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A disjunctive model to analyze and redefine the logistic of replenishing goods of retailing stores

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Abstract

This paper analyzes the distribution logistics for a retail business that has hundreds of stores located long distances from their warehouses. Given narrow revenue margins, retail companies must optimize the cost of the merchandise delivery to its stores. In general, the structure of the distribution consists of warehouses that concentrate goods which are then delivered to the stores according to a replenishment policy that contemplates its characteristics and location. The cost of the distribution logistics is significant and deserves special consideration. This paper presents a disjunctive multi period model to redesign the logistic infrastructure of delivering goods from warehouses to stores located in a wide geographical region. In the model, a warehouse can be installed, closed, expanded or replaced by a cross-docking terminal. The objective function is to minimize the cost of the whole distribution operation. A case study is presented to show the model capabilities.

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Abbreviations

c :

Trucks

i :

Stores/shops

j :

Interval of capacity increase

k :

Cross dockings locations

r :

Warehouses locations

t :

Time periods

cap c :

Capacity of truck c

capWH0 r :

Initial capacity of warehouse r

capWHJ j :

Capacity increase of interval j

costkm c :

Cost per kilometer of truck c

costrent :

Rental average cost of third-party warehouse space

costxd k :

Cross-docking cost per volume handled of XD k

demand i,t :

Merchandise volume (in m3) to deliver to store i at time t

dist r,i :

Distance in km between warehouse r and shop i

flow r,t :

Merchandise purchased and received at warehouse r at time t (m3)

invcost j :

Investment cost of interval j to increase capacity to a warehouse ($)

laborCost0 r :

Initial labor cost of warehouse r ($)

laborincr r :

Labor cost increase of interval j ($)

minv :

Minimum number of trips to deliver goods to store i

operCost0 r :

Initial operation cost of warehouse r ($)

operincr j :

Operation cost increase of interval j ($)

perc :

Maximum percentage of full warehouse capacity to store goods

stock0 r :

Initial stock of warehouse r (m3)

stockcost :

Average financial cost ($/m3)

tax:

Interest rate

XWH r,t :

When true wearhouse r is operating at time t otherwise not

XD k,t :

When true cross-docking k is operating at time t instead of warehouse r otherwise not

Z r,j,t :

When true a capacity of size j is done for warehouse r at time t otherwise not

yri r,j :

When true a merchandise delivery is performed from warehouse r to store i at time t otherwise not

yki k,i :

When true a merchandise delivery is performed from XD k to store i at time t otherwise not

yrk r,k :

When true a merchandise delivery is performed from warehouse r to XD k at time t otherwise not

CapWH r,t :

Capacity in m3 of warehouse r at time t

OperCost r,t :

Operational cost of warehouse r at time t

LaborCost r,t :

Labor cost of warehouse r at time t

CapWHupJ r,t :

Capacity increase of warehouse r at time t

OperupJ r,t :

Operation cost increase of warehouse r at time t

LaborupJ r, :

t: Labor cost increase of warehouse r at time t

CostR r,t :

Operational cost of warehouse r at time t (includes labor and operation)

CostKI k.l.t :

Transportation cost from cross-docking k to shop i at time t

CostRI r,l,t :

Transportation cost from warehouse r to shop i at time t

CostXDk:

Cross-docking cost k per volume handled ($/m3)

FKI k,l,t :

Volume delivered (m3) from XD k to shop i at time t

FRI r,l,t :

Volume delivered (m3) from warehouse R to shop i at time t

FRK r,k,t :

Volume delivered (m3) from warehouse R to XD k at time t

Rent r,t :

Space rented (m3) to a third-party warehouse

Stock r,t :

Stock (m3) of warehouse r at time t

TripAm c,k,l,t :

Number of trips of truck c from XD k to shop at time t

TripAm c,r,l,t :

Number of trips of truck c from warehouse r to shop i at time t

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Acknowledgements

The authors gratefully acknowledge the financial support for the work presented in this article to Universidad Tecnológica Nacional (UTN) through PID EIUTIFE0005248TC and CONICET through PIP 352.

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Authors and Affiliations

  1. Universidad Nacional de Rio Negro. Centro Interdisciplinario de Telecomunicaciones, Electrónica, Computación y Ciencia Aplicada, Viedma, Río Negro, Argentina

    Julio Rolando Flores

  2. INGAR – Instituto de Desarrollo y Diseño – CONICET-UTN, Santa Fe, Argentina

    Maria Laura Cúnico & Aldo Vecchietti

Authors
  1. Julio Rolando Flores
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  2. Maria Laura Cúnico
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  3. Aldo Vecchietti
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Correspondence to Aldo Vecchietti.

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Flores, J.R., Cúnico, M.L. & Vecchietti, A. A disjunctive model to analyze and redefine the logistic of replenishing goods of retailing stores. Optim Eng 24, 779–799 (2023). https://doi.org/10.1007/s11081-021-09706-z

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  • DOI: https://doi.org/10.1007/s11081-021-09706-z

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