Question

A biomedical intrumentation company sells its main product at the rate of 5 units per day. The instrument is manufactured in lots run every few days. It costs the company $2000 to setup for production of a lot and $40 per unit per day to hold finished instruments in inventory between runs. The company would like to choose a lot size that minimizes average inventory and setup cost per day assuming that demand occurs smoothly at the given rate. (a) Formulate a 1-variable unconstrained NLP to choose an optimum lot size. (b) Plot the objective function of your model and compute an optimum lot size graphically.

Answer 1

(a) Let:

L be the lot size

D be the demand rate in units per day

S be the setup cost per lot

H be the holding cost per unit per day

The total demand in days necessary to exhaust the lot is L / D. The average inventory, in units, is given by L / 2. Therefore, the average inventory and setup cost per day can be calculated as:

Average inventory cost per day = (L / 2) * H

Setup cost per day = S / (L / D)

The objective is to minimize the sum of the average inventory cost per day and the setup cost per day. Therefore, the objective function is:

f(L) = (L / 2) * H + S / (L / D)

(b) To plot the objective function and compute the optimum lot size graphically, we need to choose specific values for D, S, and H. Let's say D = 5 units/day, S = $2000, and H = $40/unit/day.

Substituting these values into the objective function, we get:

f(L) = (L / 2) * 40 + 2000 / (L / 5)

To graphically determine the optimum lot size, we can plot f(L) as a function of L and find the minimum point on the graph. We can use a graphing calculator or software to do this.

Step-by-step explanation: