Case: Optimising Operational Cost at Factories & Cold Stores

The Company is planning to onboard five factories and three cold stores. The Procurement team has been given a target to purchase $20$ Tons$/$ Day of materials. These materials are a mix of Fresh vegetables: Vegetable$-$A$,$ Vegetable$-$B$,$ and Vegetable$-$C in the ratio of $2$:$3$:$5.$ The materials purchased are already Pre$-$processed and only need to be Frozen and packed as per customer specifications. All the factories are equipped with advanced Freezing methods, as explained below:

BLAST FREEZING: The general process for blast freezing involves pushing cold air across the vegetable at a very high velocity and a very low temperature in an enclosed chamber$/$ room.

INDIVIDUAL FREEZING $($IF$)$: The freezing process is the same as Blast freezing. In Individual freezing,

INDIVIDUAL QUICK FREEZING $($IQF$)$: IQF involves ultra$-$quick freezing, i$.$e$.,$ the products are frozen quickly at very low temperatures to terminate the microbial activity that can lead to food spoilage.

BLOCK FREEZING: Materials are dipped inside water in a small plastic bag and put over Trays. The trays are then arranged over plates that go inside the freezer.

Table $1$: Factory$-$wise availability of Freezing Methods and their respective Freezing capacity

FACTORY

Freezing capacity

FG storage capacity

FAC$-01$

Freezing method

Blast and IF

Block

IQF

$6$

$20$ Tons

Capacity in tons

$3$

$1$

$2$

FAC$-02$

Freezing method

Blast and IF

IQF

$5$

$15$ Tons

Capacity in tons

$2$

$3$

FAC$-03$

Freezing method

Blast and IF

Block

$3$

$15$ Tons

Capacity in tons

$1$

$2$

FAC$-04$

Freezing method

Blast and IF

Block

$2$

$10$ Tons

Capacity in tons

$0\mathrm{.}5$

$1\mathrm{.}5$

FAC$-05$

Freezing method

Blast and IF

IQF

$4$

$20$

Capacity in tons

$2\mathrm{.}5$

$1\mathrm{.}5$

Table $2$: Vegetable type$-$wise applicable Freezing Methods

VEGETABLES

FREEZING METHODS

Vegetable$-$A

Blast Freezing

Individual Freezing

Vegetable$-$B

Individual Quick Freezing

Block Freezing

Vegetable$-$C

Individual Quick Freezing

Block Freezing

Table $3$: Freezing method with their respective duration

FREEZING METHOD

DURATION

Blast & Individual Freezing

$8$ hours for $5$ Tons $+2$ hours of Changeover

Individual Quick Freezing

$0\mathrm{.}6$ Ton$/$hour $+0\mathrm{.}5-$hour break before next lot freezing

Block Freezing

$3$ hours for $3$ Tons $+2$ hours for Changeover

The company will pay on a per$-$kg basis for every process that happens in the factory. These processes include unloading raw materials, storing FG materials in the factory, freezing, and handling FG during packaging and loading SFG$/$FG materials. For simplicity purposes, consider only the freezing and storage costs. Due to limited storage capacity yet higher storage costs at factories, the operations team decided to minimise the storage at the factory and optimize it at Cold Store. The storage rationale should justify the Optimal cost $($Note:FG$-$Finished Goods, SFG$-$Semi$-$Finished Goods$).$

Table $4$: Factory$-$wise Freezing cost $($Rs$/$Kg$)$ of respective Freezing Methods and factory Storage cost

FACTORY

Storage cost

FAC$-01$

Freezing method

Blast

Block

IQF

IF

Rs$.20/$Kg$/$Day

Freezing Cost $($Rs$/$Kg$)$

$350$

$450$

$1200$

$1100$

FAC$-02$

Freezing method

Blast

Block

IQF

$20/$Kg$/$Day

Freezing Cost $($Rs$/$Kg$)$

$500$

$400$

$1100$

$1000$

FAC$-03$

Freezing method

Blast

Block

$20/$Kg$/$Day

Freezing Cost $($Rs$/$Kg$)$

$450$

$550$

FAC$-04$

Freezing method

Blast

Block

IF

$20/$Kg$/$Day

Freezing Cost $($Rs$/$Kg$)$

$500$

$450$

$1100$

FAC$-05$

Freezing met