Capconn

The CAPCONN Supply Chain Model

CAPCONN [Stutterheim, P., Bezuidenhout, C.N., Lyne, P.W.L, 2008. A framework to simulate the sugarcane supply chain, from harvest to raw sugar. Sugar Cane International, 26(1):7-11.] stands for Capacity Constricted Conveyence and is a diagnostics model for analysing certain supply chain issues, especially with respect to material handling. The model graphically illustrates efficiencies in a supply chain. Mathematically, the concept works similar to a series of conveyor belts, each with a different width and rolling at a different speed. If a product, like sand, had to be passed through the series of conveyor belts, then normally one belt would constrict the amount of sand that could ultimately be transferred. However, by not just looking at the 'constrictor' component of the chain, but also the differences in withds and speeds, a supply chain analyst could potentially derive more diagnostic information about the system. [Stutterheim, P. 2007. An integrated sugarcane supply chain model: Development and demonstration. Unpublished MScEng Seminar, School of Bioresources Engineering and Environmental Hydrology, University of KwaZulu-Natal, Pietermaritzburg, RSA.]

The following steps are typically followed:

Step 1: Decide on a discrete time step size, say "W". A separate CAPCONN graph needs to be drawn for each time step. Typically, a good time step would coincide with other reporting protocols in a supply chain. For example, if a factory generates a weekly report, then a weekly CAPCONN time step will be appropriate. The choice of time step size depends on the issues that are under investigation. E.g. strategic infrastructure issues will not need a daily time step model, nor will it be appropriate to have a monthly time step if day to day inventory levels are being investigated.

Step 2: Assume "j" is one material handling component in the supply chain (e.g. produce off-loading). assume "y_j" is the rate of work per individual working component (e.g. the number of boxes that can be off-loaded per hour per forklift). Assume "n_j" is the number of forklifts and "x_j" is the total time of work during time step "W", "i.e. y_j ≤ W".

Step 3 It is now easy to calculate the total work "P_j" that can be performed by component "j" as follows:
"P_j = (n_jy_j)×(x_j)"

"P_j" can also be graphically presented as the surface of a rectangle with a vertical "Y-axis" being the value "n_j×y_j" and a horizontal "X-axis" being the value "x_j".

Step 4: A rectangle can be graphically represented for each component "j" (e.g. "P₁", "P₂", "P₃", ... , "P_N" ) of the supply chain and these rectangles can be placed in sequence next to each other.

Step 5: We now have "P_N" rectangles or containers standing next to each other, each representing the material handling capacity of a supply chain component within a predefined time step "W". Now, assume we pour water into the first container and "P₁" reflects the amount of water that Container 1 can hold. Now pour Container 1 into Container 2. If "P₁" > "P₂", then container number 2 will overflow and some water will be lost. Pursue by pouring the water in Container 2 over into Container 3 and carry on passing the water from container to container until the last container (Container N) is reached.

"Step 6" Assume the amount of water that reached Container N is "P’" where "P’ ≤ P_N". Mathematically, "P’ =" min("P₁, P₂, P₃, ... , P_N").

"Step 7" Insert the same amount of water that reached Container N ("P’") into all the other containers (Containers 1 to N-1). This will produce "N" number of rectangles next to each other. If "P’" is coloured in as a surface within each rectangle, then each rectangle will be partly or completely filled. Note that since some rectagles could be wider than others ("x_j > x_j+1"), it may not appear as if all the coloured areas in the different containers are of equal surface, but theoretically they will be.

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How to interpret a CAPCONN graph

Typically no supply chain will end up with 100% utilisation, i.e. a CAPCONN graph where all the containers are full ("P’ = P₁ = P₂ = ... = P_N"). This can be attributed to many reasons, such as:
1. Bouncing bottle necks:- Different components of the supply chain can become "full" under different conditions. In other words, the conditions assumed for time step "W_i" may be different compared to time step "W_i+1", which may imply that another component of the supply chain could become the constrictor.
2. Built in agility:- For some reason, such as supply chain security, additional material handling capacity has been inserted during the design process.
3. Incompatable capacities:- Certain work units, such as ships or trucks, have discrete handling capacities and can be incompatable with the units used the other components of the chain. For example, 10.75 trucks will fill up one ship. We will buy 11 trucks and hence end up with unused capacity.

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References