Assessment $2$ Case study

Smartt Distribution Group $($SDG$)$ is a distribution company operating in Wollongong. SRG has been the main distributor of a type of washing machine for the past few years. They are planning for their next operational year and are looking to optimize their operations, mainly, warehousing and delivery management to maximise their profits while meeting the fluctuating demand. Washing machines are imported from one provider based overseas and arrive at Port Kembla every Sunday. They can be shipped to any of SRG distribution centres $($warehouses$)$ in the same day they arrive to the port, and hence, all warehouses are replenished to their full capacities at the beginning of each week. There are three potential locations to establish warehouses, each with a known capacity. SRG has enough budget to establish two warehouses, but the management team is not sure which two locations are the best. The

decision about establishing the warehouses will be made at the beginning of each year. SRG distributes washing machines to its $7$ partner retailers at the beginning of every week. A retailer receives washing machines only from one warehouse. The demand for washing machines at each retailer can be estimated based on historical data. SRG has already processed the demand data and fitted a distribution to the demand at each retailer. Details of the assumptions are as following: The wholesale price $($the price the retailers pay to SDG$)$ is $$400$ per washing machine. At the beginning of the first week, both selected warehouses can be assumed to be

full. The shipment cost to all SRG distribution centres can be considered the same as the main shipping cost incurs from the international shipment. The estimated cost is

fixed and known $($as provided in the Excel file$).$ The fixed cost of opening a warehouse at each location is fixed and known $($given in the Excel file$).$ The capacity of each potential warehouse is fixed and known $($as provided in the Excel file$).$The shipment cost from each potential warehouse to each retailer is $$4$ per kilometre

distance per washing machine, if SDG operates the shipments. Distances from each

potential warehouse to each retailer are provided in the Excel file.There is no need to consider holding cost as all warehouses are replenished to full capacity every week. There is also no need to consider stock$-$out costs. The main decisions to be made at this stage are: $1-$ Which two potential warehouse locations to be chosen for the next year operations.

$(70\%$ weight in marking$)$

$2-$ The management team wants to establish a "service level" for their growth strategy. In particular, they want to find a metric representing their service level in order to use in future negotiations. The service level should be based on their ability to fulfill customer demands. Based on the model and the simulation results, advise the

management on an appropriate definition for the service level. Also let the

management team know the service level that can achieve under the current

capacity limits weight in marking$).$

$3-$ There is an offer from a shipment company to deliver the washing machines to

retailers. The offer is as follows $(10\%$ weight in marking$)$: $$4\mathrm{.}5$ per kilometre per washing machine for deliveries containing up to $30$ washing machines to a retailer. $$3$ per kilometre per washing machine for deliveries containing more than $30$

washing machines.

Help the management team decide whether this offer reduces their shipment costs.

Objective Function: maximising total profit $($question$1)$

maxz$=400*{\displaystyle \underset{j=1}{\overset{7}{}}}{\displaystyle \underset{i=1}{\overset{2}{}}}{f}_{ij}-4*{\displaystyle \underset{j=1}{\overset{7}{}}}{\displaystyle \underset{i=1}{\overset{2}{}}}{d}_{ij}*f_{ij}-50*{\displaystyle \underset{j=1}{\overset{7}{}}}$Write a report, following the format described on the third page of this document, and address the above concerns of the SDG management team. Upload your report $($in word or pdf format$)$ as well as a supporting Python file used for implementation.

${\displaystyle \underset{i=1}{\overset{2}{}}}{f}_{ij}$

Constraints

All washing machines shipped from warehouse i should be less than its capacity $C_i$ :

${\displaystyle \underset{j=1}{\overset{7}{}}}{f}_{ij}{C}_i,$iin$\{1,2\}$

All washing machines shipped to retailer $j$ should not exceed its demand $D_j$ :

${\displaystyle \underset{i=1}{\overset{2}{}}}{f}_{ij}{D}_j,$jin$\{1,2,$dots,$7\}$

Shipment from warehouse $i$ to retailer $j$ can take a positive value only if $x_{ij}=1$ :

$f_{ij}{d}_j{x}_{ij},$iin$\{1,2\},$jin$\{1,2,$dots,$7\}$

Only one warehouse is assigned to each retailer:Binary variables:

$x_{ij},in\{0,1\},$iin$\{1,2\},$jin$\{1,2,$dots,$7\}$

Non$-$negative variables:

$f_{ij}0,$

can i have a detailed for question $1$ please