Simulation-based optimal production planning model using dynamic lead time estimation

Abstract

Production planning and scheduling models for the semiconductor fabrication manufacturing are suggested in various types according to the objectives and factors taken into consideration. The lead time is one of the important factors in production planning, but there does not exist a simple way to describe and include it in the model. In this paper, the clearing time method is suggested to model the lead time in the fabrication process of the semiconductor manufacturing, so that the dynamically changing environment on the lead time and work in process (WIP) status are considered. It is shown through the experimental computation that the suggested model yields the accurate description on the lead time on the planning model, and the appropriate planning model with good results for the important performance measures in the semiconductor manufacturing.

Appendix: Procedure of plan-based adaptive dispatching algorithm

1.1 Plan-based adaptive dispatching algorithm

• Step 1: Initialization

  • Step 1.1: SubK = ∅ and SubE = ∅

  • Step 1.2: For (i = 0; i < I; i++, j = 0; j < J; j++, k = 0; k < K; k++)

    $$ \mathrm{AS}\kern0.5em \left( i, j, k\right)\kern0.5em =\kern0.5em 0 $$

• Step 2: Checking to verify the equipment is available

  • Step 2.1 For (k = 0; k < K; k++)

    If P (k) = 0 and NDE (k) ≥ 1 and Assign (k) = 0

    Then

    Add the k into SubK

• Step 3: Setting the AS (i, j, k) = 1

  • Step 3.1 For (i = 0; i < I; i++, j = 0; j < J; j++, k = 0; k < K; k++)

    If M (i, j, k) = 1 and Queue (i, j) ≥ 1 and k ∈ SubK and TCP (i, j, k) − CPA (i, j, k) > 0

    Then

    $$ AS\left( i, j, k\right)=1 $$

  • Step 3.2 If ${\displaystyle \sum_{i, j, k}}\mathrm{AS}\kern0.5em \left( i, j, k\right)\kern0.5em =\kern0.5em 0$

    Then

    End the algorithm

    Else

    Then

    Go to the Step 4

• Step 4: Selecting the device, layer and equipment

  • Step 4.1: For (i = 0; i < I; i++, j = 0; j < J; j++)

    If j = J

    Then

    $$ \mathrm{WB}\kern0.5em \left( i, j\right)\kern0.5em =\kern0.5em \mathrm{CPL}\kern0.5em (i)\kern0.5em /\kern0.5em \mathrm{CD}\kern0.5em (i) $$

    Else

    Then

    $$ \mathrm{WB}\left( i, j\right)\kern0.5em =\kern0.5em \left({\displaystyle \sum_{j^{\hbox{'}}=\kern0.5em j\kern0.5em +\kern0.5em 1}^J}\mathrm{CW}\kern0.5em \left( i,{j}^{\hbox{'}}\right)\kern0.5em +\kern0.5em \mathrm{CPL}\kern0.5em (i)\right)\kern0.5em /\kern0.5em \left({\displaystyle \sum_{j^{\hbox{'}}\kern0.5em =\kern0.5em j\kern0.5em +\kern0.5em 1}^J}\mathrm{PW}\kern0.5em \left( i,{j}^{\hbox{'}}\right)\kern0.5em +\kern0.5em \mathrm{CD}\kern0.5em (i)\right) $$

  • Step 4.2: For (i = 0; i < I; i++, j = 0; j < J; j++, k = 0; k < K; k++)

    $$ \mathrm{EP}\kern0.5em \left( i, j, k\right)\kern0.5em =\kern0.5em \left(\mathrm{TCP}\kern0.5em \left( i, j, k\right)\kern0.5em -\kern0.5em \mathrm{CPA}\kern0.5em \left( i, j, k\right)\right)\kern0.5em /\kern0.5em \mathrm{WB}\kern0.5em \left( i, j\right) $$

  • Step 4.3: For (i = 0; i < I; i++, j = 0; j < J; j++, k = 0; k < K; k++)

    If $\mathrm{EP}\kern0.5em \left( i, j, k\right)\kern0.5em =\kern0.5em \underset{A\left({i}^{\hbox{'}},{j}^{\hbox{'}},{k}^{\hbox{'}}\right)=1}{ \max \kern0.5em }\left(\mathrm{EP}\kern0.5em \left({i}^{\hbox{'}},{j}^{\hbox{'}},{k}^{\hbox{'}}\right)\right)$ and A (i, j, k) = 1

    Then

    Set SI = i and SJ = j and SK = k

    Step 4.3:

    Assign (SK) = 1 and AP (SK) = max (0, TCP (SI, SJ, SK) − CPA (SI, SJ, SK)) and AD (SK) = SI and AL (SK) = SJ

• Step 5: Adding device entities into a entity group

  Step 5.1:

  For (e = 0; e < E; e++)

  If D (e) = SI and L (e) = SJ

  Then

  Add the e into SubE

• Step 6: Selecting the device entities that have the earliest start time

  Step 6.1:

  For (e = 0; e < E; e++)

  If $\mathrm{ST}\kern0.5em (e)\kern0.5em \ne \kern0.5em \underset{e\hbox{'}\in SubE}{ \min \kern0.5em }\left(\mathrm{ST}\kern0.5em \left( e\hbox{'}\right)\right)$ and e ∈ SubE

  Then

  Remove the device entity e from SubE

• Step 7: Choose any device entity in SubE and set the chosen device entity as the SE

• Step 8: Allocate SE to the SK and P (SK) = 1

• Step 9: Go to the Step 1

The PBA dispatching algorithm is embodied in the virtual semiconductor line, which is composed of both non-bottleneck and bottleneck processes. Non-bottleneck processes are not described in detail so as to lessen the computational burden of the model. The device entities thus simply pass the non-bottleneck processes in the planned lead time without capacity limits and wait for the operations in front of the bottleneck processes. The dispatching algorithms are performed every minute after updating the status of the machines and entities.

The main idea of the PBA dispatching algorithm is to minimize the emergency parameter, EP (i, j, k) = (TCP (i, j, k) − CPA (i, j, k)) / WB (i, j), where the numerator is the difference between the target production and the current production output and the denominator is the WIP balance, which indicates the ratio of current WIP to the planned WIP. There is a need to consider the WIP balance from the perspective of the overall system. Therefore, the WIP balance is cumulatively computed from the last layer to a certain layer, which is explained in Step 4.1 in the PBA dispatching algorithm procedure. The planned WIP from the optimization models are based on long-term data; however, the dispatching rule is used on shorter-term models. The target WIP for the dispatching algorithm is computed by gradually changing the WIP (i, j, t) to the WIP (i, j, t + 1).

Simply dispatching devices according to the emergency parameter causes a high number of setups, so assignment is required to reduce the number of setups. Whenever new allocations are performed, it is imposed on the equipment to operate the same type of device as much as TCP (i, j, k) − CPA (i, j, k). The equipment can operate another type of device when it reaches the assigned production target or there are no longer any device entities of the same type as the assigned device in the queue.

The input of device entities in the virtual semiconductor line using the PBA dispatching algorithm is performed with uniform time intervals determined by the amounts input to the plan. Input per interval will be calculated as period length/input amount of the plan and is required to use the PBA dispatching algorithm to generate initial device entities. It is assumed that the initial device entities are ideally distributed to fulfill the plan.