The simulation exercise Hwai undertook pertained to a consumer electronics company $($CEC$).$ Prominent among its line of products were $32"$ and $42"$ LCD TV sets $($LCD$32"$ and LCD$42").$ Production of the LCD TV sets was subcontracted to various original design manufacturers $($ODMs$)$ located in China and Taiwan. The responsibility of DHL Supply Chain was to ship the LCD TV sets from the ODMs to the distribution centre $($DC$)$ located in Shanghai. In the latest contract, the CEC had allocated a budget of CNY $3$ billion $($Chinese renminbi$)$ for the production and shipping of $920,000$ units of LCD$42"$ and $530,000$ units of LCD$32"$ TV sets to its DC$.$ Hwai had worked with the CEC to configure the optimal supply chain that would fulfill this order within the CNY $3$ billion budget while satisfying various constraints pertaining to economy of scale, production capacity, supplier risk management and service level requirements on the shipping front. At that point, this optimization exercise did not consider the volume of CO$2$ emissions.

The CEC had a list of seven ODMs to which it could subcontract the production of LCD TV sets according to their availability and prices. ODM$1$ and ODM$2$ were the only companies that could produce both LCD$32"$ and LCD$42".$ The remaining five ODMs produced LCD$42"$ exclusively. Their unit production costs are listed in the data sheet $($see Exhibit $1).$ To engender economies of scale in the production, the CEC guaranteed a minimum order of $200,000$ to any selected ODMs. Also, to mitigate dependency risk on any ODM, the maximum order for either LCD$32"$ or LCD$42"$ was capped at $600,000$ units. ODM$1$ and ODM$2$ had high production capacities and, if chosen, they each had the ability to produce $600,000$ units of LCD$32",$ as well as $600,000$ units of LCD$42".$

Several transportation modes were available to ship the TV sets from the ODMs to the DC regular air, air express, road, road LTL $($less than truckload$),$ road network, rail and water. The distances from the ODMs to the DC and the various shipping rates are tabulated in the data sheet. ODM$5$ was located near the DC$,$ restricting shipping to road, road LTL and road network. ODM$6$ was located in Taiwan and shipping could only be conducted via air or water. Across shipping modes, the rates of carbon emission $($see data sheet in Exhibit $1)$ varied greatly from as high as $1\mathrm{.}44($regular air or air express$)$ to $0\mathrm{.}007($water$)$ kilogram $($kg$)$ per ton shipped per kilometer $($km$)$ travelled. Each LCD$32"$ weighed about $16\mathrm{.}5$ kgs and each LCD$42"$ weighed about $22$ kgs$.$

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When ignoring CO$2$ emissions and just minimising cost, what would be the best sourcing strategy? Formulate and solve the problem $($including decision variable, constraint and objective function$)$