Hi , i need to write some maple functions for the equations below and i am not sure if this should be arrays or not. please see the question below;
Consider a factory which manufactures only one product. Raw material is bought from external supplier and stored until required.
Finished items are held in a warehouse. The operation of factory and its warehouse
can be modelled as a set of equations as folllows.
Let us define at time t :
R(t) = Raw material stored (units)
F(t) = finished goods stock (units)
B(t) = order backlog (units)
T(t) = target stock level for finished goods (units)
All variables defined above give quantities at the start of week t.
X( t, t+1 )= weekly orders received from customers
M( t, t+1 )= raw material supplied per week.
P( t, t+1 )= production per week.
D(t, t+1 )= amount dispatched to customers per week.
All variables defined above give quantities over week t to t+1
(i.e over the week t). The operation of the factory and its warehouse can be expressed
as a set of equations given as follows:
Backlog and Stock Position
(1) B(t+1) = B(t)+X (t,t+1)–D(t,t+1)
(2) T(t+1) =(m +1)/m(X(t,t+1)+X(t–1,t)+…+X (t–m+1,t–m+2))
(assuming that the company wishes to maintain m (suppose m=5)) weeks stock of
finish items and hence the target level is m times the average of the last m–1 weeks)
(3) R (t+1)=R(t)+M(t,t+1)–P(t,t+1)
(4) F (t+1)=F (t) +P(t,t+1)–D(t,t+1)
(5) D (t,t+1) = B(t) if B(t)<F(t)
F (t) otherwise
(6) M (t,t+1) = P(t–1,t)
(7) P (t,t+1) = T(t) – F(t) + D(t,t+1)
= R(t) if result exceeds R(t)
= 0 if the result is negative
Given the initial values for the variables, it is possible to simulate this system to study
how the system will respond to the order rate. Suppose that all is calm, and the factory
has operated as follows for the last five weeks.
Target warehouse stock = 250
Finished goods stock = 250
Raw material stock = 150
Production rate = 50/week
Material supply rate = 50/week
Order rate = 50/week
Order backlog = 50
Suppose the behaviour continues for the first week of the simulation but that during
next week orders double due to the sales promotion. During the third week orders
drops to zero as all demand returns of the previous week was satisfied. For the fourth
week and the succeeding weeks, demand returns to an order rate of 50/week. What
happens elsewhere in the system? A deterministic simulation will provide the answer
to the above mentioned question.
For this compute the following.
i) The values of the equations (1)–(4) at the start of week t.
ii) The values of the equations (5)–(7) i.e. the new values of the rates during
the following week.
iii) Move simulation time to the start of the next week.
Next simulation should be presented in tabular form and plot production and demand
rate to examine the performance of the system.
All help will be much appreciated.