Parameters

: set of stores

: set of customers

: shipping cost from store

to customer

: demand of customer

: product inventory in store

Decision variables

: binary variable: $1$ if customer

is served by store

; $0$ otherwise

Constraints

Objective function

Minimize

Lab Instructions

Code and solve this retail problem $($use the formulation provided$).$

Report the allocation of customers to stores and the total cost of this plan.

Model, code, and solve the following variants to this retail problem $($variants are independent and should be implemented separately$).$

Variant $1$: Demands can be satisfied by multiple stores $($i$.$e$.,$ a customer can receive units from multiple stores$).$

Variant $2$: Stores can request no more than $10$ additional units from a nearby warehouse at a flat cost of

$,$ shown in the table below.