# Collaborative Distributed Planning with Asymmetric Information. A Technological Driver for Sustainable Development

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Coordination Mechanism Review

## 3. Methodology

## 4. Proposed Coordination Mechanism with GMOP Formulation to Model Multisite and Multiproduct Operations Planning for the Sustainable Resource Sharing of Independent Companies

## 5. Numerical Experiments

_{t}for each period t, set at 500 units; noise Z

_{t}, calculated by a random uniform function of type +/− 5 units; and a linear increasing function with constant slope B

_{t}.

^{®}7.0.2 64 bits optimiser for Linux, because of its superior performance [79].

#### 5.1. Centralised Coordination Resolution and Incoordination Resolution

#### 5.2. Distributed Coordination Resolution for Sustainable Resource Sharing of Independent Companies

^{th}period and penalties can be found during the 49

^{th}period, with increasing demand in all three entities. In the total number of executed periods, 64 periods, the entities share capacity during 9 periods, but only during 6 of these periods are unit penalties set. During 3 of the executed periods, capacities are shared with no unit penalty for right to use.

## 6. Conclusions and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**The total costs for decentralised–uncoordinated and centralised coordination for the 52 studied periods, in which all three entities share the capacities of the first resource with trend demand (the TTP1R00 trend demand, product type P1, resource at 100).

**Figure 6.**The total costs for decentralised–uncoordinated and centralised coordination for the 52 studied periods, in which all three entities share the capacities of the first resource with seasonal trend demand (the STP1R00 seasonal trend demand, product type P1, resource at 100%; the TCR_52_Centralised total cost values for the 52 studied periods with the entities sharing a resource in centralised coordination; the TCR_52_Uncoordinated total cost for the 52 studied periods with decentralised uncoordinated entities).

**Figure 7.**The service level of decentralised–uncoordinated and centralised coordination during the 52 studied periods, in which all three entities share the capacities of the first resource with trend demand (the TTP1R00 trend demand, product type P1, resource at 100%; NSR_Centralised Service level for the 52 studied periods with the entities sharing a resource in centralised coordination; the NSR_Uncoordinated service level for the 52 studied periods with decentralised uncoordinated entities).

**Figure 8.**The service level for decentralised–uncoordinated and centralised coordination for the 52 studied periods, in which all three entities share the capacities of the first resource with seasonal trend demand (the STP1R00 seasonal trend demand, product type P1, resource at 100%; the NSR_Centralised Service level for the 52 studied periods with the entities sharing a resource in centralised coordination; the NSR_Uncoordinated service level for the 52 studied periods with decentralised uncoordinated entities).

**Figure 9.**Lagrange multiplier values on the 49th planning horizon of instance STP1R30_4 coordinated with STP1R30_5 and STP1R30_6 (the STP1R30_4 Seasonal trend demand, product type P1, resource at 30%, instance 4).

**Figure 10.**Distribution of the total costs in relation to centralised coordination, uncoordinated and decentralised coordination (the TTP1R30 trend demand, product type P1, resource at 30%; the TCR_52_Centralised total cost values for the 52 studied periods with entities sharing a resource in centralised coordination; the TCR_52_Uncoordinated total cost for the 52 studied periods with decentralised uncoordinated entities; the TCR52_Coor_dist total cost for the 52 studied periods with the implemented coordination mechanism).

**Figure 11.**Distribution of service level in relation to centralised coordination, uncoordinated and decentralised coordination (the TTP4R30 trend demand, product type P4, resource at 30%; the NSR_Centralised service level for the 52 studied periods with the entities sharing a resource in centralised coordination; the NSR_Uncoordinated service level for the 52 studied periods with decentralised uncoordinated entities; the NSR_Coor_dist total cost for the 52 studied periods with the implemented coordination mechanism).

**Figure 12.**Number of executed periods where capacity is shared among the entities (source: the Authors).

**Figure 13.**Graph of the aggregate demand for the products of entities STP1R30_4, 5 and 6 and the capacities shared among entities (STP1R30_4 seasonal trend demand, product type P1, resource at 30%, instance 4).

**Figure 14.**Graph of the resources shared among entities STP1R30_4, 5 and 6 during the first period and penalties (Shared Capacity, shared resources; Coordination Cost, penalties between entities).

**Figure 15.**Periods with capacity shared by STP130_5 with entities STP1R30_4 and STP1R30_6 (Orange shading denotes the planned coordination periods when capacity is required from another entity. Blue shading represents planned coordination periods when capacity is released to other entities and figures are offsets).

Indices | |
---|---|

$i$ | Index set of SKUs (including products, packaging and site) |

$t$ | Index set of planning periods in each PH (t’ refers to the total studied horizons) |

$r$ | Index set of resources |

$k$ | Index set of strokes |

$ro$ | Index set of each Planning Horizon (PH) |

c | Index set of each company |

j | Index set of Lagrange iteration |

Parameters | |

${D}_{i,t,\mathrm{ro},c}$ | Demand for SKU i for period t to company con PH ro |

${H}_{i,t,c}$ | Cost of storing one unit of SKU I during period t at company c |

$C{O}_{k,t,c}$ | Cost of stroke k during period t at company c |

$C{S}_{k,t,c}$ | Cost of setting up stroke k during period t at company c |

$C{B}_{i,t,c}$ | Cost of delay of SKU I during period t at company c |

$S{O}_{i,k,c}$ | Number of units of SKU i that generates a stroke k at company c |

$S{I}_{i,k,c}$ | Number of units of SKU i that stroke k uses at company c |

$L{T}_{k,c}$ | Lead time of stroke k at company c |

$KA{P}_{r,c}$ | Capacity availability of resource r during period t at company c (in time units) |

$KA{P}_{r=1,c}$ | Capacity availability of shared resource r during period t at company c (in time units) |

${KA{P}^{\prime}}_{r=1,c}$ | Capacity availability with coordination of shared resource r during period t at company c (in time units) |

${M}_{c}$ | A sufficiently large number at company c |

$T{O}_{k,r,c}$ | Capacity of resource r required to execute one unit of stroke k at company c (in time units) |

$T{S}_{k,r,c}$ | Capacity required of resource r for setting up stroke k at company c (in time units) |

Variables | |

${z}_{k,t,\mathrm{ro},c}$ | Amount of strokes k to be k to be performed during period t on PH ro at company c |

${\delta}_{k,t,\mathrm{ro},c}$ | =1 if stroke k is performed during period t on PH ro (0 otherwise) at company c |

${f}_{i,t,\mathrm{ro},c}$ | Delay quantity of SKU i during period t on PH ro at company c |

${x}_{k,t,\mathrm{ro},c}$ | Stock level of SKU i on hand at the end of period t on PH ro at company c |

Pareto | Demand | Uncertainty | BOM/BOP | Saturation | Instance |
---|---|---|---|---|---|

Par00, Par05, Par10, Par15, Par20, Par25 | CC, TT, SS, ST, SD | CV00, CV10, CV20, CV3, CV40, CV50 | P1, P2, P3, P4, P5, P6 | R00, R75, R50, R30 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 |

Demand Type | Function |
---|---|

Trend (TT) | D_{t} = μ_{t} + B_{t} + Z_{t} |

Seasonal + Trend (ST) | D_{t} = μ_{t} (1 + sin(2πt/52 + π/2)) + B_{t} + Z_{t} |

_{t}average demand, B

_{t}demand with a constant increase slope, Z

_{t}noise.

Pareto | Demand | Uncertainty | BOM | Saturation | Instance |
---|---|---|---|---|---|

Par00 | TT, ST | CV10 | P1, P4, P6 | R30, R75, R00 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 |

42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | |
---|---|---|---|---|---|---|---|---|

t | 20 | 16 | 147 | 131 | ||||

t + 1 | 11 | 10 | 44 | 49 | 129 | 124 | ||

t + 2 | 2 | 5 | 53 | 25 | 103 | |||

t + 3 | 10 | 11 | 32 | 87 | ||||

t + 4 | 79 | 66 | ||||||

t + 5 | 56 | 43 | ||||||

t + 6 | ||||||||

t + 7 |

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**MDPI and ACS Style**

Rius-Sorolla, G.; Maheut, J.; Estelles-Miguel, S.; Garcia-Sabater, J.P. Collaborative Distributed Planning with Asymmetric Information. A Technological Driver for Sustainable Development. *Sustainability* **2021**, *13*, 6628.
https://doi.org/10.3390/su13126628

**AMA Style**

Rius-Sorolla G, Maheut J, Estelles-Miguel S, Garcia-Sabater JP. Collaborative Distributed Planning with Asymmetric Information. A Technological Driver for Sustainable Development. *Sustainability*. 2021; 13(12):6628.
https://doi.org/10.3390/su13126628

**Chicago/Turabian Style**

Rius-Sorolla, Gregorio, Julien Maheut, Sofia Estelles-Miguel, and Jose P. Garcia-Sabater. 2021. "Collaborative Distributed Planning with Asymmetric Information. A Technological Driver for Sustainable Development" *Sustainability* 13, no. 12: 6628.
https://doi.org/10.3390/su13126628