze and evaluate activity duration risks, establishing suitable measuring system to confirm activity planning time and safety time and providing quantitative basis for buffer sizing based on duration risks; (2) evaluating multi-resource limits of projects by aiming at the resource flow network relation of specific project plans, combining with activity demands for resources to integrate and estimate resource constraint risks, and regarding it as the adjustment basis of buffer sizing.

The proposed method is particularly suitable for SCM Projcet fields with larger uncertainty, higher risks and stronger resource dependency. The projects require for shorter period and high on-time completion rate, so as to propose a higher requirement for enterprises’ ability to cope with risks. In practice, engineering enterprises generally have certain risk data and offer a condition to apply the proposed method and improve schedule performance. The case adopted in the paper can’t contain the physical truth encountered by large-scale complex SCM projects, but it offers certain reference value to compile a scheduling plan of large-scale complicated projects and scheduling risk management. How to consider influences of risk variables on SCM project costs and quality, etc., targets, as managing schedule risks is the research direction in the future for the critical chain project to regulate and control comprehensively.

Footnotes

Acknowledgments

This work was supported in part by NSFC under Grant Nos. 71402048 and 71403085, Hubei Provincial Department of Education under Grant No. D20162204 and Research Center of Hubei Logistics Development, under Grant No. 2016A05.

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Methods	PCT	TDT	TPCP
			δ= 165	δ= 170	δ= 175
Proposed method	148.44	134.09	0.942	0.972	0.993
Shearing method	146.82	159.87	0.956	0.980	0.993
Root variance method	149.33	149.74	0.929	0.971	0.984
APRT	150.81	156.97	0.916	0.964	0.982
Comparative method one	149.83	150.74	0.928	0.970	0.987

Schedule of supply chain management project based on TOC

Abstract

Keywords

1 Introduction

2 Measurement methods for influence of buffer sizing

2.1 Activity duration risk evaluation based on BN

4.1 Calculating-example introduction

Table 3 Buffer sizing and project Makespan of methods Method Feeding Buffer Project Buffer PB Project Makespan FB1 FB2 FB3 Proposed method 7 16 6 39 173 Shearing method 8 25 8 53 187 Root variance method 8 20 8 27 161 APRT 9 24 9 35 170 Comparative method 8 20 7 38 172

Footnotes

Acknowledgments

References

Table 3
Buffer sizing and project Makespan of methods

Method Feeding Buffer Project Buffer PB Project Makespan

FB₁ FB₂ FB₃

Proposed method 7 16 6 39 173

Shearing method 8 25 8 53 187

Root variance method 8 20 8 27 161

APRT 9 24 9 35 170

Comparative method 8 20 7 38 172