Table A2 Variable notation and...

Table A2

Variable notation and descriptions

Variables	Notation	Short description of variables
SIR and SIV Loops
Susceptible Population	S	The number of people susceptible to infection
Infectious Population	I	The number of susceptible people get infected
Recovered Population	R	The number of people recovered from infection
Contact Rate	CR	The number of Infectious people contact with susceptible people
Average Duration of Infectivity	D	The average length of time people are infectious
Infection Rate	IR	Total number of contacts
Infectivity	IF	The likelihood of a person contracting an infection
Recovery Rate	RR	Total number of people recover from an infection
Vaccinated Population	V	The number of vaccinated people
Vaccination Rate	VR	Total number of vaccinated people
Average Duration of Inoculation	DI	The average length of time people are inoculated
VSC Order Fulfillment Loop
Vaccine Demand	VD	Population eligible for receiving vaccines
Vaccine Order Rate	VOR	The total number of vaccine orders for vaccination
Vaccine Order Backlog	VOB	Unsatisfied/ unfulfilled vaccine orders
Desired Supply Rate for Vaccine	DSRV	Vaccination site's target supply rate
Target Delivery Delay	TDD	A certain amount of time required to fill the vaccine orders
Vaccine Inventory	VI	Vaccine inventory on hand
Vaccine Supply Rate	VSR	The total number of vaccine orders supplied
Vaccine Order Fulfillment Ratio	VOFR	A function of maximum vaccine supply rate and desired vaccine supply rate
Vaccine Delivery Delay	VDD	The average delay between the placement and the receipt of the vaccination order
Inventory Control Loop
Maximum Vaccine Supply Rate	MVSR	The maximum number of supplies given the VI in stock and VMOPT
Vaccine Minimum Order Processing Time	VMOPT	The amount of time it takes between the vaccine order being placed and shipped
Vaccine Inventory Coverage Ratio	VICR	The number of days the vaccination site could supply (service level of the vaccination site)
Desired Vaccine Inventory	DVI	The volume of inventory required to keep a vaccination site's desired service level of full and dependable delivery
Expected Vaccination Demand	EVD	Expected/forecasted demand
Vaccine Safety Stock	VSS	Additional vaccine inventory in stock to prevent stockouts
Change in Vaccination Demand	CVD	The discrepancy between EVD and the vaccination site’s VOR over a period determined by the TAOR
Time to Average Order Rate	TAOR	The time between vaccine orders
Vaccine Inventory Gap	VIG	The disparity between DVI and VI
Vaccine Inventory Adjustment Time	VIAT	The time required to take the inventory to the desired level
Order Placement Loop
Desired Vaccine Order	DVO	The vaccination site's desired vaccine order
Vaccination Site's Order Rate	VSOR	The total number of vaccine orders placed
Vaccine Transhipment Rate	VTR	The number of vaccines shipped to vaccination site via transshipment
Vaccine Transhipment Delivery Rate	VTDR	The total number of vaccines delivered to vaccination site via transshipment
Production Loop
Desired Production	DP	Desired number of vaccines to be produced
Expected Vaccination Site's Demand	EVSD	Expected/forecasted vaccination site's demand
Production Release Rate	PRR	The total number of vaccines released for manufacturing
Work In Process Inventory	WIPI	The number of vaccines accumulated by difference between PRR and PC
Product Completion	PC	The total number of vaccines produced
Work in Process Gap	WIPG	The pending production line (the difference between DWIP and WIPAT)
Desired Work In Process	DWIP	Desired number of vaccines to be accumulated in the production line
Work In Process Adjustment Time	WIPAT	The time it takes to modify WIPG in line with the desired level
Manufacturing Lead Time	MLT	The average cycle time for the vaccine production
Manufacturer's Inventory	MI	Manufacturer's vaccine inventory on hand
Manufacturer's Inventory Gap	MIG	The disparity between DMI and MI
Maximum Manufacturer Shipment Rate	MMSR	The maximum number of shipments given the MI in stock and MMOPT
Manufacturer Shipment Rate	MSR	The total number of vaccines shipped from Manufacturer
Manufacturer Minimum Order Processing Time	MMOPT	The amount of time it takes between the vaccine order being placed and shipped at the manufacturer
Closing the Loop
Vaccine Usage Duration	VUD	Vaccine usage until expiration or expired vaccines which depends on the vaccine’s shelf life
Used Vaccine	UV	Used or expired vaccines
Uncontrollable Vaccine Disposal	UVD	The flow of used vaccines to disposal due to the limited collection capacity
Uncontrollably Disposed Vaccines	UDV	A variable that accumulates the uncontrollably disposed vaccines
Collection
Vaccine Collection Rate	VCR	The flow of used vaccines to the collection and inspection facilities
Collected Vaccines	CV	The inventory of collected reused vaccines
Collection Capacity	CC	The maximum volume of vaccines handled by the collection and inspection facilities per week
Vaccines Accepted for Reuse	VAR	The flow of used products that have passed inspection and are appropriate to be remanufactured
Vaccines Rejected for Reuse	VRFR	The flow of used products that have not passed inspection and are appropriate to be remanufactured
Inspection Time	IT	The time inspect calculated based on several reuses (remaining non-expired doses) and remaining shelf life
Failure Percentage	FR	A percentage of failing in inspection
Remanufacturing
Remanufacturing Capacity	RC	The maximum volume of reused products that can be remanufactured per week
Vaccine Remanufacturing Rate	VRR	The flow of remanufactured vaccines
Reusable Vaccines	RV	The inventory of used products that passed inspection and are ready to be remanufactured
Controllable Vaccine Disposal	CVD	The flow of surplus stock of used vaccines to prevent costly accumulation if there is not enough remanufacturing capacity to handle them
Uncontrollable Disposal	UCD	The flow of used vaccines to disposal due to the limited collection capacity
Reusable Stock Keeping Time	RST	Unused vaccines for some time
Reuse Ratio	RR	The ratio of ERR to the number of EUV
Expected Remanufacturing Rate	ERR	The forecast of remanufacturing rate
Expected Used Vaccines	EUV	The forecast of used products
Vehicle Capacity
Desired Number of Vehicles	DNV	The desired number of vehicles to transport vaccines
Average Capacity of Vehicles	ACV	The average amount of vaccines can be transported by vehicles
Vehicle Capacity	VC	The maximum vaccine transshipment rate that is restricted by ACV
Number of Available Vehicles	NAV	The discrepancy between VC and VUT
Vehicle Used for Transportation	VUT	The number of vehicles used for transshipment
Vehicle Adjustment Time	VAT	The time required to prepare the vehicles
Transshipment
Vaccine Transshipment Rate	VTR	The total number of vaccines shipped from vaccine site n to vaccine site k
Aggregate Inventory Level	AIL	The total number of the available inventory across all vaccination sites
Allocate Inventory	AI	Allocation decision of inventory from available inventory stock at vaccination site n to vaccination site k based on vaccination site k's DVO, MDBV, and AFR
Allocation Fill Rate	AFR	If the vaccination site n has available inventory to allocate, the AFR score becomes one, else it is zero
Minimum Distance Between Vaccination Sites	MDBV	Ensures the minimum distanced vaccination site k is matched to vaccination site n to allocate vaccines
Transshipment Lead Time	TLT	The time that elapses between vaccine transshipment allocation and the delivery at vaccination site k

Variables	Notation	Short description of variables
SIR and SIV Loops
Susceptible Population	S	The number of people susceptible to infection
Infectious Population	I	The number of susceptible people get infected
Recovered Population	R	The number of people recovered from infection
Contact Rate	CR	The number of Infectious people contact with susceptible people
Average Duration of Infectivity	D	The average length of time people are infectious
Infection Rate	IR	Total number of contacts
Infectivity	IF	The likelihood of a person contracting an infection
Recovery Rate	RR	Total number of people recover from an infection
Vaccinated Population	V	The number of vaccinated people
Vaccination Rate	VR	Total number of vaccinated people
Average Duration of Inoculation	DI	The average length of time people are inoculated
VSC Order Fulfillment Loop
Vaccine Demand	VD	Population eligible for receiving vaccines
Vaccine Order Rate	VOR	The total number of vaccine orders for vaccination
Vaccine Order Backlog	VOB	Unsatisfied/ unfulfilled vaccine orders
Desired Supply Rate for Vaccine	DSRV	Vaccination site's target supply rate
Target Delivery Delay	TDD	A certain amount of time required to fill the vaccine orders
Vaccine Inventory	VI	Vaccine inventory on hand
Vaccine Supply Rate	VSR	The total number of vaccine orders supplied
Vaccine Order Fulfillment Ratio	VOFR	A function of maximum vaccine supply rate and desired vaccine supply rate
Vaccine Delivery Delay	VDD	The average delay between the placement and the receipt of the vaccination order
Inventory Control Loop
Maximum Vaccine Supply Rate	MVSR	The maximum number of supplies given the VI in stock and VMOPT
Vaccine Minimum Order Processing Time	VMOPT	The amount of time it takes between the vaccine order being placed and shipped
Vaccine Inventory Coverage Ratio	VICR	The number of days the vaccination site could supply (service level of the vaccination site)
Desired Vaccine Inventory	DVI	The volume of inventory required to keep a vaccination site's desired service level of full and dependable delivery
Expected Vaccination Demand	EVD	Expected/forecasted demand
Vaccine Safety Stock	VSS	Additional vaccine inventory in stock to prevent stockouts
Change in Vaccination Demand	CVD	The discrepancy between EVD and the vaccination site’s VOR over a period determined by the TAOR
Time to Average Order Rate	TAOR	The time between vaccine orders
Vaccine Inventory Gap	VIG	The disparity between DVI and VI
Vaccine Inventory Adjustment Time	VIAT	The time required to take the inventory to the desired level
Order Placement Loop
Desired Vaccine Order	DVO	The vaccination site's desired vaccine order
Vaccination Site's Order Rate	VSOR	The total number of vaccine orders placed
Vaccine Transhipment Rate	VTR	The number of vaccines shipped to vaccination site via transshipment
Vaccine Transhipment Delivery Rate	VTDR	The total number of vaccines delivered to vaccination site via transshipment
Production Loop
Desired Production	DP	Desired number of vaccines to be produced
Expected Vaccination Site's Demand	EVSD	Expected/forecasted vaccination site's demand
Production Release Rate	PRR	The total number of vaccines released for manufacturing
Work In Process Inventory	WIPI	The number of vaccines accumulated by difference between PRR and PC
Product Completion	PC	The total number of vaccines produced
Work in Process Gap	WIPG	The pending production line (the difference between DWIP and WIPAT)
Desired Work In Process	DWIP	Desired number of vaccines to be accumulated in the production line
Work In Process Adjustment Time	WIPAT	The time it takes to modify WIPG in line with the desired level
Manufacturing Lead Time	MLT	The average cycle time for the vaccine production
Manufacturer's Inventory	MI	Manufacturer's vaccine inventory on hand
Manufacturer's Inventory Gap	MIG	The disparity between DMI and MI
Maximum Manufacturer Shipment Rate	MMSR	The maximum number of shipments given the MI in stock and MMOPT
Manufacturer Shipment Rate	MSR	The total number of vaccines shipped from Manufacturer
Manufacturer Minimum Order Processing Time	MMOPT	The amount of time it takes between the vaccine order being placed and shipped at the manufacturer
Closing the Loop
Vaccine Usage Duration	VUD	Vaccine usage until expiration or expired vaccines which depends on the vaccine’s shelf life
Used Vaccine	UV	Used or expired vaccines
Uncontrollable Vaccine Disposal	UVD	The flow of used vaccines to disposal due to the limited collection capacity
Uncontrollably Disposed Vaccines	UDV	A variable that accumulates the uncontrollably disposed vaccines
Collection
Vaccine Collection Rate	VCR	The flow of used vaccines to the collection and inspection facilities
Collected Vaccines	CV	The inventory of collected reused vaccines
Collection Capacity	CC	The maximum volume of vaccines handled by the collection and inspection facilities per week
Vaccines Accepted for Reuse	VAR	The flow of used products that have passed inspection and are appropriate to be remanufactured
Vaccines Rejected for Reuse	VRFR	The flow of used products that have not passed inspection and are appropriate to be remanufactured
Inspection Time	IT	The time inspect calculated based on several reuses (remaining non-expired doses) and remaining shelf life
Failure Percentage	FR	A percentage of failing in inspection
Remanufacturing
Remanufacturing Capacity	RC	The maximum volume of reused products that can be remanufactured per week
Vaccine Remanufacturing Rate	VRR	The flow of remanufactured vaccines
Reusable Vaccines	RV	The inventory of used products that passed inspection and are ready to be remanufactured
Controllable Vaccine Disposal	CVD	The flow of surplus stock of used vaccines to prevent costly accumulation if there is not enough remanufacturing capacity to handle them
Uncontrollable Disposal	UCD	The flow of used vaccines to disposal due to the limited collection capacity
Reusable Stock Keeping Time	RST	Unused vaccines for some time
Reuse Ratio	RR	The ratio of ERR to the number of EUV
Expected Remanufacturing Rate	ERR	The forecast of remanufacturing rate
Expected Used Vaccines	EUV	The forecast of used products
Vehicle Capacity
Desired Number of Vehicles	DNV	The desired number of vehicles to transport vaccines
Average Capacity of Vehicles	ACV	The average amount of vaccines can be transported by vehicles
Vehicle Capacity	VC	The maximum vaccine transshipment rate that is restricted by ACV
Number of Available Vehicles	NAV	The discrepancy between VC and VUT
Vehicle Used for Transportation	VUT	The number of vehicles used for transshipment
Vehicle Adjustment Time	VAT	The time required to prepare the vehicles
Transshipment
Vaccine Transshipment Rate	VTR	The total number of vaccines shipped from vaccine site n to vaccine site k
Aggregate Inventory Level	AIL	The total number of the available inventory across all vaccination sites
Allocate Inventory	AI	Allocation decision of inventory from available inventory stock at vaccination site n to vaccination site k based on vaccination site k's DVO, MDBV, and AFR
Allocation Fill Rate	AFR	If the vaccination site n has available inventory to allocate, the AFR score becomes one, else it is zero
Minimum Distance Between Vaccination Sites	MDBV	Ensures the minimum distanced vaccination site k is matched to vaccination site n to allocate vaccines
Transshipment Lead Time	TLT	The time that elapses between vaccine transshipment allocation and the delivery at vaccination site k

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