Inventory Control

Question 1
With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct?

Curve P1: Total cost, Curve P2: Holding cost,
Curve P3: Setup cost, and Curve P4: Production cost.
Curve P1: Holding cost, Curve P2: Setup cost, Curve P3: Production cost, and Curve P4: Total cost.
Curve P1: Production cost, Curve P2: Holding cost,
Curve P3: Total cost, and Curve P4: Setup cost.
Curve P1: Total cost, Curve P2: Production cost,
Curve P3: Holding cost, and Curve P4: Setup cost.
GATE ME 2023   Industrial Engineering
Question 1 Explanation: 

Question 2
The demand of a certain part is 1000 parts/year and its cost is Rs. 1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering is Rs. 100/order and the lead time for receiving the orders is 5 days. If the holding cost is Rs. 20/part/year, the inventory level for placing the orders is ________ parts (round off to the nearest integer).
GATE ME 2022 SET-2   Industrial Engineering
Question 2 Explanation: 
Inventory control:
Annual demand (D) = 1000 units
Lead time (LT) = 5 days
Inventory level for placing the order = Re-order level (ROL)
Rate of consumption (d) =D/365
ROL=d \times LT=\frac{1000}{365} \times 5=13.69 \approx 14 \; units

Question 3
The product structure diagram shows the number of different components required at each level to produce one unit of the final product P. If there are 50 units of on-hand inventory of component A, the number of additional units of component A needed to produce 10 units of product P is _________ (in integer).

GATE ME 2022 SET-1   Industrial Engineering
Question 3 Explanation: 

To produce 10 units of 'P'
No. of units of 'A' required = (4x10)+(2x3x2x10) = 160 units
Net requirement of 'A' = 160 - 50 = 110 units
Question 4
Which one of the following is NOT a form of inventory?
Raw materials
Work-in-process materials
Finished goods
CNC Milling Machines
GATE ME 2022 SET-1   Industrial Engineering
Question 4 Explanation: 

CNC milling machines will not be treated as inventory.
Question 5
A factory produces m(i=1,2,...m) products, each of which requires processing on n(j=1,2,...n) workstations. Let a_{ij} be the amount of processing time that one unit of the i^{th} product requires on the j^{th} workstation. Let the revenue from selling one unit of the i^{th} product be r_i and h_i be the holding cost per unit per time period for the i^{th} product. The planning horizon consists of T \;(t=1,2,...T) time periods. The minimum demand that must be satisfied in time period t is d_{it}, and the capacity of the j^{th} workstation in time period t is c_{jt}. Consider the aggregate planning formulation below, with decision variables S_{it} (amount of product i sold in time period t ), X_{it} (amount of product i manufactured in time period t ) and I_{it} (amount of product i held in inventory at the end of time period t.

subject to
S_{it}\geq d_{it}\;\;\forall i,t
< capacity constraint >
< inventory balance constraint >
X_{it},S_{it}, I_{it} \geq 0;\; I_{i0}=0

The capacity constraints and inventory balance constraints for this formulation are
\sum_{j}^{m}a_{ij}X_{it}\leq c_{jt}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-d_{it}\; \forall \;i,t
\sum_{i}^{m}a_{ij}X_{it}\leq c_{jt}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-d_{it}\; \forall \;i,t
\sum_{i}^{m}a_{ij}X_{it}\leq d_{it}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-S_{it}\; \forall \;i,t
\sum_{i}^{m}a_{ij}X_{it}\leq d_{it}\;\forall \; i ,t\text{ and }I_{it}=I_{i,t-1}+S_{it}-X_{it}\; \forall \;i,t
GATE ME 2021 SET-2   Industrial Engineering
Question 5 Explanation: 
\begin{aligned} m & \rightarrow i \ldots m \leftarrow \text { product } \\ n & \rightarrow i \ldots n \leftarrow \text { workstation } \\ a_{\bar{j}} & \rightarrow \text { time } \end{aligned}
r_{i} \rightarrow selling price
h_{i} \rightarrow holding cost
T \rightarrow t=1,2, \ldots T
d_{i t} \rightarrow demand of product in time t
c_{j t} \rightarrow capacity of workstation in time t
S_{i t} \rightarrow Number of product sold in time t
x_{i t} \rightarrow Number of product produced in time t
I_{i t} \rightarrow Number of product i hold in inventory at end of period t
Capacity constraint
a_{i j} x_{i t} \leq c_{j t}
Inventory constraint
l_{i t}=I_{i, t-1}+x_{i t}-S_{i t}

There are 5 questions to complete.

Leave a Comment