Business Logistics Systems

Spatial Interaction Model Assignment

Suppose a Spatial Interaction Model is to be developed to help in locating a new retail store that sells a family of specialty foods. The market region to be served already includes $5$ other similar retail stores owned by competitors, denoted Store $1$ Store $5.$ To model the sales for this family of specialty foods, the market region has been divided into $9$ geographic areas as shown in the first column of the table below. This table also provides the estimated annual sales of these products from the corresponding region.

Region Annual Sales

$($in thousands of dollars$)$

NW $270$

NC $250$

NE $360$

CW $190$

CC $140$

CE $300$

SW $380$

SC $310$

SE $300$

The travel times $($in minutes$)$ between the $9$ regions and the $5$ existing stores and three possible locations for the new store are shown below. The $5$ existing stores are similar and are all deemed to have an attractiveness measure of $2.$

Travel Times to Existing Stores

Region Store $1$ Store $2$ Store $3$ Store $4$ Store $5$

NW $11\mathrm{.}4042\mathrm{.}4497\mathrm{.}6596\mathrm{.}2660\mathrm{.}21$

NC $19\mathrm{.}2435\mathrm{.}5184\mathrm{.}1282\mathrm{.}8669\mathrm{.}46$

NE $29\mathrm{.}8329\mathrm{.}6871\mathrm{.}8170\mathrm{.}6167\mathrm{.}27$

CW $48\mathrm{.}2744\mathrm{.}2885\mathrm{.}8884\mathrm{.}5325\mathrm{.}00$

CC $39\mathrm{.}565\mathrm{.}1050\mathrm{.}6149\mathrm{.}2036\mathrm{.}06$

CE $61\mathrm{.}0730\mathrm{.}0230\mathrm{.}5929\mathrm{.}4355\mathrm{.}90$

SW $67\mathrm{.}9042\mathrm{.}4456\mathrm{.}8955\mathrm{.}7311\mathrm{.}18$

SC $79\mathrm{.}3145\mathrm{.}4026\mathrm{.}0025\mathrm{.}0240\mathrm{.}31$

SE $101\mathrm{.}0267\mathrm{.}9414\mathrm{.}8716\mathrm{.}1679\mathrm{.}06$

Three possible locations have been identified for locating the new retail store, and these are denoted Loc $1,$ Loc $2,$ and Loc $3.$ The travel times $($in minutes$)$ between the $9$ regions and the three possible locations for the new store are shown below. The store to be established at Loc $1,$ Loc $2$ or Loc $3$ will not be as large as the existing stores, nor will it have as good parking availability, so the new store is estimated to be about $80\%$ as attractive; hence the new store will have an attractiveness measure of $1\mathrm{.}6(80\%$ of $2\mathrm{.}0).$

Travel Times to Three New Stores

Region Loc $1$ Loc $2$ Loc $3$

NW $81\mathrm{.}6343\mathrm{.}8332\mathrm{.}02$

NC $71\mathrm{.}0240\mathrm{.}2620\mathrm{.}62$

NE $60\mathrm{.}0335\mathrm{.}2318\mathrm{.}03$

CW $68\mathrm{.}8840\mathrm{.}0149\mathrm{.}24$

CC $34\mathrm{.}485\mathrm{.}1020\mathrm{.}00$

CE $21\mathrm{.}5431\mathrm{.}9539\mathrm{.}05$

SW $42\mathrm{.}0036\mathrm{.}8955\mathrm{.}90$

SC $15\mathrm{.}6242\mathrm{.}2060\mathrm{.}21$

SE $31\mathrm{.}7667\mathrm{.}9479\mathrm{.}06$

Build spatial interactions models to estimate the revenue that would be captured by the new store at each of the three possible locations. $($Use three spatial interaction models, where each includes the five existing stores and one of the new stores.$)$

Which new store location would be best $($Loc $1,$ Loc $2$ or Loc $3)$ and how large is the estimated annual revenue for the new store at that location?

$1.$ Best new store location $\_\_\_\_\_\_\_\_\_\_\_\_\_$

$2.$ Annual revenue for the best new store location $\_\_\_\_\_\_\_\_\_\_\_\_\_$